diff --git a/models/gpg_key.go b/models/gpg_key.go
index 862bd8859..6a5daf636 100644
--- a/models/gpg_key.go
+++ b/models/gpg_key.go
@@ -19,9 +19,9 @@ import (
 	"code.gitea.io/gitea/modules/log"
 
 	"github.com/go-xorm/xorm"
-	"golang.org/x/crypto/openpgp"
-	"golang.org/x/crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/packet"
+	"github.com/keybase/go-crypto/openpgp"
+	"github.com/keybase/go-crypto/openpgp/armor"
+	"github.com/keybase/go-crypto/openpgp/packet"
 )
 
 // GPGKey represents a GPG key.
diff --git a/models/gpg_key_test.go b/models/gpg_key_test.go
index 507cfabd2..cc70096d0 100644
--- a/models/gpg_key_test.go
+++ b/models/gpg_key_test.go
@@ -43,7 +43,28 @@ MkM/fdpyc2hY7Dl/+qFmN5MG5yGmMpQcX+RNNR222ibNC1D3wg==
 -----END PGP PUBLIC KEY BLOCK-----`
 
 	key, err := checkArmoredGPGKeyString(testGPGArmor)
-	assert.Nil(t, err, "Could not parse a valid GPG armored key", key)
+	assert.NoError(t, err, "Could not parse a valid GPG public armored rsa key", key)
+	//TODO verify value of key
+}
+
+func TestCheckArmoredbrainpoolP256r1GPGKeyString(t *testing.T) {
+	testGPGArmor := `-----BEGIN PGP PUBLIC KEY BLOCK-----
+Version: GnuPG v2
+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ZiSe
+-----END PGP PUBLIC KEY BLOCK-----`
+
+	key, err := checkArmoredGPGKeyString(testGPGArmor)
+	assert.NoError(t, err, "Could not parse a valid GPG public armored brainpoolP256r1 key", key)
 	//TODO verify value of key
 }
 
@@ -79,11 +100,11 @@ MkM/fdpyc2hY7Dl/+qFmN5MG5yGmMpQcX+RNNR222ibNC1D3wg==
 =i9b7
 -----END PGP PUBLIC KEY BLOCK-----`
 	ekey, err := checkArmoredGPGKeyString(testGPGArmor)
-	assert.Nil(t, err, "Could not parse a valid GPG armored key", ekey)
+	assert.NoError(t, err, "Could not parse a valid GPG armored key", ekey)
 
 	pubkey := ekey.PrimaryKey
 	content, err := base64EncPubKey(pubkey)
-	assert.Nil(t, err, "Could not base64 encode a valid PublicKey content", ekey)
+	assert.NoError(t, err, "Could not base64 encode a valid PublicKey content", ekey)
 
 	key := &GPGKey{
 		KeyID:             pubkey.KeyIdString(),
@@ -144,21 +165,21 @@ Unknown GPG key with good email
 `
 	//Reading Sign
 	goodSig, err := extractSignature(testGoodSigArmor)
-	assert.Nil(t, err, "Could not parse a valid GPG armored signature", testGoodSigArmor)
+	assert.NoError(t, err, "Could not parse a valid GPG armored signature", testGoodSigArmor)
 	badSig, err := extractSignature(testBadSigArmor)
-	assert.Nil(t, err, "Could not parse a valid GPG armored signature", testBadSigArmor)
+	assert.NoError(t, err, "Could not parse a valid GPG armored signature", testBadSigArmor)
 
 	//Generating hash of commit
 	goodHash, err := populateHash(goodSig.Hash, []byte(testGoodPayload))
-	assert.Nil(t, err, "Could not generate a valid hash of payload", testGoodPayload)
+	assert.NoError(t, err, "Could not generate a valid hash of payload", testGoodPayload)
 	badHash, err := populateHash(badSig.Hash, []byte(testBadPayload))
-	assert.Nil(t, err, "Could not generate a valid hash of payload", testBadPayload)
+	assert.NoError(t, err, "Could not generate a valid hash of payload", testBadPayload)
 
 	//Verify
 	err = verifySign(goodSig, goodHash, key)
-	assert.Nil(t, err, "Could not validate a good signature")
+	assert.NoError(t, err, "Could not validate a good signature")
 	err = verifySign(badSig, badHash, key)
-	assert.NotNil(t, err, "Validate a bad signature")
+	assert.Error(t, err, "Validate a bad signature")
 	err = verifySign(goodSig, goodHash, cannotsignkey)
-	assert.NotNil(t, err, "Validate a bad signature with a kay that can not sign")
+	assert.Error(t, err, "Validate a bad signature with a kay that can not sign")
 }
diff --git a/vendor/github.com/keybase/go-crypto/LICENSE b/vendor/github.com/keybase/go-crypto/LICENSE
new file mode 100644
index 000000000..6a66aea5e
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/LICENSE
@@ -0,0 +1,27 @@
+Copyright (c) 2009 The Go Authors. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+   * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+   * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+   * Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/vendor/github.com/keybase/go-crypto/PATENTS b/vendor/github.com/keybase/go-crypto/PATENTS
new file mode 100644
index 000000000..733099041
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/PATENTS
@@ -0,0 +1,22 @@
+Additional IP Rights Grant (Patents)
+
+"This implementation" means the copyrightable works distributed by
+Google as part of the Go project.
+
+Google hereby grants to You a perpetual, worldwide, non-exclusive,
+no-charge, royalty-free, irrevocable (except as stated in this section)
+patent license to make, have made, use, offer to sell, sell, import,
+transfer and otherwise run, modify and propagate the contents of this
+implementation of Go, where such license applies only to those patent
+claims, both currently owned or controlled by Google and acquired in
+the future, licensable by Google that are necessarily infringed by this
+implementation of Go.  This grant does not include claims that would be
+infringed only as a consequence of further modification of this
+implementation.  If you or your agent or exclusive licensee institute or
+order or agree to the institution of patent litigation against any
+entity (including a cross-claim or counterclaim in a lawsuit) alleging
+that this implementation of Go or any code incorporated within this
+implementation of Go constitutes direct or contributory patent
+infringement, or inducement of patent infringement, then any patent
+rights granted to you under this License for this implementation of Go
+shall terminate as of the date such litigation is filed.
diff --git a/vendor/github.com/keybase/go-crypto/brainpool/brainpool.go b/vendor/github.com/keybase/go-crypto/brainpool/brainpool.go
new file mode 100644
index 000000000..77fb8b9a0
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/brainpool/brainpool.go
@@ -0,0 +1,134 @@
+// Package brainpool implements Brainpool elliptic curves.
+// Implementation of rcurves is from github.com/ebfe/brainpool
+// Note that these curves are implemented with naive, non-constant time operations
+// and are likely not suitable for enviroments where timing attacks are a concern.
+package brainpool
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"sync"
+)
+
+var (
+	once                   sync.Once
+	p256t1, p384t1, p512t1 *elliptic.CurveParams
+	p256r1, p384r1, p512r1 *rcurve
+)
+
+func initAll() {
+	initP256t1()
+	initP384t1()
+	initP512t1()
+	initP256r1()
+	initP384r1()
+	initP512r1()
+}
+
+func initP256t1() {
+	p256t1 = &elliptic.CurveParams{Name: "brainpoolP256t1"}
+	p256t1.P, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", 16)
+	p256t1.N, _ = new(big.Int).SetString("A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", 16)
+	p256t1.B, _ = new(big.Int).SetString("662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04", 16)
+	p256t1.Gx, _ = new(big.Int).SetString("A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4", 16)
+	p256t1.Gy, _ = new(big.Int).SetString("2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE", 16)
+	p256t1.BitSize = 256
+}
+
+func initP256r1() {
+	twisted := p256t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP256r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", 16)
+	params.Gy, _ = new(big.Int).SetString("547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", 16)
+	z, _ := new(big.Int).SetString("3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0", 16)
+	p256r1 = newrcurve(twisted, params, z)
+}
+
+func initP384t1() {
+	p384t1 = &elliptic.CurveParams{Name: "brainpoolP384t1"}
+	p384t1.P, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53", 16)
+	p384t1.N, _ = new(big.Int).SetString("8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565", 16)
+	p384t1.B, _ = new(big.Int).SetString("7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE1D2074AA263B88805CED70355A33B471EE", 16)
+	p384t1.Gx, _ = new(big.Int).SetString("18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AABFFC4FF191B946A5F54D8D0AA2F418808CC", 16)
+	p384t1.Gy, _ = new(big.Int).SetString("25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CCFE469408584DC2B2912675BF5B9E582928", 16)
+	p384t1.BitSize = 384
+}
+
+func initP384r1() {
+	twisted := p384t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP384r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E", 16)
+	params.Gy, _ = new(big.Int).SetString("8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315", 16)
+	z, _ := new(big.Int).SetString("41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE97D2D63DBC87BCCDDCCC5DA39E8589291C", 16)
+	p384r1 = newrcurve(twisted, params, z)
+}
+
+func initP512t1() {
+	p512t1 = &elliptic.CurveParams{Name: "brainpoolP512t1"}
+	p512t1.P, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3", 16)
+	p512t1.N, _ = new(big.Int).SetString("AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069", 16)
+	p512t1.B, _ = new(big.Int).SetString("7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36A62BCDFA2304976540F6450085F2DAE145C22553B465763689180EA2571867423E", 16)
+	p512t1.Gx, _ = new(big.Int).SetString("640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C0313D82BA51735CDB3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA9035DA", 16)
+	p512t1.Gy, _ = new(big.Int).SetString("5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CEE9D9932184BEEF216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8B332", 16)
+	p512t1.BitSize = 512
+}
+
+func initP512r1() {
+	twisted := p512t1
+	params := &elliptic.CurveParams{
+		Name:    "brainpoolP512r1",
+		P:       twisted.P,
+		N:       twisted.N,
+		BitSize: twisted.BitSize,
+	}
+	params.Gx, _ = new(big.Int).SetString("81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822", 16)
+	params.Gy, _ = new(big.Int).SetString("7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892", 16)
+	z, _ := new(big.Int).SetString("12EE58E6764838B69782136F0F2D3BA06E27695716054092E60A80BEDB212B64E585D90BCE13761F85C3F1D2A64E3BE8FEA2220F01EBA5EEB0F35DBD29D922AB", 16)
+	p512r1 = newrcurve(twisted, params, z)
+}
+
+// P256t1 returns a Curve which implements Brainpool P256t1 (see RFC 5639, section 3.4)
+func P256t1() elliptic.Curve {
+	once.Do(initAll)
+	return p256t1
+}
+
+// P256r1 returns a Curve which implements Brainpool P256r1 (see RFC 5639, section 3.4)
+func P256r1() elliptic.Curve {
+	once.Do(initAll)
+	return p256r1
+}
+
+// P384t1 returns a Curve which implements Brainpool P384t1 (see RFC 5639, section 3.6)
+func P384t1() elliptic.Curve {
+	once.Do(initAll)
+	return p384t1
+}
+
+// P384r1 returns a Curve which implements Brainpool P384r1 (see RFC 5639, section 3.6)
+func P384r1() elliptic.Curve {
+	once.Do(initAll)
+	return p384r1
+}
+
+// P512t1 returns a Curve which implements Brainpool P512t1 (see RFC 5639, section 3.7)
+func P512t1() elliptic.Curve {
+	once.Do(initAll)
+	return p512t1
+}
+
+// P512r1 returns a Curve which implements Brainpool P512r1 (see RFC 5639, section 3.7)
+func P512r1() elliptic.Curve {
+	once.Do(initAll)
+	return p512r1
+}
diff --git a/vendor/github.com/keybase/go-crypto/brainpool/rcurve.go b/vendor/github.com/keybase/go-crypto/brainpool/rcurve.go
new file mode 100644
index 000000000..7e291d6aa
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/brainpool/rcurve.go
@@ -0,0 +1,83 @@
+package brainpool
+
+import (
+	"crypto/elliptic"
+	"math/big"
+)
+
+var _ elliptic.Curve = (*rcurve)(nil)
+
+type rcurve struct {
+	twisted elliptic.Curve
+	params  *elliptic.CurveParams
+	z       *big.Int
+	zinv    *big.Int
+	z2      *big.Int
+	z3      *big.Int
+	zinv2   *big.Int
+	zinv3   *big.Int
+}
+
+var (
+	two   = big.NewInt(2)
+	three = big.NewInt(3)
+)
+
+func newrcurve(twisted elliptic.Curve, params *elliptic.CurveParams, z *big.Int) *rcurve {
+	zinv := new(big.Int).ModInverse(z, params.P)
+	return &rcurve{
+		twisted: twisted,
+		params:  params,
+		z:       z,
+		zinv:    zinv,
+		z2:      new(big.Int).Exp(z, two, params.P),
+		z3:      new(big.Int).Exp(z, three, params.P),
+		zinv2:   new(big.Int).Exp(zinv, two, params.P),
+		zinv3:   new(big.Int).Exp(zinv, three, params.P),
+	}
+}
+
+func (curve *rcurve) toTwisted(x, y *big.Int) (*big.Int, *big.Int) {
+	var tx, ty big.Int
+	tx.Mul(x, curve.z2)
+	tx.Mod(&tx, curve.params.P)
+	ty.Mul(y, curve.z3)
+	ty.Mod(&ty, curve.params.P)
+	return &tx, &ty
+}
+
+func (curve *rcurve) fromTwisted(tx, ty *big.Int) (*big.Int, *big.Int) {
+	var x, y big.Int
+	x.Mul(tx, curve.zinv2)
+	x.Mod(&x, curve.params.P)
+	y.Mul(ty, curve.zinv3)
+	y.Mod(&y, curve.params.P)
+	return &x, &y
+}
+
+func (curve *rcurve) Params() *elliptic.CurveParams {
+	return curve.params
+}
+
+func (curve *rcurve) IsOnCurve(x, y *big.Int) bool {
+	return curve.twisted.IsOnCurve(curve.toTwisted(x, y))
+}
+
+func (curve *rcurve) Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int) {
+	tx1, ty1 := curve.toTwisted(x1, y1)
+	tx2, ty2 := curve.toTwisted(x2, y2)
+	return curve.fromTwisted(curve.twisted.Add(tx1, ty1, tx2, ty2))
+}
+
+func (curve *rcurve) Double(x1, y1 *big.Int) (x, y *big.Int) {
+	return curve.fromTwisted(curve.twisted.Double(curve.toTwisted(x1, y1)))
+}
+
+func (curve *rcurve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) {
+	tx1, ty1 := curve.toTwisted(x1, y1)
+	return curve.fromTwisted(curve.twisted.ScalarMult(tx1, ty1, scalar))
+}
+
+func (curve *rcurve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
+	return curve.fromTwisted(curve.twisted.ScalarBaseMult(scalar))
+}
diff --git a/vendor/golang.org/x/crypto/cast5/cast5.go b/vendor/github.com/keybase/go-crypto/cast5/cast5.go
similarity index 99%
rename from vendor/golang.org/x/crypto/cast5/cast5.go
rename to vendor/github.com/keybase/go-crypto/cast5/cast5.go
index 0b4af37bd..8c1b299bf 100644
--- a/vendor/golang.org/x/crypto/cast5/cast5.go
+++ b/vendor/github.com/keybase/go-crypto/cast5/cast5.go
@@ -4,7 +4,7 @@
 
 // Package cast5 implements CAST5, as defined in RFC 2144. CAST5 is a common
 // OpenPGP cipher.
-package cast5 // import "golang.org/x/crypto/cast5"
+package cast5
 
 import "errors"
 
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/const_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/const_amd64.s
new file mode 100644
index 000000000..797f9b051
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/const_amd64.s
@@ -0,0 +1,20 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+DATA ·REDMASK51(SB)/8, $0x0007FFFFFFFFFFFF
+GLOBL ·REDMASK51(SB), 8, $8
+
+DATA ·_121666_213(SB)/8, $996687872
+GLOBL ·_121666_213(SB), 8, $8
+
+DATA ·_2P0(SB)/8, $0xFFFFFFFFFFFDA
+GLOBL ·_2P0(SB), 8, $8
+
+DATA ·_2P1234(SB)/8, $0xFFFFFFFFFFFFE
+GLOBL ·_2P1234(SB), 8, $8
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/cswap_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/cswap_amd64.s
new file mode 100644
index 000000000..45484d1b5
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/cswap_amd64.s
@@ -0,0 +1,88 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+// func cswap(inout *[5]uint64, v uint64)
+TEXT ·cswap(SB),7,$0
+	MOVQ inout+0(FP),DI
+	MOVQ v+8(FP),SI
+
+	CMPQ SI,$1
+	MOVQ 0(DI),SI
+	MOVQ 80(DI),DX
+	MOVQ 8(DI),CX
+	MOVQ 88(DI),R8
+	MOVQ SI,R9
+	CMOVQEQ DX,SI
+	CMOVQEQ R9,DX
+	MOVQ CX,R9
+	CMOVQEQ R8,CX
+	CMOVQEQ R9,R8
+	MOVQ SI,0(DI)
+	MOVQ DX,80(DI)
+	MOVQ CX,8(DI)
+	MOVQ R8,88(DI)
+	MOVQ 16(DI),SI
+	MOVQ 96(DI),DX
+	MOVQ 24(DI),CX
+	MOVQ 104(DI),R8
+	MOVQ SI,R9
+	CMOVQEQ DX,SI
+	CMOVQEQ R9,DX
+	MOVQ CX,R9
+	CMOVQEQ R8,CX
+	CMOVQEQ R9,R8
+	MOVQ SI,16(DI)
+	MOVQ DX,96(DI)
+	MOVQ CX,24(DI)
+	MOVQ R8,104(DI)
+	MOVQ 32(DI),SI
+	MOVQ 112(DI),DX
+	MOVQ 40(DI),CX
+	MOVQ 120(DI),R8
+	MOVQ SI,R9
+	CMOVQEQ DX,SI
+	CMOVQEQ R9,DX
+	MOVQ CX,R9
+	CMOVQEQ R8,CX
+	CMOVQEQ R9,R8
+	MOVQ SI,32(DI)
+	MOVQ DX,112(DI)
+	MOVQ CX,40(DI)
+	MOVQ R8,120(DI)
+	MOVQ 48(DI),SI
+	MOVQ 128(DI),DX
+	MOVQ 56(DI),CX
+	MOVQ 136(DI),R8
+	MOVQ SI,R9
+	CMOVQEQ DX,SI
+	CMOVQEQ R9,DX
+	MOVQ CX,R9
+	CMOVQEQ R8,CX
+	CMOVQEQ R9,R8
+	MOVQ SI,48(DI)
+	MOVQ DX,128(DI)
+	MOVQ CX,56(DI)
+	MOVQ R8,136(DI)
+	MOVQ 64(DI),SI
+	MOVQ 144(DI),DX
+	MOVQ 72(DI),CX
+	MOVQ 152(DI),R8
+	MOVQ SI,R9
+	CMOVQEQ DX,SI
+	CMOVQEQ R9,DX
+	MOVQ CX,R9
+	CMOVQEQ R8,CX
+	CMOVQEQ R9,R8
+	MOVQ SI,64(DI)
+	MOVQ DX,144(DI)
+	MOVQ CX,72(DI)
+	MOVQ R8,152(DI)
+	MOVQ DI,AX
+	MOVQ SI,DX
+	RET
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/curve25519.go b/vendor/github.com/keybase/go-crypto/curve25519/curve25519.go
new file mode 100644
index 000000000..6918c47fc
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/curve25519.go
@@ -0,0 +1,841 @@
+// Copyright 2013 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// We have a implementation in amd64 assembly so this code is only run on
+// non-amd64 platforms. The amd64 assembly does not support gccgo.
+// +build !amd64 gccgo appengine
+
+package curve25519
+
+// This code is a port of the public domain, "ref10" implementation of
+// curve25519 from SUPERCOP 20130419 by D. J. Bernstein.
+
+// fieldElement represents an element of the field GF(2^255 - 19). An element
+// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
+// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
+// context.
+type fieldElement [10]int32
+
+func feZero(fe *fieldElement) {
+	for i := range fe {
+		fe[i] = 0
+	}
+}
+
+func feOne(fe *fieldElement) {
+	feZero(fe)
+	fe[0] = 1
+}
+
+func feAdd(dst, a, b *fieldElement) {
+	for i := range dst {
+		dst[i] = a[i] + b[i]
+	}
+}
+
+func feSub(dst, a, b *fieldElement) {
+	for i := range dst {
+		dst[i] = a[i] - b[i]
+	}
+}
+
+func feCopy(dst, src *fieldElement) {
+	for i := range dst {
+		dst[i] = src[i]
+	}
+}
+
+// feCSwap replaces (f,g) with (g,f) if b == 1; replaces (f,g) with (f,g) if b == 0.
+//
+// Preconditions: b in {0,1}.
+func feCSwap(f, g *fieldElement, b int32) {
+	var x fieldElement
+	b = -b
+	for i := range x {
+		x[i] = b & (f[i] ^ g[i])
+	}
+
+	for i := range f {
+		f[i] ^= x[i]
+	}
+	for i := range g {
+		g[i] ^= x[i]
+	}
+}
+
+// load3 reads a 24-bit, little-endian value from in.
+func load3(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	return r
+}
+
+// load4 reads a 32-bit, little-endian value from in.
+func load4(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	r |= int64(in[3]) << 24
+	return r
+}
+
+func feFromBytes(dst *fieldElement, src *[32]byte) {
+	h0 := load4(src[:])
+	h1 := load3(src[4:]) << 6
+	h2 := load3(src[7:]) << 5
+	h3 := load3(src[10:]) << 3
+	h4 := load3(src[13:]) << 2
+	h5 := load4(src[16:])
+	h6 := load3(src[20:]) << 7
+	h7 := load3(src[23:]) << 5
+	h8 := load3(src[26:]) << 4
+	h9 := load3(src[29:]) << 2
+
+	var carry [10]int64
+	carry[9] = (h9 + 1<<24) >> 25
+	h0 += carry[9] * 19
+	h9 -= carry[9] << 25
+	carry[1] = (h1 + 1<<24) >> 25
+	h2 += carry[1]
+	h1 -= carry[1] << 25
+	carry[3] = (h3 + 1<<24) >> 25
+	h4 += carry[3]
+	h3 -= carry[3] << 25
+	carry[5] = (h5 + 1<<24) >> 25
+	h6 += carry[5]
+	h5 -= carry[5] << 25
+	carry[7] = (h7 + 1<<24) >> 25
+	h8 += carry[7]
+	h7 -= carry[7] << 25
+
+	carry[0] = (h0 + 1<<25) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+	carry[2] = (h2 + 1<<25) >> 26
+	h3 += carry[2]
+	h2 -= carry[2] << 26
+	carry[4] = (h4 + 1<<25) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+	carry[6] = (h6 + 1<<25) >> 26
+	h7 += carry[6]
+	h6 -= carry[6] << 26
+	carry[8] = (h8 + 1<<25) >> 26
+	h9 += carry[8]
+	h8 -= carry[8] << 26
+
+	dst[0] = int32(h0)
+	dst[1] = int32(h1)
+	dst[2] = int32(h2)
+	dst[3] = int32(h3)
+	dst[4] = int32(h4)
+	dst[5] = int32(h5)
+	dst[6] = int32(h6)
+	dst[7] = int32(h7)
+	dst[8] = int32(h8)
+	dst[9] = int32(h9)
+}
+
+// feToBytes marshals h to s.
+// Preconditions:
+//   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Write p=2^255-19; q=floor(h/p).
+// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+//
+// Proof:
+//   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+//   Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
+//
+//   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+//   Then 0<y<1.
+//
+//   Write r=h-pq.
+//   Have 0<=r<=p-1=2^255-20.
+//   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+//
+//   Write x=r+19(2^-255)r+y.
+//   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+//
+//   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+//   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+func feToBytes(s *[32]byte, h *fieldElement) {
+	var carry [10]int32
+
+	q := (19*h[9] + (1 << 24)) >> 25
+	q = (h[0] + q) >> 26
+	q = (h[1] + q) >> 25
+	q = (h[2] + q) >> 26
+	q = (h[3] + q) >> 25
+	q = (h[4] + q) >> 26
+	q = (h[5] + q) >> 25
+	q = (h[6] + q) >> 26
+	q = (h[7] + q) >> 25
+	q = (h[8] + q) >> 26
+	q = (h[9] + q) >> 25
+
+	// Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
+	h[0] += 19 * q
+	// Goal: Output h-2^255 q, which is between 0 and 2^255-20.
+
+	carry[0] = h[0] >> 26
+	h[1] += carry[0]
+	h[0] -= carry[0] << 26
+	carry[1] = h[1] >> 25
+	h[2] += carry[1]
+	h[1] -= carry[1] << 25
+	carry[2] = h[2] >> 26
+	h[3] += carry[2]
+	h[2] -= carry[2] << 26
+	carry[3] = h[3] >> 25
+	h[4] += carry[3]
+	h[3] -= carry[3] << 25
+	carry[4] = h[4] >> 26
+	h[5] += carry[4]
+	h[4] -= carry[4] << 26
+	carry[5] = h[5] >> 25
+	h[6] += carry[5]
+	h[5] -= carry[5] << 25
+	carry[6] = h[6] >> 26
+	h[7] += carry[6]
+	h[6] -= carry[6] << 26
+	carry[7] = h[7] >> 25
+	h[8] += carry[7]
+	h[7] -= carry[7] << 25
+	carry[8] = h[8] >> 26
+	h[9] += carry[8]
+	h[8] -= carry[8] << 26
+	carry[9] = h[9] >> 25
+	h[9] -= carry[9] << 25
+	// h10 = carry9
+
+	// Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+	// Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
+	// evidently 2^255 h10-2^255 q = 0.
+	// Goal: Output h[0]+...+2^230 h[9].
+
+	s[0] = byte(h[0] >> 0)
+	s[1] = byte(h[0] >> 8)
+	s[2] = byte(h[0] >> 16)
+	s[3] = byte((h[0] >> 24) | (h[1] << 2))
+	s[4] = byte(h[1] >> 6)
+	s[5] = byte(h[1] >> 14)
+	s[6] = byte((h[1] >> 22) | (h[2] << 3))
+	s[7] = byte(h[2] >> 5)
+	s[8] = byte(h[2] >> 13)
+	s[9] = byte((h[2] >> 21) | (h[3] << 5))
+	s[10] = byte(h[3] >> 3)
+	s[11] = byte(h[3] >> 11)
+	s[12] = byte((h[3] >> 19) | (h[4] << 6))
+	s[13] = byte(h[4] >> 2)
+	s[14] = byte(h[4] >> 10)
+	s[15] = byte(h[4] >> 18)
+	s[16] = byte(h[5] >> 0)
+	s[17] = byte(h[5] >> 8)
+	s[18] = byte(h[5] >> 16)
+	s[19] = byte((h[5] >> 24) | (h[6] << 1))
+	s[20] = byte(h[6] >> 7)
+	s[21] = byte(h[6] >> 15)
+	s[22] = byte((h[6] >> 23) | (h[7] << 3))
+	s[23] = byte(h[7] >> 5)
+	s[24] = byte(h[7] >> 13)
+	s[25] = byte((h[7] >> 21) | (h[8] << 4))
+	s[26] = byte(h[8] >> 4)
+	s[27] = byte(h[8] >> 12)
+	s[28] = byte((h[8] >> 20) | (h[9] << 6))
+	s[29] = byte(h[9] >> 2)
+	s[30] = byte(h[9] >> 10)
+	s[31] = byte(h[9] >> 18)
+}
+
+// feMul calculates h = f * g
+// Can overlap h with f or g.
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//    |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Notes on implementation strategy:
+//
+// Using schoolbook multiplication.
+// Karatsuba would save a little in some cost models.
+//
+// Most multiplications by 2 and 19 are 32-bit precomputations;
+// cheaper than 64-bit postcomputations.
+//
+// There is one remaining multiplication by 19 in the carry chain;
+// one *19 precomputation can be merged into this,
+// but the resulting data flow is considerably less clean.
+//
+// There are 12 carries below.
+// 10 of them are 2-way parallelizable and vectorizable.
+// Can get away with 11 carries, but then data flow is much deeper.
+//
+// With tighter constraints on inputs can squeeze carries into int32.
+func feMul(h, f, g *fieldElement) {
+	f0 := f[0]
+	f1 := f[1]
+	f2 := f[2]
+	f3 := f[3]
+	f4 := f[4]
+	f5 := f[5]
+	f6 := f[6]
+	f7 := f[7]
+	f8 := f[8]
+	f9 := f[9]
+	g0 := g[0]
+	g1 := g[1]
+	g2 := g[2]
+	g3 := g[3]
+	g4 := g[4]
+	g5 := g[5]
+	g6 := g[6]
+	g7 := g[7]
+	g8 := g[8]
+	g9 := g[9]
+	g1_19 := 19 * g1 // 1.4*2^29
+	g2_19 := 19 * g2 // 1.4*2^30; still ok
+	g3_19 := 19 * g3
+	g4_19 := 19 * g4
+	g5_19 := 19 * g5
+	g6_19 := 19 * g6
+	g7_19 := 19 * g7
+	g8_19 := 19 * g8
+	g9_19 := 19 * g9
+	f1_2 := 2 * f1
+	f3_2 := 2 * f3
+	f5_2 := 2 * f5
+	f7_2 := 2 * f7
+	f9_2 := 2 * f9
+	f0g0 := int64(f0) * int64(g0)
+	f0g1 := int64(f0) * int64(g1)
+	f0g2 := int64(f0) * int64(g2)
+	f0g3 := int64(f0) * int64(g3)
+	f0g4 := int64(f0) * int64(g4)
+	f0g5 := int64(f0) * int64(g5)
+	f0g6 := int64(f0) * int64(g6)
+	f0g7 := int64(f0) * int64(g7)
+	f0g8 := int64(f0) * int64(g8)
+	f0g9 := int64(f0) * int64(g9)
+	f1g0 := int64(f1) * int64(g0)
+	f1g1_2 := int64(f1_2) * int64(g1)
+	f1g2 := int64(f1) * int64(g2)
+	f1g3_2 := int64(f1_2) * int64(g3)
+	f1g4 := int64(f1) * int64(g4)
+	f1g5_2 := int64(f1_2) * int64(g5)
+	f1g6 := int64(f1) * int64(g6)
+	f1g7_2 := int64(f1_2) * int64(g7)
+	f1g8 := int64(f1) * int64(g8)
+	f1g9_38 := int64(f1_2) * int64(g9_19)
+	f2g0 := int64(f2) * int64(g0)
+	f2g1 := int64(f2) * int64(g1)
+	f2g2 := int64(f2) * int64(g2)
+	f2g3 := int64(f2) * int64(g3)
+	f2g4 := int64(f2) * int64(g4)
+	f2g5 := int64(f2) * int64(g5)
+	f2g6 := int64(f2) * int64(g6)
+	f2g7 := int64(f2) * int64(g7)
+	f2g8_19 := int64(f2) * int64(g8_19)
+	f2g9_19 := int64(f2) * int64(g9_19)
+	f3g0 := int64(f3) * int64(g0)
+	f3g1_2 := int64(f3_2) * int64(g1)
+	f3g2 := int64(f3) * int64(g2)
+	f3g3_2 := int64(f3_2) * int64(g3)
+	f3g4 := int64(f3) * int64(g4)
+	f3g5_2 := int64(f3_2) * int64(g5)
+	f3g6 := int64(f3) * int64(g6)
+	f3g7_38 := int64(f3_2) * int64(g7_19)
+	f3g8_19 := int64(f3) * int64(g8_19)
+	f3g9_38 := int64(f3_2) * int64(g9_19)
+	f4g0 := int64(f4) * int64(g0)
+	f4g1 := int64(f4) * int64(g1)
+	f4g2 := int64(f4) * int64(g2)
+	f4g3 := int64(f4) * int64(g3)
+	f4g4 := int64(f4) * int64(g4)
+	f4g5 := int64(f4) * int64(g5)
+	f4g6_19 := int64(f4) * int64(g6_19)
+	f4g7_19 := int64(f4) * int64(g7_19)
+	f4g8_19 := int64(f4) * int64(g8_19)
+	f4g9_19 := int64(f4) * int64(g9_19)
+	f5g0 := int64(f5) * int64(g0)
+	f5g1_2 := int64(f5_2) * int64(g1)
+	f5g2 := int64(f5) * int64(g2)
+	f5g3_2 := int64(f5_2) * int64(g3)
+	f5g4 := int64(f5) * int64(g4)
+	f5g5_38 := int64(f5_2) * int64(g5_19)
+	f5g6_19 := int64(f5) * int64(g6_19)
+	f5g7_38 := int64(f5_2) * int64(g7_19)
+	f5g8_19 := int64(f5) * int64(g8_19)
+	f5g9_38 := int64(f5_2) * int64(g9_19)
+	f6g0 := int64(f6) * int64(g0)
+	f6g1 := int64(f6) * int64(g1)
+	f6g2 := int64(f6) * int64(g2)
+	f6g3 := int64(f6) * int64(g3)
+	f6g4_19 := int64(f6) * int64(g4_19)
+	f6g5_19 := int64(f6) * int64(g5_19)
+	f6g6_19 := int64(f6) * int64(g6_19)
+	f6g7_19 := int64(f6) * int64(g7_19)
+	f6g8_19 := int64(f6) * int64(g8_19)
+	f6g9_19 := int64(f6) * int64(g9_19)
+	f7g0 := int64(f7) * int64(g0)
+	f7g1_2 := int64(f7_2) * int64(g1)
+	f7g2 := int64(f7) * int64(g2)
+	f7g3_38 := int64(f7_2) * int64(g3_19)
+	f7g4_19 := int64(f7) * int64(g4_19)
+	f7g5_38 := int64(f7_2) * int64(g5_19)
+	f7g6_19 := int64(f7) * int64(g6_19)
+	f7g7_38 := int64(f7_2) * int64(g7_19)
+	f7g8_19 := int64(f7) * int64(g8_19)
+	f7g9_38 := int64(f7_2) * int64(g9_19)
+	f8g0 := int64(f8) * int64(g0)
+	f8g1 := int64(f8) * int64(g1)
+	f8g2_19 := int64(f8) * int64(g2_19)
+	f8g3_19 := int64(f8) * int64(g3_19)
+	f8g4_19 := int64(f8) * int64(g4_19)
+	f8g5_19 := int64(f8) * int64(g5_19)
+	f8g6_19 := int64(f8) * int64(g6_19)
+	f8g7_19 := int64(f8) * int64(g7_19)
+	f8g8_19 := int64(f8) * int64(g8_19)
+	f8g9_19 := int64(f8) * int64(g9_19)
+	f9g0 := int64(f9) * int64(g0)
+	f9g1_38 := int64(f9_2) * int64(g1_19)
+	f9g2_19 := int64(f9) * int64(g2_19)
+	f9g3_38 := int64(f9_2) * int64(g3_19)
+	f9g4_19 := int64(f9) * int64(g4_19)
+	f9g5_38 := int64(f9_2) * int64(g5_19)
+	f9g6_19 := int64(f9) * int64(g6_19)
+	f9g7_38 := int64(f9_2) * int64(g7_19)
+	f9g8_19 := int64(f9) * int64(g8_19)
+	f9g9_38 := int64(f9_2) * int64(g9_19)
+	h0 := f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38
+	h1 := f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19
+	h2 := f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38
+	h3 := f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19
+	h4 := f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38
+	h5 := f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19
+	h6 := f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38
+	h7 := f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19
+	h8 := f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38
+	h9 := f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0
+	var carry [10]int64
+
+	// |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
+	//   i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
+	// |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
+	//   i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
+
+	carry[0] = (h0 + (1 << 25)) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+	carry[4] = (h4 + (1 << 25)) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+	// |h0| <= 2^25
+	// |h4| <= 2^25
+	// |h1| <= 1.51*2^58
+	// |h5| <= 1.51*2^58
+
+	carry[1] = (h1 + (1 << 24)) >> 25
+	h2 += carry[1]
+	h1 -= carry[1] << 25
+	carry[5] = (h5 + (1 << 24)) >> 25
+	h6 += carry[5]
+	h5 -= carry[5] << 25
+	// |h1| <= 2^24; from now on fits into int32
+	// |h5| <= 2^24; from now on fits into int32
+	// |h2| <= 1.21*2^59
+	// |h6| <= 1.21*2^59
+
+	carry[2] = (h2 + (1 << 25)) >> 26
+	h3 += carry[2]
+	h2 -= carry[2] << 26
+	carry[6] = (h6 + (1 << 25)) >> 26
+	h7 += carry[6]
+	h6 -= carry[6] << 26
+	// |h2| <= 2^25; from now on fits into int32 unchanged
+	// |h6| <= 2^25; from now on fits into int32 unchanged
+	// |h3| <= 1.51*2^58
+	// |h7| <= 1.51*2^58
+
+	carry[3] = (h3 + (1 << 24)) >> 25
+	h4 += carry[3]
+	h3 -= carry[3] << 25
+	carry[7] = (h7 + (1 << 24)) >> 25
+	h8 += carry[7]
+	h7 -= carry[7] << 25
+	// |h3| <= 2^24; from now on fits into int32 unchanged
+	// |h7| <= 2^24; from now on fits into int32 unchanged
+	// |h4| <= 1.52*2^33
+	// |h8| <= 1.52*2^33
+
+	carry[4] = (h4 + (1 << 25)) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+	carry[8] = (h8 + (1 << 25)) >> 26
+	h9 += carry[8]
+	h8 -= carry[8] << 26
+	// |h4| <= 2^25; from now on fits into int32 unchanged
+	// |h8| <= 2^25; from now on fits into int32 unchanged
+	// |h5| <= 1.01*2^24
+	// |h9| <= 1.51*2^58
+
+	carry[9] = (h9 + (1 << 24)) >> 25
+	h0 += carry[9] * 19
+	h9 -= carry[9] << 25
+	// |h9| <= 2^24; from now on fits into int32 unchanged
+	// |h0| <= 1.8*2^37
+
+	carry[0] = (h0 + (1 << 25)) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+	// |h0| <= 2^25; from now on fits into int32 unchanged
+	// |h1| <= 1.01*2^24
+
+	h[0] = int32(h0)
+	h[1] = int32(h1)
+	h[2] = int32(h2)
+	h[3] = int32(h3)
+	h[4] = int32(h4)
+	h[5] = int32(h5)
+	h[6] = int32(h6)
+	h[7] = int32(h7)
+	h[8] = int32(h8)
+	h[9] = int32(h9)
+}
+
+// feSquare calculates h = f*f. Can overlap h with f.
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+func feSquare(h, f *fieldElement) {
+	f0 := f[0]
+	f1 := f[1]
+	f2 := f[2]
+	f3 := f[3]
+	f4 := f[4]
+	f5 := f[5]
+	f6 := f[6]
+	f7 := f[7]
+	f8 := f[8]
+	f9 := f[9]
+	f0_2 := 2 * f0
+	f1_2 := 2 * f1
+	f2_2 := 2 * f2
+	f3_2 := 2 * f3
+	f4_2 := 2 * f4
+	f5_2 := 2 * f5
+	f6_2 := 2 * f6
+	f7_2 := 2 * f7
+	f5_38 := 38 * f5 // 1.31*2^30
+	f6_19 := 19 * f6 // 1.31*2^30
+	f7_38 := 38 * f7 // 1.31*2^30
+	f8_19 := 19 * f8 // 1.31*2^30
+	f9_38 := 38 * f9 // 1.31*2^30
+	f0f0 := int64(f0) * int64(f0)
+	f0f1_2 := int64(f0_2) * int64(f1)
+	f0f2_2 := int64(f0_2) * int64(f2)
+	f0f3_2 := int64(f0_2) * int64(f3)
+	f0f4_2 := int64(f0_2) * int64(f4)
+	f0f5_2 := int64(f0_2) * int64(f5)
+	f0f6_2 := int64(f0_2) * int64(f6)
+	f0f7_2 := int64(f0_2) * int64(f7)
+	f0f8_2 := int64(f0_2) * int64(f8)
+	f0f9_2 := int64(f0_2) * int64(f9)
+	f1f1_2 := int64(f1_2) * int64(f1)
+	f1f2_2 := int64(f1_2) * int64(f2)
+	f1f3_4 := int64(f1_2) * int64(f3_2)
+	f1f4_2 := int64(f1_2) * int64(f4)
+	f1f5_4 := int64(f1_2) * int64(f5_2)
+	f1f6_2 := int64(f1_2) * int64(f6)
+	f1f7_4 := int64(f1_2) * int64(f7_2)
+	f1f8_2 := int64(f1_2) * int64(f8)
+	f1f9_76 := int64(f1_2) * int64(f9_38)
+	f2f2 := int64(f2) * int64(f2)
+	f2f3_2 := int64(f2_2) * int64(f3)
+	f2f4_2 := int64(f2_2) * int64(f4)
+	f2f5_2 := int64(f2_2) * int64(f5)
+	f2f6_2 := int64(f2_2) * int64(f6)
+	f2f7_2 := int64(f2_2) * int64(f7)
+	f2f8_38 := int64(f2_2) * int64(f8_19)
+	f2f9_38 := int64(f2) * int64(f9_38)
+	f3f3_2 := int64(f3_2) * int64(f3)
+	f3f4_2 := int64(f3_2) * int64(f4)
+	f3f5_4 := int64(f3_2) * int64(f5_2)
+	f3f6_2 := int64(f3_2) * int64(f6)
+	f3f7_76 := int64(f3_2) * int64(f7_38)
+	f3f8_38 := int64(f3_2) * int64(f8_19)
+	f3f9_76 := int64(f3_2) * int64(f9_38)
+	f4f4 := int64(f4) * int64(f4)
+	f4f5_2 := int64(f4_2) * int64(f5)
+	f4f6_38 := int64(f4_2) * int64(f6_19)
+	f4f7_38 := int64(f4) * int64(f7_38)
+	f4f8_38 := int64(f4_2) * int64(f8_19)
+	f4f9_38 := int64(f4) * int64(f9_38)
+	f5f5_38 := int64(f5) * int64(f5_38)
+	f5f6_38 := int64(f5_2) * int64(f6_19)
+	f5f7_76 := int64(f5_2) * int64(f7_38)
+	f5f8_38 := int64(f5_2) * int64(f8_19)
+	f5f9_76 := int64(f5_2) * int64(f9_38)
+	f6f6_19 := int64(f6) * int64(f6_19)
+	f6f7_38 := int64(f6) * int64(f7_38)
+	f6f8_38 := int64(f6_2) * int64(f8_19)
+	f6f9_38 := int64(f6) * int64(f9_38)
+	f7f7_38 := int64(f7) * int64(f7_38)
+	f7f8_38 := int64(f7_2) * int64(f8_19)
+	f7f9_76 := int64(f7_2) * int64(f9_38)
+	f8f8_19 := int64(f8) * int64(f8_19)
+	f8f9_38 := int64(f8) * int64(f9_38)
+	f9f9_38 := int64(f9) * int64(f9_38)
+	h0 := f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38
+	h1 := f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38
+	h2 := f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19
+	h3 := f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38
+	h4 := f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38
+	h5 := f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38
+	h6 := f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19
+	h7 := f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38
+	h8 := f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38
+	h9 := f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2
+	var carry [10]int64
+
+	carry[0] = (h0 + (1 << 25)) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+	carry[4] = (h4 + (1 << 25)) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+
+	carry[1] = (h1 + (1 << 24)) >> 25
+	h2 += carry[1]
+	h1 -= carry[1] << 25
+	carry[5] = (h5 + (1 << 24)) >> 25
+	h6 += carry[5]
+	h5 -= carry[5] << 25
+
+	carry[2] = (h2 + (1 << 25)) >> 26
+	h3 += carry[2]
+	h2 -= carry[2] << 26
+	carry[6] = (h6 + (1 << 25)) >> 26
+	h7 += carry[6]
+	h6 -= carry[6] << 26
+
+	carry[3] = (h3 + (1 << 24)) >> 25
+	h4 += carry[3]
+	h3 -= carry[3] << 25
+	carry[7] = (h7 + (1 << 24)) >> 25
+	h8 += carry[7]
+	h7 -= carry[7] << 25
+
+	carry[4] = (h4 + (1 << 25)) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+	carry[8] = (h8 + (1 << 25)) >> 26
+	h9 += carry[8]
+	h8 -= carry[8] << 26
+
+	carry[9] = (h9 + (1 << 24)) >> 25
+	h0 += carry[9] * 19
+	h9 -= carry[9] << 25
+
+	carry[0] = (h0 + (1 << 25)) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+
+	h[0] = int32(h0)
+	h[1] = int32(h1)
+	h[2] = int32(h2)
+	h[3] = int32(h3)
+	h[4] = int32(h4)
+	h[5] = int32(h5)
+	h[6] = int32(h6)
+	h[7] = int32(h7)
+	h[8] = int32(h8)
+	h[9] = int32(h9)
+}
+
+// feMul121666 calculates h = f * 121666. Can overlap h with f.
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+func feMul121666(h, f *fieldElement) {
+	h0 := int64(f[0]) * 121666
+	h1 := int64(f[1]) * 121666
+	h2 := int64(f[2]) * 121666
+	h3 := int64(f[3]) * 121666
+	h4 := int64(f[4]) * 121666
+	h5 := int64(f[5]) * 121666
+	h6 := int64(f[6]) * 121666
+	h7 := int64(f[7]) * 121666
+	h8 := int64(f[8]) * 121666
+	h9 := int64(f[9]) * 121666
+	var carry [10]int64
+
+	carry[9] = (h9 + (1 << 24)) >> 25
+	h0 += carry[9] * 19
+	h9 -= carry[9] << 25
+	carry[1] = (h1 + (1 << 24)) >> 25
+	h2 += carry[1]
+	h1 -= carry[1] << 25
+	carry[3] = (h3 + (1 << 24)) >> 25
+	h4 += carry[3]
+	h3 -= carry[3] << 25
+	carry[5] = (h5 + (1 << 24)) >> 25
+	h6 += carry[5]
+	h5 -= carry[5] << 25
+	carry[7] = (h7 + (1 << 24)) >> 25
+	h8 += carry[7]
+	h7 -= carry[7] << 25
+
+	carry[0] = (h0 + (1 << 25)) >> 26
+	h1 += carry[0]
+	h0 -= carry[0] << 26
+	carry[2] = (h2 + (1 << 25)) >> 26
+	h3 += carry[2]
+	h2 -= carry[2] << 26
+	carry[4] = (h4 + (1 << 25)) >> 26
+	h5 += carry[4]
+	h4 -= carry[4] << 26
+	carry[6] = (h6 + (1 << 25)) >> 26
+	h7 += carry[6]
+	h6 -= carry[6] << 26
+	carry[8] = (h8 + (1 << 25)) >> 26
+	h9 += carry[8]
+	h8 -= carry[8] << 26
+
+	h[0] = int32(h0)
+	h[1] = int32(h1)
+	h[2] = int32(h2)
+	h[3] = int32(h3)
+	h[4] = int32(h4)
+	h[5] = int32(h5)
+	h[6] = int32(h6)
+	h[7] = int32(h7)
+	h[8] = int32(h8)
+	h[9] = int32(h9)
+}
+
+// feInvert sets out = z^-1.
+func feInvert(out, z *fieldElement) {
+	var t0, t1, t2, t3 fieldElement
+	var i int
+
+	feSquare(&t0, z)
+	for i = 1; i < 1; i++ {
+		feSquare(&t0, &t0)
+	}
+	feSquare(&t1, &t0)
+	for i = 1; i < 2; i++ {
+		feSquare(&t1, &t1)
+	}
+	feMul(&t1, z, &t1)
+	feMul(&t0, &t0, &t1)
+	feSquare(&t2, &t0)
+	for i = 1; i < 1; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t1, &t1, &t2)
+	feSquare(&t2, &t1)
+	for i = 1; i < 5; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t1, &t2, &t1)
+	feSquare(&t2, &t1)
+	for i = 1; i < 10; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t2, &t2, &t1)
+	feSquare(&t3, &t2)
+	for i = 1; i < 20; i++ {
+		feSquare(&t3, &t3)
+	}
+	feMul(&t2, &t3, &t2)
+	feSquare(&t2, &t2)
+	for i = 1; i < 10; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t1, &t2, &t1)
+	feSquare(&t2, &t1)
+	for i = 1; i < 50; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t2, &t2, &t1)
+	feSquare(&t3, &t2)
+	for i = 1; i < 100; i++ {
+		feSquare(&t3, &t3)
+	}
+	feMul(&t2, &t3, &t2)
+	feSquare(&t2, &t2)
+	for i = 1; i < 50; i++ {
+		feSquare(&t2, &t2)
+	}
+	feMul(&t1, &t2, &t1)
+	feSquare(&t1, &t1)
+	for i = 1; i < 5; i++ {
+		feSquare(&t1, &t1)
+	}
+	feMul(out, &t1, &t0)
+}
+
+func scalarMult(out, in, base *[32]byte) {
+	var e [32]byte
+
+	copy(e[:], in[:])
+	e[0] &= 248
+	e[31] &= 127
+	e[31] |= 64
+
+	var x1, x2, z2, x3, z3, tmp0, tmp1 fieldElement
+	feFromBytes(&x1, base)
+	feOne(&x2)
+	feCopy(&x3, &x1)
+	feOne(&z3)
+
+	swap := int32(0)
+	for pos := 254; pos >= 0; pos-- {
+		b := e[pos/8] >> uint(pos&7)
+		b &= 1
+		swap ^= int32(b)
+		feCSwap(&x2, &x3, swap)
+		feCSwap(&z2, &z3, swap)
+		swap = int32(b)
+
+		feSub(&tmp0, &x3, &z3)
+		feSub(&tmp1, &x2, &z2)
+		feAdd(&x2, &x2, &z2)
+		feAdd(&z2, &x3, &z3)
+		feMul(&z3, &tmp0, &x2)
+		feMul(&z2, &z2, &tmp1)
+		feSquare(&tmp0, &tmp1)
+		feSquare(&tmp1, &x2)
+		feAdd(&x3, &z3, &z2)
+		feSub(&z2, &z3, &z2)
+		feMul(&x2, &tmp1, &tmp0)
+		feSub(&tmp1, &tmp1, &tmp0)
+		feSquare(&z2, &z2)
+		feMul121666(&z3, &tmp1)
+		feSquare(&x3, &x3)
+		feAdd(&tmp0, &tmp0, &z3)
+		feMul(&z3, &x1, &z2)
+		feMul(&z2, &tmp1, &tmp0)
+	}
+
+	feCSwap(&x2, &x3, swap)
+	feCSwap(&z2, &z3, swap)
+
+	feInvert(&z2, &z2)
+	feMul(&x2, &x2, &z2)
+	feToBytes(out, &x2)
+}
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/curve_impl.go b/vendor/github.com/keybase/go-crypto/curve25519/curve_impl.go
new file mode 100644
index 000000000..5f9eebebf
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/curve_impl.go
@@ -0,0 +1,113 @@
+package curve25519
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"sync"
+)
+
+var cv25519 cv25519Curve
+
+type cv25519Curve struct {
+	*elliptic.CurveParams
+}
+
+func copyReverse(dst []byte, src []byte) {
+	// Curve 25519 multiplication functions expect scalars in reverse
+	// order than PGP. To keep the curve25519Curve type consistent
+	// with other curves, we reverse it here.
+	for i, j := 0, len(src)-1; j >= 0; i, j = i+1, j-1 {
+		dst[i] = src[j]
+	}
+}
+
+func (cv25519Curve) ScalarMult(x1, y1 *big.Int, scalar []byte) (x, y *big.Int) {
+	// Assume y1 is 0 with cv25519.
+	var dst [32]byte
+	var x1Bytes [32]byte
+	var scalarBytes [32]byte
+
+	copy(x1Bytes[:], x1.Bytes()[:32])
+	copyReverse(scalarBytes[:], scalar[:32])
+
+	scalarMult(&dst, &scalarBytes, &x1Bytes)
+
+	x = new(big.Int).SetBytes(dst[:])
+	y = new(big.Int)
+	return x, y
+}
+
+func (cv25519Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) {
+	var dst [32]byte
+	var scalarBytes [32]byte
+	copyReverse(scalarBytes[:], scalar[:32])
+	scalarMult(&dst, &scalarBytes, &basePoint)
+	x = new(big.Int).SetBytes(dst[:])
+	y = new(big.Int)
+	return x, y
+}
+
+func (cv25519Curve) IsOnCurve(bigX, bigY *big.Int) bool {
+	return bigY.Sign() == 0 // bigY == 0 ?
+}
+
+// More information about 0x40 point format:
+// https://tools.ietf.org/html/draft-koch-eddsa-for-openpgp-00#section-3
+// In addition to uncompressed point format described here:
+// https://tools.ietf.org/html/rfc6637#section-6
+
+func (cv25519Curve) MarshalType40(x, y *big.Int) []byte {
+	byteLen := 32
+
+	ret := make([]byte, 1+byteLen)
+	ret[0] = 0x40
+
+	xBytes := x.Bytes()
+	copy(ret[1+byteLen-len(xBytes):], xBytes)
+	return ret
+}
+
+func (cv25519Curve) UnmarshalType40(data []byte) (x, y *big.Int) {
+	if len(data) != 1+32 {
+		return nil, nil
+	}
+	if data[0] != 0x40 {
+		return nil, nil
+	}
+	x = new(big.Int).SetBytes(data[1:])
+	// Any x is a valid curve point.
+	return x, new(big.Int)
+}
+
+// ToCurve25519 casts given elliptic.Curve type to Curve25519 type, or
+// returns nil, false if cast was unsuccessful.
+func ToCurve25519(cv elliptic.Curve) (cv25519Curve, bool) {
+	cv2, ok := cv.(cv25519Curve)
+	return cv2, ok
+}
+
+func initCv25519() {
+	cv25519.CurveParams = &elliptic.CurveParams{Name: "Curve 25519"}
+	// Some code relies on these parameters being available for
+	// checking Curve coordinate length. They should not be used
+	// directly for any calculations.
+	cv25519.P, _ = new (big.Int).SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16)
+	cv25519.N, _ = new (big.Int).SetString("1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed", 16)
+	cv25519.Gx, _ = new (big.Int).SetString("9", 16)
+	cv25519.Gy, _ = new (big.Int).SetString("20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9", 16)
+	cv25519.BitSize = 256
+}
+
+var initonce sync.Once
+
+// Cv25519 returns a Curve which (partially) implements Cv25519. Only
+// ScalarMult and ScalarBaseMult are valid for this curve. Add and
+// Double should not be used.
+func Cv25519() elliptic.Curve {
+	initonce.Do(initCv25519)
+	return cv25519
+}
+
+func (curve cv25519Curve) Params() *elliptic.CurveParams {
+	return curve.CurveParams
+}
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/doc.go b/vendor/github.com/keybase/go-crypto/curve25519/doc.go
new file mode 100644
index 000000000..f7db9c1ce
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/doc.go
@@ -0,0 +1,23 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package curve25519 provides an implementation of scalar multiplication on
+// the elliptic curve known as curve25519. See http://cr.yp.to/ecdh.html
+package curve25519
+
+// basePoint is the x coordinate of the generator of the curve.
+var basePoint = [32]byte{9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
+
+// ScalarMult sets dst to the product in*base where dst and base are the x
+// coordinates of group points and all values are in little-endian form.
+func ScalarMult(dst, in, base *[32]byte) {
+	scalarMult(dst, in, base)
+}
+
+// ScalarBaseMult sets dst to the product in*base where dst and base are the x
+// coordinates of group points, base is the standard generator and all values
+// are in little-endian form.
+func ScalarBaseMult(dst, in *[32]byte) {
+	ScalarMult(dst, in, &basePoint)
+}
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/freeze_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/freeze_amd64.s
new file mode 100644
index 000000000..37599fac0
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/freeze_amd64.s
@@ -0,0 +1,94 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+// func freeze(inout *[5]uint64)
+TEXT ·freeze(SB),7,$96-8
+	MOVQ inout+0(FP), DI
+
+	MOVQ SP,R11
+	MOVQ $31,CX
+	NOTQ CX
+	ANDQ CX,SP
+	ADDQ $32,SP
+
+	MOVQ R11,0(SP)
+	MOVQ R12,8(SP)
+	MOVQ R13,16(SP)
+	MOVQ R14,24(SP)
+	MOVQ R15,32(SP)
+	MOVQ BX,40(SP)
+	MOVQ BP,48(SP)
+	MOVQ 0(DI),SI
+	MOVQ 8(DI),DX
+	MOVQ 16(DI),CX
+	MOVQ 24(DI),R8
+	MOVQ 32(DI),R9
+	MOVQ ·REDMASK51(SB),AX
+	MOVQ AX,R10
+	SUBQ $18,R10
+	MOVQ $3,R11
+REDUCELOOP:
+	MOVQ SI,R12
+	SHRQ $51,R12
+	ANDQ AX,SI
+	ADDQ R12,DX
+	MOVQ DX,R12
+	SHRQ $51,R12
+	ANDQ AX,DX
+	ADDQ R12,CX
+	MOVQ CX,R12
+	SHRQ $51,R12
+	ANDQ AX,CX
+	ADDQ R12,R8
+	MOVQ R8,R12
+	SHRQ $51,R12
+	ANDQ AX,R8
+	ADDQ R12,R9
+	MOVQ R9,R12
+	SHRQ $51,R12
+	ANDQ AX,R9
+	IMUL3Q $19,R12,R12
+	ADDQ R12,SI
+	SUBQ $1,R11
+	JA REDUCELOOP
+	MOVQ $1,R12
+	CMPQ R10,SI
+	CMOVQLT R11,R12
+	CMPQ AX,DX
+	CMOVQNE R11,R12
+	CMPQ AX,CX
+	CMOVQNE R11,R12
+	CMPQ AX,R8
+	CMOVQNE R11,R12
+	CMPQ AX,R9
+	CMOVQNE R11,R12
+	NEGQ R12
+	ANDQ R12,AX
+	ANDQ R12,R10
+	SUBQ R10,SI
+	SUBQ AX,DX
+	SUBQ AX,CX
+	SUBQ AX,R8
+	SUBQ AX,R9
+	MOVQ SI,0(DI)
+	MOVQ DX,8(DI)
+	MOVQ CX,16(DI)
+	MOVQ R8,24(DI)
+	MOVQ R9,32(DI)
+	MOVQ 0(SP),R11
+	MOVQ 8(SP),R12
+	MOVQ 16(SP),R13
+	MOVQ 24(SP),R14
+	MOVQ 32(SP),R15
+	MOVQ 40(SP),BX
+	MOVQ 48(SP),BP
+	MOVQ R11,SP
+	MOVQ DI,AX
+	MOVQ SI,DX
+	RET
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/ladderstep_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/ladderstep_amd64.s
new file mode 100644
index 000000000..3949f9cfa
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/ladderstep_amd64.s
@@ -0,0 +1,1398 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+// func ladderstep(inout *[5][5]uint64)
+TEXT ·ladderstep(SB),0,$384-8
+	MOVQ inout+0(FP),DI
+
+	MOVQ SP,R11
+	MOVQ $31,CX
+	NOTQ CX
+	ANDQ CX,SP
+	ADDQ $32,SP
+
+	MOVQ R11,0(SP)
+	MOVQ R12,8(SP)
+	MOVQ R13,16(SP)
+	MOVQ R14,24(SP)
+	MOVQ R15,32(SP)
+	MOVQ BX,40(SP)
+	MOVQ BP,48(SP)
+	MOVQ 40(DI),SI
+	MOVQ 48(DI),DX
+	MOVQ 56(DI),CX
+	MOVQ 64(DI),R8
+	MOVQ 72(DI),R9
+	MOVQ SI,AX
+	MOVQ DX,R10
+	MOVQ CX,R11
+	MOVQ R8,R12
+	MOVQ R9,R13
+	ADDQ ·_2P0(SB),AX
+	ADDQ ·_2P1234(SB),R10
+	ADDQ ·_2P1234(SB),R11
+	ADDQ ·_2P1234(SB),R12
+	ADDQ ·_2P1234(SB),R13
+	ADDQ 80(DI),SI
+	ADDQ 88(DI),DX
+	ADDQ 96(DI),CX
+	ADDQ 104(DI),R8
+	ADDQ 112(DI),R9
+	SUBQ 80(DI),AX
+	SUBQ 88(DI),R10
+	SUBQ 96(DI),R11
+	SUBQ 104(DI),R12
+	SUBQ 112(DI),R13
+	MOVQ SI,56(SP)
+	MOVQ DX,64(SP)
+	MOVQ CX,72(SP)
+	MOVQ R8,80(SP)
+	MOVQ R9,88(SP)
+	MOVQ AX,96(SP)
+	MOVQ R10,104(SP)
+	MOVQ R11,112(SP)
+	MOVQ R12,120(SP)
+	MOVQ R13,128(SP)
+	MOVQ 96(SP),AX
+	MULQ 96(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 96(SP),AX
+	SHLQ $1,AX
+	MULQ 104(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 96(SP),AX
+	SHLQ $1,AX
+	MULQ 112(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 96(SP),AX
+	SHLQ $1,AX
+	MULQ 120(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 96(SP),AX
+	SHLQ $1,AX
+	MULQ 128(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 104(SP),AX
+	MULQ 104(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 104(SP),AX
+	SHLQ $1,AX
+	MULQ 112(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 104(SP),AX
+	SHLQ $1,AX
+	MULQ 120(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 104(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 112(SP),AX
+	MULQ 112(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 112(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 120(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 112(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 120(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 120(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 120(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 128(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	ANDQ DX,SI
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ADDQ R10,CX
+	ANDQ DX,R8
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ADDQ R12,CX
+	ANDQ DX,R9
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ADDQ R14,CX
+	ANDQ DX,AX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,136(SP)
+	MOVQ R8,144(SP)
+	MOVQ R9,152(SP)
+	MOVQ AX,160(SP)
+	MOVQ R10,168(SP)
+	MOVQ 56(SP),AX
+	MULQ 56(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 56(SP),AX
+	SHLQ $1,AX
+	MULQ 64(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 56(SP),AX
+	SHLQ $1,AX
+	MULQ 72(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 56(SP),AX
+	SHLQ $1,AX
+	MULQ 80(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 56(SP),AX
+	SHLQ $1,AX
+	MULQ 88(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 64(SP),AX
+	MULQ 64(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 64(SP),AX
+	SHLQ $1,AX
+	MULQ 72(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 64(SP),AX
+	SHLQ $1,AX
+	MULQ 80(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 64(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 72(SP),AX
+	MULQ 72(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 72(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 80(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 72(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 80(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 80(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 80(SP),DX
+	IMUL3Q $38,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 88(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	ANDQ DX,SI
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ADDQ R10,CX
+	ANDQ DX,R8
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ADDQ R12,CX
+	ANDQ DX,R9
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ADDQ R14,CX
+	ANDQ DX,AX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,176(SP)
+	MOVQ R8,184(SP)
+	MOVQ R9,192(SP)
+	MOVQ AX,200(SP)
+	MOVQ R10,208(SP)
+	MOVQ SI,SI
+	MOVQ R8,DX
+	MOVQ R9,CX
+	MOVQ AX,R8
+	MOVQ R10,R9
+	ADDQ ·_2P0(SB),SI
+	ADDQ ·_2P1234(SB),DX
+	ADDQ ·_2P1234(SB),CX
+	ADDQ ·_2P1234(SB),R8
+	ADDQ ·_2P1234(SB),R9
+	SUBQ 136(SP),SI
+	SUBQ 144(SP),DX
+	SUBQ 152(SP),CX
+	SUBQ 160(SP),R8
+	SUBQ 168(SP),R9
+	MOVQ SI,216(SP)
+	MOVQ DX,224(SP)
+	MOVQ CX,232(SP)
+	MOVQ R8,240(SP)
+	MOVQ R9,248(SP)
+	MOVQ 120(DI),SI
+	MOVQ 128(DI),DX
+	MOVQ 136(DI),CX
+	MOVQ 144(DI),R8
+	MOVQ 152(DI),R9
+	MOVQ SI,AX
+	MOVQ DX,R10
+	MOVQ CX,R11
+	MOVQ R8,R12
+	MOVQ R9,R13
+	ADDQ ·_2P0(SB),AX
+	ADDQ ·_2P1234(SB),R10
+	ADDQ ·_2P1234(SB),R11
+	ADDQ ·_2P1234(SB),R12
+	ADDQ ·_2P1234(SB),R13
+	ADDQ 160(DI),SI
+	ADDQ 168(DI),DX
+	ADDQ 176(DI),CX
+	ADDQ 184(DI),R8
+	ADDQ 192(DI),R9
+	SUBQ 160(DI),AX
+	SUBQ 168(DI),R10
+	SUBQ 176(DI),R11
+	SUBQ 184(DI),R12
+	SUBQ 192(DI),R13
+	MOVQ SI,256(SP)
+	MOVQ DX,264(SP)
+	MOVQ CX,272(SP)
+	MOVQ R8,280(SP)
+	MOVQ R9,288(SP)
+	MOVQ AX,296(SP)
+	MOVQ R10,304(SP)
+	MOVQ R11,312(SP)
+	MOVQ R12,320(SP)
+	MOVQ R13,328(SP)
+	MOVQ 280(SP),SI
+	IMUL3Q $19,SI,AX
+	MOVQ AX,336(SP)
+	MULQ 112(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 288(SP),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,344(SP)
+	MULQ 104(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 256(SP),AX
+	MULQ 96(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 256(SP),AX
+	MULQ 104(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 256(SP),AX
+	MULQ 112(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 256(SP),AX
+	MULQ 120(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 256(SP),AX
+	MULQ 128(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 264(SP),AX
+	MULQ 96(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 264(SP),AX
+	MULQ 104(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 264(SP),AX
+	MULQ 112(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 264(SP),AX
+	MULQ 120(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 264(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 272(SP),AX
+	MULQ 96(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 272(SP),AX
+	MULQ 104(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 272(SP),AX
+	MULQ 112(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 272(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 120(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 272(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 128(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 280(SP),AX
+	MULQ 96(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 280(SP),AX
+	MULQ 104(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 336(SP),AX
+	MULQ 120(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 336(SP),AX
+	MULQ 128(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 288(SP),AX
+	MULQ 96(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 344(SP),AX
+	MULQ 112(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 344(SP),AX
+	MULQ 120(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 344(SP),AX
+	MULQ 128(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ANDQ DX,SI
+	ADDQ R10,CX
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ANDQ DX,R8
+	ADDQ R12,CX
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ANDQ DX,R9
+	ADDQ R14,CX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	ANDQ DX,AX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,96(SP)
+	MOVQ R8,104(SP)
+	MOVQ R9,112(SP)
+	MOVQ AX,120(SP)
+	MOVQ R10,128(SP)
+	MOVQ 320(SP),SI
+	IMUL3Q $19,SI,AX
+	MOVQ AX,256(SP)
+	MULQ 72(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 328(SP),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,264(SP)
+	MULQ 64(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 296(SP),AX
+	MULQ 56(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 296(SP),AX
+	MULQ 64(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 296(SP),AX
+	MULQ 72(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 296(SP),AX
+	MULQ 80(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 296(SP),AX
+	MULQ 88(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 304(SP),AX
+	MULQ 56(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 304(SP),AX
+	MULQ 64(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 304(SP),AX
+	MULQ 72(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 304(SP),AX
+	MULQ 80(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 304(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 312(SP),AX
+	MULQ 56(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 312(SP),AX
+	MULQ 64(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 312(SP),AX
+	MULQ 72(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 312(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 80(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 312(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 88(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 320(SP),AX
+	MULQ 56(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 320(SP),AX
+	MULQ 64(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 256(SP),AX
+	MULQ 80(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 256(SP),AX
+	MULQ 88(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 328(SP),AX
+	MULQ 56(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 264(SP),AX
+	MULQ 72(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 264(SP),AX
+	MULQ 80(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 264(SP),AX
+	MULQ 88(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ANDQ DX,SI
+	ADDQ R10,CX
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ANDQ DX,R8
+	ADDQ R12,CX
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ANDQ DX,R9
+	ADDQ R14,CX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	ANDQ DX,AX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,DX
+	MOVQ R8,CX
+	MOVQ R9,R11
+	MOVQ AX,R12
+	MOVQ R10,R13
+	ADDQ ·_2P0(SB),DX
+	ADDQ ·_2P1234(SB),CX
+	ADDQ ·_2P1234(SB),R11
+	ADDQ ·_2P1234(SB),R12
+	ADDQ ·_2P1234(SB),R13
+	ADDQ 96(SP),SI
+	ADDQ 104(SP),R8
+	ADDQ 112(SP),R9
+	ADDQ 120(SP),AX
+	ADDQ 128(SP),R10
+	SUBQ 96(SP),DX
+	SUBQ 104(SP),CX
+	SUBQ 112(SP),R11
+	SUBQ 120(SP),R12
+	SUBQ 128(SP),R13
+	MOVQ SI,120(DI)
+	MOVQ R8,128(DI)
+	MOVQ R9,136(DI)
+	MOVQ AX,144(DI)
+	MOVQ R10,152(DI)
+	MOVQ DX,160(DI)
+	MOVQ CX,168(DI)
+	MOVQ R11,176(DI)
+	MOVQ R12,184(DI)
+	MOVQ R13,192(DI)
+	MOVQ 120(DI),AX
+	MULQ 120(DI)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 120(DI),AX
+	SHLQ $1,AX
+	MULQ 128(DI)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 120(DI),AX
+	SHLQ $1,AX
+	MULQ 136(DI)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 120(DI),AX
+	SHLQ $1,AX
+	MULQ 144(DI)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 120(DI),AX
+	SHLQ $1,AX
+	MULQ 152(DI)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 128(DI),AX
+	MULQ 128(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 128(DI),AX
+	SHLQ $1,AX
+	MULQ 136(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 128(DI),AX
+	SHLQ $1,AX
+	MULQ 144(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 128(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 152(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 136(DI),AX
+	MULQ 136(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 136(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 144(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 136(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 152(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 144(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 144(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 144(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 152(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 152(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 152(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	ANDQ DX,SI
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ADDQ R10,CX
+	ANDQ DX,R8
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ADDQ R12,CX
+	ANDQ DX,R9
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ADDQ R14,CX
+	ANDQ DX,AX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,120(DI)
+	MOVQ R8,128(DI)
+	MOVQ R9,136(DI)
+	MOVQ AX,144(DI)
+	MOVQ R10,152(DI)
+	MOVQ 160(DI),AX
+	MULQ 160(DI)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 160(DI),AX
+	SHLQ $1,AX
+	MULQ 168(DI)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 160(DI),AX
+	SHLQ $1,AX
+	MULQ 176(DI)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 160(DI),AX
+	SHLQ $1,AX
+	MULQ 184(DI)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 160(DI),AX
+	SHLQ $1,AX
+	MULQ 192(DI)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 168(DI),AX
+	MULQ 168(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 168(DI),AX
+	SHLQ $1,AX
+	MULQ 176(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 168(DI),AX
+	SHLQ $1,AX
+	MULQ 184(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 168(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 192(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(DI),AX
+	MULQ 176(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 176(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 184(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 192(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 184(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 184(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 184(DI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 192(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 192(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 192(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	ANDQ DX,SI
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ADDQ R10,CX
+	ANDQ DX,R8
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ADDQ R12,CX
+	ANDQ DX,R9
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ADDQ R14,CX
+	ANDQ DX,AX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,160(DI)
+	MOVQ R8,168(DI)
+	MOVQ R9,176(DI)
+	MOVQ AX,184(DI)
+	MOVQ R10,192(DI)
+	MOVQ 184(DI),SI
+	IMUL3Q $19,SI,AX
+	MOVQ AX,56(SP)
+	MULQ 16(DI)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 192(DI),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,64(SP)
+	MULQ 8(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 160(DI),AX
+	MULQ 0(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 160(DI),AX
+	MULQ 8(DI)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 160(DI),AX
+	MULQ 16(DI)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 160(DI),AX
+	MULQ 24(DI)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 160(DI),AX
+	MULQ 32(DI)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 168(DI),AX
+	MULQ 0(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 168(DI),AX
+	MULQ 8(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 168(DI),AX
+	MULQ 16(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 168(DI),AX
+	MULQ 24(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 168(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 32(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(DI),AX
+	MULQ 0(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 176(DI),AX
+	MULQ 8(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 176(DI),AX
+	MULQ 16(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 176(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 24(DI)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 32(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 184(DI),AX
+	MULQ 0(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 184(DI),AX
+	MULQ 8(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 56(SP),AX
+	MULQ 24(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 56(SP),AX
+	MULQ 32(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 192(DI),AX
+	MULQ 0(DI)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 64(SP),AX
+	MULQ 16(DI)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 64(SP),AX
+	MULQ 24(DI)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 64(SP),AX
+	MULQ 32(DI)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ANDQ DX,SI
+	ADDQ R10,CX
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ANDQ DX,R8
+	ADDQ R12,CX
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ANDQ DX,R9
+	ADDQ R14,CX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	ANDQ DX,AX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,160(DI)
+	MOVQ R8,168(DI)
+	MOVQ R9,176(DI)
+	MOVQ AX,184(DI)
+	MOVQ R10,192(DI)
+	MOVQ 200(SP),SI
+	IMUL3Q $19,SI,AX
+	MOVQ AX,56(SP)
+	MULQ 152(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 208(SP),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,64(SP)
+	MULQ 144(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(SP),AX
+	MULQ 136(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 176(SP),AX
+	MULQ 144(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 176(SP),AX
+	MULQ 152(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 176(SP),AX
+	MULQ 160(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 176(SP),AX
+	MULQ 168(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 184(SP),AX
+	MULQ 136(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 184(SP),AX
+	MULQ 144(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 184(SP),AX
+	MULQ 152(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 184(SP),AX
+	MULQ 160(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 184(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 168(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 192(SP),AX
+	MULQ 136(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 192(SP),AX
+	MULQ 144(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 192(SP),AX
+	MULQ 152(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 192(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 160(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 192(SP),DX
+	IMUL3Q $19,DX,AX
+	MULQ 168(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 200(SP),AX
+	MULQ 136(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 200(SP),AX
+	MULQ 144(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 56(SP),AX
+	MULQ 160(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 56(SP),AX
+	MULQ 168(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 208(SP),AX
+	MULQ 136(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 64(SP),AX
+	MULQ 152(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 64(SP),AX
+	MULQ 160(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 64(SP),AX
+	MULQ 168(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ANDQ DX,SI
+	ADDQ R10,CX
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ANDQ DX,R8
+	ADDQ R12,CX
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ANDQ DX,R9
+	ADDQ R14,CX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	ANDQ DX,AX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,40(DI)
+	MOVQ R8,48(DI)
+	MOVQ R9,56(DI)
+	MOVQ AX,64(DI)
+	MOVQ R10,72(DI)
+	MOVQ 216(SP),AX
+	MULQ ·_121666_213(SB)
+	SHRQ $13,AX
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 224(SP),AX
+	MULQ ·_121666_213(SB)
+	SHRQ $13,AX
+	ADDQ AX,CX
+	MOVQ DX,R8
+	MOVQ 232(SP),AX
+	MULQ ·_121666_213(SB)
+	SHRQ $13,AX
+	ADDQ AX,R8
+	MOVQ DX,R9
+	MOVQ 240(SP),AX
+	MULQ ·_121666_213(SB)
+	SHRQ $13,AX
+	ADDQ AX,R9
+	MOVQ DX,R10
+	MOVQ 248(SP),AX
+	MULQ ·_121666_213(SB)
+	SHRQ $13,AX
+	ADDQ AX,R10
+	IMUL3Q $19,DX,DX
+	ADDQ DX,SI
+	ADDQ 136(SP),SI
+	ADDQ 144(SP),CX
+	ADDQ 152(SP),R8
+	ADDQ 160(SP),R9
+	ADDQ 168(SP),R10
+	MOVQ SI,80(DI)
+	MOVQ CX,88(DI)
+	MOVQ R8,96(DI)
+	MOVQ R9,104(DI)
+	MOVQ R10,112(DI)
+	MOVQ 104(DI),SI
+	IMUL3Q $19,SI,AX
+	MOVQ AX,56(SP)
+	MULQ 232(SP)
+	MOVQ AX,SI
+	MOVQ DX,CX
+	MOVQ 112(DI),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,64(SP)
+	MULQ 224(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 80(DI),AX
+	MULQ 216(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 80(DI),AX
+	MULQ 224(SP)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 80(DI),AX
+	MULQ 232(SP)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 80(DI),AX
+	MULQ 240(SP)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 80(DI),AX
+	MULQ 248(SP)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 88(DI),AX
+	MULQ 216(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 88(DI),AX
+	MULQ 224(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 88(DI),AX
+	MULQ 232(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 88(DI),AX
+	MULQ 240(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 88(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 248(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 96(DI),AX
+	MULQ 216(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 96(DI),AX
+	MULQ 224(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 96(DI),AX
+	MULQ 232(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 96(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 240(SP)
+	ADDQ AX,SI
+	ADCQ DX,CX
+	MOVQ 96(DI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 248(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 104(DI),AX
+	MULQ 216(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 104(DI),AX
+	MULQ 224(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 56(SP),AX
+	MULQ 240(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 56(SP),AX
+	MULQ 248(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 112(DI),AX
+	MULQ 216(SP)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 64(SP),AX
+	MULQ 232(SP)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 64(SP),AX
+	MULQ 240(SP)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 64(SP),AX
+	MULQ 248(SP)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ ·REDMASK51(SB),DX
+	SHLQ $13,CX:SI
+	ANDQ DX,SI
+	SHLQ $13,R9:R8
+	ANDQ DX,R8
+	ADDQ CX,R8
+	SHLQ $13,R11:R10
+	ANDQ DX,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ DX,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ DX,R14
+	ADDQ R13,R14
+	IMUL3Q $19,R15,CX
+	ADDQ CX,SI
+	MOVQ SI,CX
+	SHRQ $51,CX
+	ADDQ R8,CX
+	MOVQ CX,R8
+	SHRQ $51,CX
+	ANDQ DX,SI
+	ADDQ R10,CX
+	MOVQ CX,R9
+	SHRQ $51,CX
+	ANDQ DX,R8
+	ADDQ R12,CX
+	MOVQ CX,AX
+	SHRQ $51,CX
+	ANDQ DX,R9
+	ADDQ R14,CX
+	MOVQ CX,R10
+	SHRQ $51,CX
+	ANDQ DX,AX
+	IMUL3Q $19,CX,CX
+	ADDQ CX,SI
+	ANDQ DX,R10
+	MOVQ SI,80(DI)
+	MOVQ R8,88(DI)
+	MOVQ R9,96(DI)
+	MOVQ AX,104(DI)
+	MOVQ R10,112(DI)
+	MOVQ 0(SP),R11
+	MOVQ 8(SP),R12
+	MOVQ 16(SP),R13
+	MOVQ 24(SP),R14
+	MOVQ 32(SP),R15
+	MOVQ 40(SP),BX
+	MOVQ 48(SP),BP
+	MOVQ R11,SP
+	MOVQ DI,AX
+	MOVQ SI,DX
+	RET
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/mont25519_amd64.go b/vendor/github.com/keybase/go-crypto/curve25519/mont25519_amd64.go
new file mode 100644
index 000000000..5822bd533
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/mont25519_amd64.go
@@ -0,0 +1,240 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// +build amd64,!gccgo,!appengine
+
+package curve25519
+
+// These functions are implemented in the .s files. The names of the functions
+// in the rest of the file are also taken from the SUPERCOP sources to help
+// people following along.
+
+//go:noescape
+
+func cswap(inout *[5]uint64, v uint64)
+
+//go:noescape
+
+func ladderstep(inout *[5][5]uint64)
+
+//go:noescape
+
+func freeze(inout *[5]uint64)
+
+//go:noescape
+
+func mul(dest, a, b *[5]uint64)
+
+//go:noescape
+
+func square(out, in *[5]uint64)
+
+// mladder uses a Montgomery ladder to calculate (xr/zr) *= s.
+func mladder(xr, zr *[5]uint64, s *[32]byte) {
+	var work [5][5]uint64
+
+	work[0] = *xr
+	setint(&work[1], 1)
+	setint(&work[2], 0)
+	work[3] = *xr
+	setint(&work[4], 1)
+
+	j := uint(6)
+	var prevbit byte
+
+	for i := 31; i >= 0; i-- {
+		for j < 8 {
+			bit := ((*s)[i] >> j) & 1
+			swap := bit ^ prevbit
+			prevbit = bit
+			cswap(&work[1], uint64(swap))
+			ladderstep(&work)
+			j--
+		}
+		j = 7
+	}
+
+	*xr = work[1]
+	*zr = work[2]
+}
+
+func scalarMult(out, in, base *[32]byte) {
+	var e [32]byte
+	copy(e[:], (*in)[:])
+	e[0] &= 248
+	e[31] &= 127
+	e[31] |= 64
+
+	var t, z [5]uint64
+	unpack(&t, base)
+	mladder(&t, &z, &e)
+	invert(&z, &z)
+	mul(&t, &t, &z)
+	pack(out, &t)
+}
+
+func setint(r *[5]uint64, v uint64) {
+	r[0] = v
+	r[1] = 0
+	r[2] = 0
+	r[3] = 0
+	r[4] = 0
+}
+
+// unpack sets r = x where r consists of 5, 51-bit limbs in little-endian
+// order.
+func unpack(r *[5]uint64, x *[32]byte) {
+	r[0] = uint64(x[0]) |
+		uint64(x[1])<<8 |
+		uint64(x[2])<<16 |
+		uint64(x[3])<<24 |
+		uint64(x[4])<<32 |
+		uint64(x[5])<<40 |
+		uint64(x[6]&7)<<48
+
+	r[1] = uint64(x[6])>>3 |
+		uint64(x[7])<<5 |
+		uint64(x[8])<<13 |
+		uint64(x[9])<<21 |
+		uint64(x[10])<<29 |
+		uint64(x[11])<<37 |
+		uint64(x[12]&63)<<45
+
+	r[2] = uint64(x[12])>>6 |
+		uint64(x[13])<<2 |
+		uint64(x[14])<<10 |
+		uint64(x[15])<<18 |
+		uint64(x[16])<<26 |
+		uint64(x[17])<<34 |
+		uint64(x[18])<<42 |
+		uint64(x[19]&1)<<50
+
+	r[3] = uint64(x[19])>>1 |
+		uint64(x[20])<<7 |
+		uint64(x[21])<<15 |
+		uint64(x[22])<<23 |
+		uint64(x[23])<<31 |
+		uint64(x[24])<<39 |
+		uint64(x[25]&15)<<47
+
+	r[4] = uint64(x[25])>>4 |
+		uint64(x[26])<<4 |
+		uint64(x[27])<<12 |
+		uint64(x[28])<<20 |
+		uint64(x[29])<<28 |
+		uint64(x[30])<<36 |
+		uint64(x[31]&127)<<44
+}
+
+// pack sets out = x where out is the usual, little-endian form of the 5,
+// 51-bit limbs in x.
+func pack(out *[32]byte, x *[5]uint64) {
+	t := *x
+	freeze(&t)
+
+	out[0] = byte(t[0])
+	out[1] = byte(t[0] >> 8)
+	out[2] = byte(t[0] >> 16)
+	out[3] = byte(t[0] >> 24)
+	out[4] = byte(t[0] >> 32)
+	out[5] = byte(t[0] >> 40)
+	out[6] = byte(t[0] >> 48)
+
+	out[6] ^= byte(t[1]<<3) & 0xf8
+	out[7] = byte(t[1] >> 5)
+	out[8] = byte(t[1] >> 13)
+	out[9] = byte(t[1] >> 21)
+	out[10] = byte(t[1] >> 29)
+	out[11] = byte(t[1] >> 37)
+	out[12] = byte(t[1] >> 45)
+
+	out[12] ^= byte(t[2]<<6) & 0xc0
+	out[13] = byte(t[2] >> 2)
+	out[14] = byte(t[2] >> 10)
+	out[15] = byte(t[2] >> 18)
+	out[16] = byte(t[2] >> 26)
+	out[17] = byte(t[2] >> 34)
+	out[18] = byte(t[2] >> 42)
+	out[19] = byte(t[2] >> 50)
+
+	out[19] ^= byte(t[3]<<1) & 0xfe
+	out[20] = byte(t[3] >> 7)
+	out[21] = byte(t[3] >> 15)
+	out[22] = byte(t[3] >> 23)
+	out[23] = byte(t[3] >> 31)
+	out[24] = byte(t[3] >> 39)
+	out[25] = byte(t[3] >> 47)
+
+	out[25] ^= byte(t[4]<<4) & 0xf0
+	out[26] = byte(t[4] >> 4)
+	out[27] = byte(t[4] >> 12)
+	out[28] = byte(t[4] >> 20)
+	out[29] = byte(t[4] >> 28)
+	out[30] = byte(t[4] >> 36)
+	out[31] = byte(t[4] >> 44)
+}
+
+// invert calculates r = x^-1 mod p using Fermat's little theorem.
+func invert(r *[5]uint64, x *[5]uint64) {
+	var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t [5]uint64
+
+	square(&z2, x)        /* 2 */
+	square(&t, &z2)       /* 4 */
+	square(&t, &t)        /* 8 */
+	mul(&z9, &t, x)       /* 9 */
+	mul(&z11, &z9, &z2)   /* 11 */
+	square(&t, &z11)      /* 22 */
+	mul(&z2_5_0, &t, &z9) /* 2^5 - 2^0 = 31 */
+
+	square(&t, &z2_5_0)      /* 2^6 - 2^1 */
+	for i := 1; i < 5; i++ { /* 2^20 - 2^10 */
+		square(&t, &t)
+	}
+	mul(&z2_10_0, &t, &z2_5_0) /* 2^10 - 2^0 */
+
+	square(&t, &z2_10_0)      /* 2^11 - 2^1 */
+	for i := 1; i < 10; i++ { /* 2^20 - 2^10 */
+		square(&t, &t)
+	}
+	mul(&z2_20_0, &t, &z2_10_0) /* 2^20 - 2^0 */
+
+	square(&t, &z2_20_0)      /* 2^21 - 2^1 */
+	for i := 1; i < 20; i++ { /* 2^40 - 2^20 */
+		square(&t, &t)
+	}
+	mul(&t, &t, &z2_20_0) /* 2^40 - 2^0 */
+
+	square(&t, &t)            /* 2^41 - 2^1 */
+	for i := 1; i < 10; i++ { /* 2^50 - 2^10 */
+		square(&t, &t)
+	}
+	mul(&z2_50_0, &t, &z2_10_0) /* 2^50 - 2^0 */
+
+	square(&t, &z2_50_0)      /* 2^51 - 2^1 */
+	for i := 1; i < 50; i++ { /* 2^100 - 2^50 */
+		square(&t, &t)
+	}
+	mul(&z2_100_0, &t, &z2_50_0) /* 2^100 - 2^0 */
+
+	square(&t, &z2_100_0)      /* 2^101 - 2^1 */
+	for i := 1; i < 100; i++ { /* 2^200 - 2^100 */
+		square(&t, &t)
+	}
+	mul(&t, &t, &z2_100_0) /* 2^200 - 2^0 */
+
+	square(&t, &t)            /* 2^201 - 2^1 */
+	for i := 1; i < 50; i++ { /* 2^250 - 2^50 */
+		square(&t, &t)
+	}
+	mul(&t, &t, &z2_50_0) /* 2^250 - 2^0 */
+
+	square(&t, &t) /* 2^251 - 2^1 */
+	square(&t, &t) /* 2^252 - 2^2 */
+	square(&t, &t) /* 2^253 - 2^3 */
+
+	square(&t, &t) /* 2^254 - 2^4 */
+
+	square(&t, &t)   /* 2^255 - 2^5 */
+	mul(r, &t, &z11) /* 2^255 - 21 */
+}
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/mul_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/mul_amd64.s
new file mode 100644
index 000000000..e48d183ee
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/mul_amd64.s
@@ -0,0 +1,191 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+// func mul(dest, a, b *[5]uint64)
+TEXT ·mul(SB),0,$128-24
+	MOVQ dest+0(FP), DI
+	MOVQ a+8(FP), SI
+	MOVQ b+16(FP), DX
+
+	MOVQ SP,R11
+	MOVQ $31,CX
+	NOTQ CX
+	ANDQ CX,SP
+	ADDQ $32,SP
+
+	MOVQ R11,0(SP)
+	MOVQ R12,8(SP)
+	MOVQ R13,16(SP)
+	MOVQ R14,24(SP)
+	MOVQ R15,32(SP)
+	MOVQ BX,40(SP)
+	MOVQ BP,48(SP)
+	MOVQ DI,56(SP)
+	MOVQ DX,CX
+	MOVQ 24(SI),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,64(SP)
+	MULQ 16(CX)
+	MOVQ AX,R8
+	MOVQ DX,R9
+	MOVQ 32(SI),DX
+	IMUL3Q $19,DX,AX
+	MOVQ AX,72(SP)
+	MULQ 8(CX)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 0(SI),AX
+	MULQ 0(CX)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 0(SI),AX
+	MULQ 8(CX)
+	MOVQ AX,R10
+	MOVQ DX,R11
+	MOVQ 0(SI),AX
+	MULQ 16(CX)
+	MOVQ AX,R12
+	MOVQ DX,R13
+	MOVQ 0(SI),AX
+	MULQ 24(CX)
+	MOVQ AX,R14
+	MOVQ DX,R15
+	MOVQ 0(SI),AX
+	MULQ 32(CX)
+	MOVQ AX,BX
+	MOVQ DX,BP
+	MOVQ 8(SI),AX
+	MULQ 0(CX)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 8(SI),AX
+	MULQ 8(CX)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 8(SI),AX
+	MULQ 16(CX)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 8(SI),AX
+	MULQ 24(CX)
+	ADDQ AX,BX
+	ADCQ DX,BP
+	MOVQ 8(SI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 32(CX)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 16(SI),AX
+	MULQ 0(CX)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 16(SI),AX
+	MULQ 8(CX)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 16(SI),AX
+	MULQ 16(CX)
+	ADDQ AX,BX
+	ADCQ DX,BP
+	MOVQ 16(SI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 24(CX)
+	ADDQ AX,R8
+	ADCQ DX,R9
+	MOVQ 16(SI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 32(CX)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 24(SI),AX
+	MULQ 0(CX)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ 24(SI),AX
+	MULQ 8(CX)
+	ADDQ AX,BX
+	ADCQ DX,BP
+	MOVQ 64(SP),AX
+	MULQ 24(CX)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 64(SP),AX
+	MULQ 32(CX)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 32(SI),AX
+	MULQ 0(CX)
+	ADDQ AX,BX
+	ADCQ DX,BP
+	MOVQ 72(SP),AX
+	MULQ 16(CX)
+	ADDQ AX,R10
+	ADCQ DX,R11
+	MOVQ 72(SP),AX
+	MULQ 24(CX)
+	ADDQ AX,R12
+	ADCQ DX,R13
+	MOVQ 72(SP),AX
+	MULQ 32(CX)
+	ADDQ AX,R14
+	ADCQ DX,R15
+	MOVQ ·REDMASK51(SB),SI
+	SHLQ $13,R9:R8
+	ANDQ SI,R8
+	SHLQ $13,R11:R10
+	ANDQ SI,R10
+	ADDQ R9,R10
+	SHLQ $13,R13:R12
+	ANDQ SI,R12
+	ADDQ R11,R12
+	SHLQ $13,R15:R14
+	ANDQ SI,R14
+	ADDQ R13,R14
+	SHLQ $13,BP:BX
+	ANDQ SI,BX
+	ADDQ R15,BX
+	IMUL3Q $19,BP,DX
+	ADDQ DX,R8
+	MOVQ R8,DX
+	SHRQ $51,DX
+	ADDQ R10,DX
+	MOVQ DX,CX
+	SHRQ $51,DX
+	ANDQ SI,R8
+	ADDQ R12,DX
+	MOVQ DX,R9
+	SHRQ $51,DX
+	ANDQ SI,CX
+	ADDQ R14,DX
+	MOVQ DX,AX
+	SHRQ $51,DX
+	ANDQ SI,R9
+	ADDQ BX,DX
+	MOVQ DX,R10
+	SHRQ $51,DX
+	ANDQ SI,AX
+	IMUL3Q $19,DX,DX
+	ADDQ DX,R8
+	ANDQ SI,R10
+	MOVQ R8,0(DI)
+	MOVQ CX,8(DI)
+	MOVQ R9,16(DI)
+	MOVQ AX,24(DI)
+	MOVQ R10,32(DI)
+	MOVQ 0(SP),R11
+	MOVQ 8(SP),R12
+	MOVQ 16(SP),R13
+	MOVQ 24(SP),R14
+	MOVQ 32(SP),R15
+	MOVQ 40(SP),BX
+	MOVQ 48(SP),BP
+	MOVQ R11,SP
+	MOVQ DI,AX
+	MOVQ SI,DX
+	RET
diff --git a/vendor/github.com/keybase/go-crypto/curve25519/square_amd64.s b/vendor/github.com/keybase/go-crypto/curve25519/square_amd64.s
new file mode 100644
index 000000000..78d1a50dd
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/curve25519/square_amd64.s
@@ -0,0 +1,153 @@
+// Copyright 2012 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This code was translated into a form compatible with 6a from the public
+// domain sources in SUPERCOP: http://bench.cr.yp.to/supercop.html
+
+// +build amd64,!gccgo,!appengine
+
+// func square(out, in *[5]uint64)
+TEXT ·square(SB),7,$96-16
+	MOVQ out+0(FP), DI
+	MOVQ in+8(FP), SI
+
+	MOVQ SP,R11
+	MOVQ $31,CX
+	NOTQ CX
+	ANDQ CX,SP
+	ADDQ $32, SP
+
+	MOVQ R11,0(SP)
+	MOVQ R12,8(SP)
+	MOVQ R13,16(SP)
+	MOVQ R14,24(SP)
+	MOVQ R15,32(SP)
+	MOVQ BX,40(SP)
+	MOVQ BP,48(SP)
+	MOVQ 0(SI),AX
+	MULQ 0(SI)
+	MOVQ AX,CX
+	MOVQ DX,R8
+	MOVQ 0(SI),AX
+	SHLQ $1,AX
+	MULQ 8(SI)
+	MOVQ AX,R9
+	MOVQ DX,R10
+	MOVQ 0(SI),AX
+	SHLQ $1,AX
+	MULQ 16(SI)
+	MOVQ AX,R11
+	MOVQ DX,R12
+	MOVQ 0(SI),AX
+	SHLQ $1,AX
+	MULQ 24(SI)
+	MOVQ AX,R13
+	MOVQ DX,R14
+	MOVQ 0(SI),AX
+	SHLQ $1,AX
+	MULQ 32(SI)
+	MOVQ AX,R15
+	MOVQ DX,BX
+	MOVQ 8(SI),AX
+	MULQ 8(SI)
+	ADDQ AX,R11
+	ADCQ DX,R12
+	MOVQ 8(SI),AX
+	SHLQ $1,AX
+	MULQ 16(SI)
+	ADDQ AX,R13
+	ADCQ DX,R14
+	MOVQ 8(SI),AX
+	SHLQ $1,AX
+	MULQ 24(SI)
+	ADDQ AX,R15
+	ADCQ DX,BX
+	MOVQ 8(SI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 32(SI)
+	ADDQ AX,CX
+	ADCQ DX,R8
+	MOVQ 16(SI),AX
+	MULQ 16(SI)
+	ADDQ AX,R15
+	ADCQ DX,BX
+	MOVQ 16(SI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 24(SI)
+	ADDQ AX,CX
+	ADCQ DX,R8
+	MOVQ 16(SI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 32(SI)
+	ADDQ AX,R9
+	ADCQ DX,R10
+	MOVQ 24(SI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 24(SI)
+	ADDQ AX,R9
+	ADCQ DX,R10
+	MOVQ 24(SI),DX
+	IMUL3Q $38,DX,AX
+	MULQ 32(SI)
+	ADDQ AX,R11
+	ADCQ DX,R12
+	MOVQ 32(SI),DX
+	IMUL3Q $19,DX,AX
+	MULQ 32(SI)
+	ADDQ AX,R13
+	ADCQ DX,R14
+	MOVQ ·REDMASK51(SB),SI
+	SHLQ $13,R8:CX
+	ANDQ SI,CX
+	SHLQ $13,R10:R9
+	ANDQ SI,R9
+	ADDQ R8,R9
+	SHLQ $13,R12:R11
+	ANDQ SI,R11
+	ADDQ R10,R11
+	SHLQ $13,R14:R13
+	ANDQ SI,R13
+	ADDQ R12,R13
+	SHLQ $13,BX:R15
+	ANDQ SI,R15
+	ADDQ R14,R15
+	IMUL3Q $19,BX,DX
+	ADDQ DX,CX
+	MOVQ CX,DX
+	SHRQ $51,DX
+	ADDQ R9,DX
+	ANDQ SI,CX
+	MOVQ DX,R8
+	SHRQ $51,DX
+	ADDQ R11,DX
+	ANDQ SI,R8
+	MOVQ DX,R9
+	SHRQ $51,DX
+	ADDQ R13,DX
+	ANDQ SI,R9
+	MOVQ DX,AX
+	SHRQ $51,DX
+	ADDQ R15,DX
+	ANDQ SI,AX
+	MOVQ DX,R10
+	SHRQ $51,DX
+	IMUL3Q $19,DX,DX
+	ADDQ DX,CX
+	ANDQ SI,R10
+	MOVQ CX,0(DI)
+	MOVQ R8,8(DI)
+	MOVQ R9,16(DI)
+	MOVQ AX,24(DI)
+	MOVQ R10,32(DI)
+	MOVQ 0(SP),R11
+	MOVQ 8(SP),R12
+	MOVQ 16(SP),R13
+	MOVQ 24(SP),R14
+	MOVQ 32(SP),R15
+	MOVQ 40(SP),BX
+	MOVQ 48(SP),BP
+	MOVQ R11,SP
+	MOVQ DI,AX
+	MOVQ SI,DX
+	RET
diff --git a/vendor/github.com/keybase/go-crypto/ed25519/ed25519.go b/vendor/github.com/keybase/go-crypto/ed25519/ed25519.go
new file mode 100644
index 000000000..9c7a88807
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/ed25519/ed25519.go
@@ -0,0 +1,181 @@
+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package ed25519 implements the Ed25519 signature algorithm. See
+// http://ed25519.cr.yp.to/.
+//
+// These functions are also compatible with the “Ed25519” function defined in
+// https://tools.ietf.org/html/draft-irtf-cfrg-eddsa-05.
+package ed25519
+
+// This code is a port of the public domain, “ref10” implementation of ed25519
+// from SUPERCOP.
+
+import (
+	"crypto"
+	cryptorand "crypto/rand"
+	"crypto/sha512"
+	"crypto/subtle"
+	"errors"
+	"io"
+	"strconv"
+
+	"github.com/keybase/go-crypto/ed25519/internal/edwards25519"
+)
+
+const (
+	// PublicKeySize is the size, in bytes, of public keys as used in this package.
+	PublicKeySize = 32
+	// PrivateKeySize is the size, in bytes, of private keys as used in this package.
+	PrivateKeySize = 64
+	// SignatureSize is the size, in bytes, of signatures generated and verified by this package.
+	SignatureSize = 64
+)
+
+// PublicKey is the type of Ed25519 public keys.
+type PublicKey []byte
+
+// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer.
+type PrivateKey []byte
+
+// Public returns the PublicKey corresponding to priv.
+func (priv PrivateKey) Public() crypto.PublicKey {
+	publicKey := make([]byte, PublicKeySize)
+	copy(publicKey, priv[32:])
+	return PublicKey(publicKey)
+}
+
+// Sign signs the given message with priv.
+// Ed25519 performs two passes over messages to be signed and therefore cannot
+// handle pre-hashed messages. Thus opts.HashFunc() must return zero to
+// indicate the message hasn't been hashed. This can be achieved by passing
+// crypto.Hash(0) as the value for opts.
+func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) {
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, errors.New("ed25519: cannot sign hashed message")
+	}
+
+	return Sign(priv, message), nil
+}
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (publicKey PublicKey, privateKey PrivateKey, err error) {
+	if rand == nil {
+		rand = cryptorand.Reader
+	}
+
+	privateKey = make([]byte, PrivateKeySize)
+	publicKey = make([]byte, PublicKeySize)
+	_, err = io.ReadFull(rand, privateKey[:32])
+	if err != nil {
+		return nil, nil, err
+	}
+
+	digest := sha512.Sum512(privateKey[:32])
+	digest[0] &= 248
+	digest[31] &= 127
+	digest[31] |= 64
+
+	var A edwards25519.ExtendedGroupElement
+	var hBytes [32]byte
+	copy(hBytes[:], digest[:])
+	edwards25519.GeScalarMultBase(&A, &hBytes)
+	var publicKeyBytes [32]byte
+	A.ToBytes(&publicKeyBytes)
+
+	copy(privateKey[32:], publicKeyBytes[:])
+	copy(publicKey, publicKeyBytes[:])
+
+	return publicKey, privateKey, nil
+}
+
+// Sign signs the message with privateKey and returns a signature. It will
+// panic if len(privateKey) is not PrivateKeySize.
+func Sign(privateKey PrivateKey, message []byte) []byte {
+	if l := len(privateKey); l != PrivateKeySize {
+		panic("ed25519: bad private key length: " + strconv.Itoa(l))
+	}
+
+	h := sha512.New()
+	h.Write(privateKey[:32])
+
+	var digest1, messageDigest, hramDigest [64]byte
+	var expandedSecretKey [32]byte
+	h.Sum(digest1[:0])
+	copy(expandedSecretKey[:], digest1[:])
+	expandedSecretKey[0] &= 248
+	expandedSecretKey[31] &= 63
+	expandedSecretKey[31] |= 64
+
+	h.Reset()
+	h.Write(digest1[32:])
+	h.Write(message)
+	h.Sum(messageDigest[:0])
+
+	var messageDigestReduced [32]byte
+	edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
+	var R edwards25519.ExtendedGroupElement
+	edwards25519.GeScalarMultBase(&R, &messageDigestReduced)
+
+	var encodedR [32]byte
+	R.ToBytes(&encodedR)
+
+	h.Reset()
+	h.Write(encodedR[:])
+	h.Write(privateKey[32:])
+	h.Write(message)
+	h.Sum(hramDigest[:0])
+	var hramDigestReduced [32]byte
+	edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
+
+	var s [32]byte
+	edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced)
+
+	signature := make([]byte, SignatureSize)
+	copy(signature[:], encodedR[:])
+	copy(signature[32:], s[:])
+
+	return signature
+}
+
+// Verify reports whether sig is a valid signature of message by publicKey. It
+// will panic if len(publicKey) is not PublicKeySize.
+func Verify(publicKey PublicKey, message, sig []byte) bool {
+	if l := len(publicKey); l != PublicKeySize {
+		panic("ed25519: bad public key length: " + strconv.Itoa(l))
+	}
+
+	if len(sig) != SignatureSize || sig[63]&224 != 0 {
+		return false
+	}
+
+	var A edwards25519.ExtendedGroupElement
+	var publicKeyBytes [32]byte
+	copy(publicKeyBytes[:], publicKey)
+	if !A.FromBytes(&publicKeyBytes) {
+		return false
+	}
+	edwards25519.FeNeg(&A.X, &A.X)
+	edwards25519.FeNeg(&A.T, &A.T)
+
+	h := sha512.New()
+	h.Write(sig[:32])
+	h.Write(publicKey[:])
+	h.Write(message)
+	var digest [64]byte
+	h.Sum(digest[:0])
+
+	var hReduced [32]byte
+	edwards25519.ScReduce(&hReduced, &digest)
+
+	var R edwards25519.ProjectiveGroupElement
+	var b [32]byte
+	copy(b[:], sig[32:])
+	edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &b)
+
+	var checkR [32]byte
+	R.ToBytes(&checkR)
+	return subtle.ConstantTimeCompare(sig[:32], checkR[:]) == 1
+}
diff --git a/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/const.go b/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/const.go
new file mode 100644
index 000000000..e39f086c1
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/const.go
@@ -0,0 +1,1422 @@
+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package edwards25519
+
+// These values are from the public domain, “ref10” implementation of ed25519
+// from SUPERCOP.
+
+// d is a constant in the Edwards curve equation.
+var d = FieldElement{
+	-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116,
+}
+
+// d2 is 2*d.
+var d2 = FieldElement{
+	-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199,
+}
+
+// SqrtM1 is the square-root of -1 in the field.
+var SqrtM1 = FieldElement{
+	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
+}
+
+// A is a constant in the Montgomery-form of curve25519.
+var A = FieldElement{
+	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+}
+
+// bi contains precomputed multiples of the base-point. See the Ed25519 paper
+// for a discussion about how these values are used.
+var bi = [8]PreComputedGroupElement{
+	{
+		FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
+		FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
+		FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
+	},
+	{
+		FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
+		FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
+		FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
+	},
+	{
+		FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
+		FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
+		FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
+	},
+	{
+		FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
+		FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
+		FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
+	},
+	{
+		FieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877},
+		FieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951},
+		FieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784},
+	},
+	{
+		FieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436},
+		FieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918},
+		FieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877},
+	},
+	{
+		FieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800},
+		FieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305},
+		FieldElement{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300},
+	},
+	{
+		FieldElement{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876},
+		FieldElement{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619},
+		FieldElement{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683},
+	},
+}
+
+// base contains precomputed multiples of the base-point. See the Ed25519 paper
+// for a discussion about how these values are used.
+var base = [32][8]PreComputedGroupElement{
+	{
+		{
+			FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
+			FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
+			FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
+		},
+		{
+			FieldElement{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303},
+			FieldElement{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081},
+			FieldElement{26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697},
+		},
+		{
+			FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
+			FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
+			FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
+		},
+		{
+			FieldElement{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540},
+			FieldElement{23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397},
+			FieldElement{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325},
+		},
+		{
+			FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
+			FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
+			FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
+		},
+		{
+			FieldElement{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777},
+			FieldElement{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737},
+			FieldElement{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652},
+		},
+		{
+			FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
+			FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
+			FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
+		},
+		{
+			FieldElement{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726},
+			FieldElement{-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955},
+			FieldElement{27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425},
+		},
+	},
+	{
+		{
+			FieldElement{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171},
+			FieldElement{27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510},
+			FieldElement{17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660},
+		},
+		{
+			FieldElement{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639},
+			FieldElement{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963},
+			FieldElement{5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950},
+		},
+		{
+			FieldElement{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568},
+			FieldElement{12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335},
+			FieldElement{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628},
+		},
+		{
+			FieldElement{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007},
+			FieldElement{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772},
+			FieldElement{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653},
+		},
+		{
+			FieldElement{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567},
+			FieldElement{13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686},
+			FieldElement{21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372},
+		},
+		{
+			FieldElement{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887},
+			FieldElement{-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954},
+			FieldElement{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953},
+		},
+		{
+			FieldElement{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833},
+			FieldElement{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532},
+			FieldElement{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876},
+		},
+		{
+			FieldElement{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268},
+			FieldElement{33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214},
+			FieldElement{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038},
+		},
+	},
+	{
+		{
+			FieldElement{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800},
+			FieldElement{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645},
+			FieldElement{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664},
+		},
+		{
+			FieldElement{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933},
+			FieldElement{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182},
+			FieldElement{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222},
+		},
+		{
+			FieldElement{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991},
+			FieldElement{20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880},
+			FieldElement{9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092},
+		},
+		{
+			FieldElement{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295},
+			FieldElement{19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788},
+			FieldElement{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553},
+		},
+		{
+			FieldElement{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026},
+			FieldElement{11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347},
+			FieldElement{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033},
+		},
+		{
+			FieldElement{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395},
+			FieldElement{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278},
+			FieldElement{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890},
+		},
+		{
+			FieldElement{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995},
+			FieldElement{-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596},
+			FieldElement{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891},
+		},
+		{
+			FieldElement{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060},
+			FieldElement{11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608},
+			FieldElement{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606},
+		},
+	},
+	{
+		{
+			FieldElement{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389},
+			FieldElement{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016},
+			FieldElement{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341},
+		},
+		{
+			FieldElement{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505},
+			FieldElement{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553},
+			FieldElement{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655},
+		},
+		{
+			FieldElement{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220},
+			FieldElement{12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631},
+			FieldElement{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099},
+		},
+		{
+			FieldElement{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556},
+			FieldElement{14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749},
+			FieldElement{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930},
+		},
+		{
+			FieldElement{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391},
+			FieldElement{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253},
+			FieldElement{20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066},
+		},
+		{
+			FieldElement{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958},
+			FieldElement{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082},
+			FieldElement{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383},
+		},
+		{
+			FieldElement{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521},
+			FieldElement{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807},
+			FieldElement{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948},
+		},
+		{
+			FieldElement{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134},
+			FieldElement{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455},
+			FieldElement{27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629},
+		},
+	},
+	{
+		{
+			FieldElement{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069},
+			FieldElement{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746},
+			FieldElement{24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919},
+		},
+		{
+			FieldElement{11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837},
+			FieldElement{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906},
+			FieldElement{-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771},
+		},
+		{
+			FieldElement{-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817},
+			FieldElement{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098},
+			FieldElement{10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409},
+		},
+		{
+			FieldElement{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504},
+			FieldElement{-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727},
+			FieldElement{28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420},
+		},
+		{
+			FieldElement{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003},
+			FieldElement{-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605},
+			FieldElement{-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384},
+		},
+		{
+			FieldElement{-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701},
+			FieldElement{-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683},
+			FieldElement{29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708},
+		},
+		{
+			FieldElement{-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563},
+			FieldElement{-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260},
+			FieldElement{-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387},
+		},
+		{
+			FieldElement{-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672},
+			FieldElement{23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686},
+			FieldElement{-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665},
+		},
+	},
+	{
+		{
+			FieldElement{11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182},
+			FieldElement{-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277},
+			FieldElement{14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628},
+		},
+		{
+			FieldElement{-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474},
+			FieldElement{-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539},
+			FieldElement{-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822},
+		},
+		{
+			FieldElement{-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970},
+			FieldElement{19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756},
+			FieldElement{-24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508},
+		},
+		{
+			FieldElement{-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683},
+			FieldElement{-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655},
+			FieldElement{-20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158},
+		},
+		{
+			FieldElement{-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125},
+			FieldElement{-15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839},
+			FieldElement{-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664},
+		},
+		{
+			FieldElement{27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294},
+			FieldElement{-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899},
+			FieldElement{-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070},
+		},
+		{
+			FieldElement{3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294},
+			FieldElement{-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949},
+			FieldElement{-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083},
+		},
+		{
+			FieldElement{31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420},
+			FieldElement{-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940},
+			FieldElement{29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396},
+		},
+	},
+	{
+		{
+			FieldElement{-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567},
+			FieldElement{20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127},
+			FieldElement{-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294},
+		},
+		{
+			FieldElement{-12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887},
+			FieldElement{22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964},
+			FieldElement{16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195},
+		},
+		{
+			FieldElement{9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244},
+			FieldElement{24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999},
+			FieldElement{-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762},
+		},
+		{
+			FieldElement{-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274},
+			FieldElement{-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236},
+			FieldElement{-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605},
+		},
+		{
+			FieldElement{-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761},
+			FieldElement{-22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884},
+			FieldElement{-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482},
+		},
+		{
+			FieldElement{-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638},
+			FieldElement{-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490},
+			FieldElement{-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170},
+		},
+		{
+			FieldElement{5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736},
+			FieldElement{10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124},
+			FieldElement{-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392},
+		},
+		{
+			FieldElement{8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029},
+			FieldElement{6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048},
+			FieldElement{28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958},
+		},
+	},
+	{
+		{
+			FieldElement{24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593},
+			FieldElement{26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071},
+			FieldElement{-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692},
+		},
+		{
+			FieldElement{11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687},
+			FieldElement{-160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441},
+			FieldElement{-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001},
+		},
+		{
+			FieldElement{-938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460},
+			FieldElement{-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007},
+			FieldElement{-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762},
+		},
+		{
+			FieldElement{15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005},
+			FieldElement{-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674},
+			FieldElement{4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035},
+		},
+		{
+			FieldElement{7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590},
+			FieldElement{-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957},
+			FieldElement{-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812},
+		},
+		{
+			FieldElement{33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740},
+			FieldElement{-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122},
+			FieldElement{-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158},
+		},
+		{
+			FieldElement{8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885},
+			FieldElement{26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140},
+			FieldElement{19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857},
+		},
+		{
+			FieldElement{801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155},
+			FieldElement{19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260},
+			FieldElement{19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483},
+		},
+	},
+	{
+		{
+			FieldElement{-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677},
+			FieldElement{32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815},
+			FieldElement{22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751},
+		},
+		{
+			FieldElement{-16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203},
+			FieldElement{-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208},
+			FieldElement{1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230},
+		},
+		{
+			FieldElement{16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850},
+			FieldElement{-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389},
+			FieldElement{-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968},
+		},
+		{
+			FieldElement{-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689},
+			FieldElement{14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880},
+			FieldElement{5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304},
+		},
+		{
+			FieldElement{30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632},
+			FieldElement{-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412},
+			FieldElement{20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566},
+		},
+		{
+			FieldElement{-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038},
+			FieldElement{-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232},
+			FieldElement{-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943},
+		},
+		{
+			FieldElement{17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856},
+			FieldElement{23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738},
+			FieldElement{15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971},
+		},
+		{
+			FieldElement{-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718},
+			FieldElement{-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697},
+			FieldElement{-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883},
+		},
+	},
+	{
+		{
+			FieldElement{5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912},
+			FieldElement{-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358},
+			FieldElement{3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849},
+		},
+		{
+			FieldElement{29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307},
+			FieldElement{-14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977},
+			FieldElement{-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335},
+		},
+		{
+			FieldElement{-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644},
+			FieldElement{-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616},
+			FieldElement{-27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735},
+		},
+		{
+			FieldElement{-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099},
+			FieldElement{29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341},
+			FieldElement{-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336},
+		},
+		{
+			FieldElement{-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646},
+			FieldElement{31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425},
+			FieldElement{-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388},
+		},
+		{
+			FieldElement{-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743},
+			FieldElement{-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822},
+			FieldElement{-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462},
+		},
+		{
+			FieldElement{18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985},
+			FieldElement{9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702},
+			FieldElement{-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797},
+		},
+		{
+			FieldElement{21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293},
+			FieldElement{27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100},
+			FieldElement{19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688},
+		},
+	},
+	{
+		{
+			FieldElement{12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186},
+			FieldElement{2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610},
+			FieldElement{-2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707},
+		},
+		{
+			FieldElement{7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220},
+			FieldElement{915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025},
+			FieldElement{32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044},
+		},
+		{
+			FieldElement{32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992},
+			FieldElement{-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027},
+			FieldElement{21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197},
+		},
+		{
+			FieldElement{8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901},
+			FieldElement{31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952},
+			FieldElement{19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878},
+		},
+		{
+			FieldElement{-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390},
+			FieldElement{32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730},
+			FieldElement{2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730},
+		},
+		{
+			FieldElement{-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180},
+			FieldElement{-30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272},
+			FieldElement{-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715},
+		},
+		{
+			FieldElement{-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970},
+			FieldElement{-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772},
+			FieldElement{-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865},
+		},
+		{
+			FieldElement{15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750},
+			FieldElement{20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373},
+			FieldElement{32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348},
+		},
+	},
+	{
+		{
+			FieldElement{9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144},
+			FieldElement{-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195},
+			FieldElement{5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086},
+		},
+		{
+			FieldElement{-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684},
+			FieldElement{-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518},
+			FieldElement{-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233},
+		},
+		{
+			FieldElement{-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793},
+			FieldElement{-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794},
+			FieldElement{580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435},
+		},
+		{
+			FieldElement{23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921},
+			FieldElement{13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518},
+			FieldElement{2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563},
+		},
+		{
+			FieldElement{14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278},
+			FieldElement{-27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024},
+			FieldElement{4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030},
+		},
+		{
+			FieldElement{10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783},
+			FieldElement{27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717},
+			FieldElement{6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844},
+		},
+		{
+			FieldElement{14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333},
+			FieldElement{16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048},
+			FieldElement{22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760},
+		},
+		{
+			FieldElement{-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760},
+			FieldElement{-15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757},
+			FieldElement{-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112},
+		},
+	},
+	{
+		{
+			FieldElement{-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468},
+			FieldElement{3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184},
+			FieldElement{10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289},
+		},
+		{
+			FieldElement{15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066},
+			FieldElement{24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882},
+			FieldElement{13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226},
+		},
+		{
+			FieldElement{16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101},
+			FieldElement{29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279},
+			FieldElement{-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811},
+		},
+		{
+			FieldElement{27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709},
+			FieldElement{20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714},
+			FieldElement{-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121},
+		},
+		{
+			FieldElement{9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464},
+			FieldElement{12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847},
+			FieldElement{13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400},
+		},
+		{
+			FieldElement{4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414},
+			FieldElement{-15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158},
+			FieldElement{17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045},
+		},
+		{
+			FieldElement{-461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415},
+			FieldElement{-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459},
+			FieldElement{-31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079},
+		},
+		{
+			FieldElement{21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412},
+			FieldElement{-20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743},
+			FieldElement{-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836},
+		},
+	},
+	{
+		{
+			FieldElement{12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022},
+			FieldElement{18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429},
+			FieldElement{-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065},
+		},
+		{
+			FieldElement{30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861},
+			FieldElement{10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000},
+			FieldElement{-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101},
+		},
+		{
+			FieldElement{32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815},
+			FieldElement{29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642},
+			FieldElement{10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966},
+		},
+		{
+			FieldElement{25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574},
+			FieldElement{-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742},
+			FieldElement{-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689},
+		},
+		{
+			FieldElement{12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020},
+			FieldElement{-10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772},
+			FieldElement{3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982},
+		},
+		{
+			FieldElement{-14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953},
+			FieldElement{-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218},
+			FieldElement{-17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265},
+		},
+		{
+			FieldElement{29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073},
+			FieldElement{-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325},
+			FieldElement{-11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798},
+		},
+		{
+			FieldElement{-4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870},
+			FieldElement{-7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863},
+			FieldElement{-13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927},
+		},
+	},
+	{
+		{
+			FieldElement{-2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267},
+			FieldElement{-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663},
+			FieldElement{22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862},
+		},
+		{
+			FieldElement{-25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673},
+			FieldElement{15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943},
+			FieldElement{15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020},
+		},
+		{
+			FieldElement{-4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238},
+			FieldElement{11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064},
+			FieldElement{14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795},
+		},
+		{
+			FieldElement{15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052},
+			FieldElement{-10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904},
+			FieldElement{29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531},
+		},
+		{
+			FieldElement{-13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979},
+			FieldElement{-5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841},
+			FieldElement{10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431},
+		},
+		{
+			FieldElement{10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324},
+			FieldElement{-31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940},
+			FieldElement{10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320},
+		},
+		{
+			FieldElement{-15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184},
+			FieldElement{14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114},
+			FieldElement{30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878},
+		},
+		{
+			FieldElement{12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784},
+			FieldElement{-2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091},
+			FieldElement{-16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585},
+		},
+	},
+	{
+		{
+			FieldElement{-8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208},
+			FieldElement{10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864},
+			FieldElement{17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661},
+		},
+		{
+			FieldElement{7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233},
+			FieldElement{26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212},
+			FieldElement{-12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525},
+		},
+		{
+			FieldElement{-24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068},
+			FieldElement{9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397},
+			FieldElement{-8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988},
+		},
+		{
+			FieldElement{5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889},
+			FieldElement{32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038},
+			FieldElement{14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697},
+		},
+		{
+			FieldElement{20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875},
+			FieldElement{-25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905},
+			FieldElement{-25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656},
+		},
+		{
+			FieldElement{11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818},
+			FieldElement{27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714},
+			FieldElement{10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203},
+		},
+		{
+			FieldElement{20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931},
+			FieldElement{-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024},
+			FieldElement{-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084},
+		},
+		{
+			FieldElement{-1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204},
+			FieldElement{20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817},
+			FieldElement{27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667},
+		},
+	},
+	{
+		{
+			FieldElement{11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504},
+			FieldElement{-12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768},
+			FieldElement{-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255},
+		},
+		{
+			FieldElement{6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790},
+			FieldElement{1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438},
+			FieldElement{-22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333},
+		},
+		{
+			FieldElement{17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971},
+			FieldElement{31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905},
+			FieldElement{29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409},
+		},
+		{
+			FieldElement{12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409},
+			FieldElement{6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499},
+			FieldElement{-8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363},
+		},
+		{
+			FieldElement{28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664},
+			FieldElement{-11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324},
+			FieldElement{-21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940},
+		},
+		{
+			FieldElement{13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990},
+			FieldElement{-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914},
+			FieldElement{-25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290},
+		},
+		{
+			FieldElement{24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257},
+			FieldElement{-6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433},
+			FieldElement{-16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236},
+		},
+		{
+			FieldElement{-12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045},
+			FieldElement{11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093},
+			FieldElement{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347},
+		},
+	},
+	{
+		{
+			FieldElement{-28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191},
+			FieldElement{-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507},
+			FieldElement{-12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906},
+		},
+		{
+			FieldElement{3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018},
+			FieldElement{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109},
+			FieldElement{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926},
+		},
+		{
+			FieldElement{-24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528},
+			FieldElement{8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625},
+			FieldElement{-32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286},
+		},
+		{
+			FieldElement{2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033},
+			FieldElement{27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866},
+			FieldElement{21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896},
+		},
+		{
+			FieldElement{30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075},
+			FieldElement{26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347},
+			FieldElement{-22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437},
+		},
+		{
+			FieldElement{-5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165},
+			FieldElement{-18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588},
+			FieldElement{-32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193},
+		},
+		{
+			FieldElement{-19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017},
+			FieldElement{-28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883},
+			FieldElement{21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961},
+		},
+		{
+			FieldElement{8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043},
+			FieldElement{29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663},
+			FieldElement{-20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362},
+		},
+	},
+	{
+		{
+			FieldElement{-33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860},
+			FieldElement{2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466},
+			FieldElement{-24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063},
+		},
+		{
+			FieldElement{-26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997},
+			FieldElement{-1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295},
+			FieldElement{-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369},
+		},
+		{
+			FieldElement{9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385},
+			FieldElement{18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109},
+			FieldElement{2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906},
+		},
+		{
+			FieldElement{4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424},
+			FieldElement{-19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185},
+			FieldElement{7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962},
+		},
+		{
+			FieldElement{-7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325},
+			FieldElement{10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593},
+			FieldElement{696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404},
+		},
+		{
+			FieldElement{-11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644},
+			FieldElement{17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801},
+			FieldElement{26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804},
+		},
+		{
+			FieldElement{-31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884},
+			FieldElement{-586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577},
+			FieldElement{-9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849},
+		},
+		{
+			FieldElement{32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473},
+			FieldElement{-8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644},
+			FieldElement{-2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319},
+		},
+	},
+	{
+		{
+			FieldElement{-11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599},
+			FieldElement{-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768},
+			FieldElement{-27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084},
+		},
+		{
+			FieldElement{-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328},
+			FieldElement{-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369},
+			FieldElement{20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920},
+		},
+		{
+			FieldElement{12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815},
+			FieldElement{-32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025},
+			FieldElement{-21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397},
+		},
+		{
+			FieldElement{-20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448},
+			FieldElement{6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981},
+			FieldElement{30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165},
+		},
+		{
+			FieldElement{32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501},
+			FieldElement{17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073},
+			FieldElement{-1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861},
+		},
+		{
+			FieldElement{14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845},
+			FieldElement{-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211},
+			FieldElement{18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870},
+		},
+		{
+			FieldElement{10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096},
+			FieldElement{33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803},
+			FieldElement{-32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168},
+		},
+		{
+			FieldElement{30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965},
+			FieldElement{-14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505},
+			FieldElement{18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598},
+		},
+	},
+	{
+		{
+			FieldElement{5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782},
+			FieldElement{5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900},
+			FieldElement{-31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479},
+		},
+		{
+			FieldElement{-12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208},
+			FieldElement{8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232},
+			FieldElement{17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719},
+		},
+		{
+			FieldElement{16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271},
+			FieldElement{-4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326},
+			FieldElement{-8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132},
+		},
+		{
+			FieldElement{14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300},
+			FieldElement{8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570},
+			FieldElement{15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670},
+		},
+		{
+			FieldElement{-2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994},
+			FieldElement{-12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913},
+			FieldElement{31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317},
+		},
+		{
+			FieldElement{-25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730},
+			FieldElement{842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096},
+			FieldElement{-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078},
+		},
+		{
+			FieldElement{-15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411},
+			FieldElement{-19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905},
+			FieldElement{-9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654},
+		},
+		{
+			FieldElement{-28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870},
+			FieldElement{-23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498},
+			FieldElement{12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579},
+		},
+	},
+	{
+		{
+			FieldElement{14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677},
+			FieldElement{10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647},
+			FieldElement{-2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743},
+		},
+		{
+			FieldElement{-25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468},
+			FieldElement{21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375},
+			FieldElement{-25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155},
+		},
+		{
+			FieldElement{6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725},
+			FieldElement{-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612},
+			FieldElement{-10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943},
+		},
+		{
+			FieldElement{-30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944},
+			FieldElement{30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928},
+			FieldElement{9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406},
+		},
+		{
+			FieldElement{22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139},
+			FieldElement{-8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963},
+			FieldElement{-31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693},
+		},
+		{
+			FieldElement{1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734},
+			FieldElement{-448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680},
+			FieldElement{-24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410},
+		},
+		{
+			FieldElement{-9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931},
+			FieldElement{-16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654},
+			FieldElement{22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710},
+		},
+		{
+			FieldElement{29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180},
+			FieldElement{-26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684},
+			FieldElement{-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895},
+		},
+	},
+	{
+		{
+			FieldElement{22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501},
+			FieldElement{-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413},
+			FieldElement{6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880},
+		},
+		{
+			FieldElement{-8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874},
+			FieldElement{22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962},
+			FieldElement{-7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899},
+		},
+		{
+			FieldElement{21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152},
+			FieldElement{9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063},
+			FieldElement{7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080},
+		},
+		{
+			FieldElement{-9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146},
+			FieldElement{-17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183},
+			FieldElement{-19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133},
+		},
+		{
+			FieldElement{-32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421},
+			FieldElement{-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622},
+			FieldElement{-4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197},
+		},
+		{
+			FieldElement{2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663},
+			FieldElement{31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753},
+			FieldElement{4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755},
+		},
+		{
+			FieldElement{-9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862},
+			FieldElement{-26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118},
+			FieldElement{26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171},
+		},
+		{
+			FieldElement{15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380},
+			FieldElement{16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824},
+			FieldElement{28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270},
+		},
+	},
+	{
+		{
+			FieldElement{-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438},
+			FieldElement{-31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584},
+			FieldElement{-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562},
+		},
+		{
+			FieldElement{30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471},
+			FieldElement{18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610},
+			FieldElement{19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269},
+		},
+		{
+			FieldElement{-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650},
+			FieldElement{14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369},
+			FieldElement{19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461},
+		},
+		{
+			FieldElement{30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462},
+			FieldElement{-5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793},
+			FieldElement{-2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218},
+		},
+		{
+			FieldElement{-24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226},
+			FieldElement{18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019},
+			FieldElement{-15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037},
+		},
+		{
+			FieldElement{31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171},
+			FieldElement{-17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132},
+			FieldElement{-28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841},
+		},
+		{
+			FieldElement{21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181},
+			FieldElement{-33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210},
+			FieldElement{-1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040},
+		},
+		{
+			FieldElement{3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935},
+			FieldElement{24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105},
+			FieldElement{-28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814},
+		},
+	},
+	{
+		{
+			FieldElement{793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852},
+			FieldElement{5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581},
+			FieldElement{-4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646},
+		},
+		{
+			FieldElement{10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844},
+			FieldElement{10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025},
+			FieldElement{27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453},
+		},
+		{
+			FieldElement{-23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068},
+			FieldElement{4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192},
+			FieldElement{-17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921},
+		},
+		{
+			FieldElement{-9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259},
+			FieldElement{-12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426},
+			FieldElement{-5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072},
+		},
+		{
+			FieldElement{-17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305},
+			FieldElement{13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832},
+			FieldElement{28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943},
+		},
+		{
+			FieldElement{-16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011},
+			FieldElement{24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447},
+			FieldElement{17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494},
+		},
+		{
+			FieldElement{-28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245},
+			FieldElement{-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859},
+			FieldElement{28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915},
+		},
+		{
+			FieldElement{16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707},
+			FieldElement{10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848},
+			FieldElement{-11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224},
+		},
+	},
+	{
+		{
+			FieldElement{-25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391},
+			FieldElement{15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215},
+			FieldElement{-23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101},
+		},
+		{
+			FieldElement{23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713},
+			FieldElement{21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849},
+			FieldElement{-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930},
+		},
+		{
+			FieldElement{-29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940},
+			FieldElement{-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031},
+			FieldElement{-17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404},
+		},
+		{
+			FieldElement{-25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243},
+			FieldElement{-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116},
+			FieldElement{-24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525},
+		},
+		{
+			FieldElement{-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509},
+			FieldElement{-10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883},
+			FieldElement{15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865},
+		},
+		{
+			FieldElement{-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660},
+			FieldElement{4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273},
+			FieldElement{-28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138},
+		},
+		{
+			FieldElement{-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560},
+			FieldElement{-10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135},
+			FieldElement{2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941},
+		},
+		{
+			FieldElement{-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739},
+			FieldElement{18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756},
+			FieldElement{-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819},
+		},
+	},
+	{
+		{
+			FieldElement{-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347},
+			FieldElement{-27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028},
+			FieldElement{21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075},
+		},
+		{
+			FieldElement{16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799},
+			FieldElement{-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609},
+			FieldElement{-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817},
+		},
+		{
+			FieldElement{-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989},
+			FieldElement{-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523},
+			FieldElement{4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278},
+		},
+		{
+			FieldElement{31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045},
+			FieldElement{19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377},
+			FieldElement{24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480},
+		},
+		{
+			FieldElement{17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016},
+			FieldElement{510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426},
+			FieldElement{18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525},
+		},
+		{
+			FieldElement{13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396},
+			FieldElement{9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080},
+			FieldElement{12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892},
+		},
+		{
+			FieldElement{15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275},
+			FieldElement{11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074},
+			FieldElement{20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140},
+		},
+		{
+			FieldElement{-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717},
+			FieldElement{-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101},
+			FieldElement{24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127},
+		},
+	},
+	{
+		{
+			FieldElement{-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632},
+			FieldElement{-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415},
+			FieldElement{-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160},
+		},
+		{
+			FieldElement{31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876},
+			FieldElement{22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625},
+			FieldElement{-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478},
+		},
+		{
+			FieldElement{27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164},
+			FieldElement{26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595},
+			FieldElement{-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248},
+		},
+		{
+			FieldElement{-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858},
+			FieldElement{15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193},
+			FieldElement{8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184},
+		},
+		{
+			FieldElement{-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942},
+			FieldElement{-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635},
+			FieldElement{21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948},
+		},
+		{
+			FieldElement{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935},
+			FieldElement{-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415},
+			FieldElement{-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416},
+		},
+		{
+			FieldElement{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018},
+			FieldElement{4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778},
+			FieldElement{366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659},
+		},
+		{
+			FieldElement{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385},
+			FieldElement{18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503},
+			FieldElement{476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329},
+		},
+	},
+	{
+		{
+			FieldElement{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056},
+			FieldElement{-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838},
+			FieldElement{24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948},
+		},
+		{
+			FieldElement{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691},
+			FieldElement{-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118},
+			FieldElement{-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517},
+		},
+		{
+			FieldElement{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269},
+			FieldElement{-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904},
+			FieldElement{-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589},
+		},
+		{
+			FieldElement{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193},
+			FieldElement{-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910},
+			FieldElement{-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930},
+		},
+		{
+			FieldElement{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667},
+			FieldElement{25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481},
+			FieldElement{-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876},
+		},
+		{
+			FieldElement{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640},
+			FieldElement{-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278},
+			FieldElement{-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112},
+		},
+		{
+			FieldElement{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272},
+			FieldElement{17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012},
+			FieldElement{-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221},
+		},
+		{
+			FieldElement{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046},
+			FieldElement{13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345},
+			FieldElement{-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310},
+		},
+	},
+	{
+		{
+			FieldElement{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937},
+			FieldElement{31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636},
+			FieldElement{-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008},
+		},
+		{
+			FieldElement{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429},
+			FieldElement{-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576},
+			FieldElement{31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066},
+		},
+		{
+			FieldElement{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490},
+			FieldElement{-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104},
+			FieldElement{33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053},
+		},
+		{
+			FieldElement{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275},
+			FieldElement{-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511},
+			FieldElement{22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095},
+		},
+		{
+			FieldElement{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439},
+			FieldElement{23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939},
+			FieldElement{-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424},
+		},
+		{
+			FieldElement{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310},
+			FieldElement{3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608},
+			FieldElement{-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079},
+		},
+		{
+			FieldElement{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101},
+			FieldElement{21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418},
+			FieldElement{18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576},
+		},
+		{
+			FieldElement{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356},
+			FieldElement{9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996},
+			FieldElement{-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099},
+		},
+	},
+	{
+		{
+			FieldElement{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728},
+			FieldElement{-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658},
+			FieldElement{-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242},
+		},
+		{
+			FieldElement{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001},
+			FieldElement{-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766},
+			FieldElement{18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373},
+		},
+		{
+			FieldElement{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458},
+			FieldElement{-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628},
+			FieldElement{-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657},
+		},
+		{
+			FieldElement{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062},
+			FieldElement{25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616},
+			FieldElement{31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014},
+		},
+		{
+			FieldElement{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383},
+			FieldElement{-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814},
+			FieldElement{-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718},
+		},
+		{
+			FieldElement{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417},
+			FieldElement{2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222},
+			FieldElement{33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444},
+		},
+		{
+			FieldElement{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597},
+			FieldElement{23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970},
+			FieldElement{1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799},
+		},
+		{
+			FieldElement{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647},
+			FieldElement{13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511},
+			FieldElement{-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032},
+		},
+	},
+	{
+		{
+			FieldElement{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834},
+			FieldElement{-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461},
+			FieldElement{29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062},
+		},
+		{
+			FieldElement{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516},
+			FieldElement{-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547},
+			FieldElement{-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240},
+		},
+		{
+			FieldElement{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038},
+			FieldElement{-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741},
+			FieldElement{16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103},
+		},
+		{
+			FieldElement{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747},
+			FieldElement{-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323},
+			FieldElement{31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016},
+		},
+		{
+			FieldElement{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373},
+			FieldElement{15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228},
+			FieldElement{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141},
+		},
+		{
+			FieldElement{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399},
+			FieldElement{11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831},
+			FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376},
+		},
+		{
+			FieldElement{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
+			FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
+			FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
+		},
+		{
+			FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
+			FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
+			FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
+		},
+	},
+}
diff --git a/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/edwards25519.go b/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/edwards25519.go
new file mode 100644
index 000000000..5f8b99478
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/ed25519/internal/edwards25519/edwards25519.go
@@ -0,0 +1,1771 @@
+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package edwards25519
+
+// This code is a port of the public domain, “ref10” implementation of ed25519
+// from SUPERCOP.
+
+// FieldElement represents an element of the field GF(2^255 - 19).  An element
+// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
+// t[3]+2^102 t[4]+...+2^230 t[9].  Bounds on each t[i] vary depending on
+// context.
+type FieldElement [10]int32
+
+var zero FieldElement
+
+func FeZero(fe *FieldElement) {
+	copy(fe[:], zero[:])
+}
+
+func FeOne(fe *FieldElement) {
+	FeZero(fe)
+	fe[0] = 1
+}
+
+func FeAdd(dst, a, b *FieldElement) {
+	dst[0] = a[0] + b[0]
+	dst[1] = a[1] + b[1]
+	dst[2] = a[2] + b[2]
+	dst[3] = a[3] + b[3]
+	dst[4] = a[4] + b[4]
+	dst[5] = a[5] + b[5]
+	dst[6] = a[6] + b[6]
+	dst[7] = a[7] + b[7]
+	dst[8] = a[8] + b[8]
+	dst[9] = a[9] + b[9]
+}
+
+func FeSub(dst, a, b *FieldElement) {
+	dst[0] = a[0] - b[0]
+	dst[1] = a[1] - b[1]
+	dst[2] = a[2] - b[2]
+	dst[3] = a[3] - b[3]
+	dst[4] = a[4] - b[4]
+	dst[5] = a[5] - b[5]
+	dst[6] = a[6] - b[6]
+	dst[7] = a[7] - b[7]
+	dst[8] = a[8] - b[8]
+	dst[9] = a[9] - b[9]
+}
+
+func FeCopy(dst, src *FieldElement) {
+	copy(dst[:], src[:])
+}
+
+// Replace (f,g) with (g,g) if b == 1;
+// replace (f,g) with (f,g) if b == 0.
+//
+// Preconditions: b in {0,1}.
+func FeCMove(f, g *FieldElement, b int32) {
+	b = -b
+	f[0] ^= b & (f[0] ^ g[0])
+	f[1] ^= b & (f[1] ^ g[1])
+	f[2] ^= b & (f[2] ^ g[2])
+	f[3] ^= b & (f[3] ^ g[3])
+	f[4] ^= b & (f[4] ^ g[4])
+	f[5] ^= b & (f[5] ^ g[5])
+	f[6] ^= b & (f[6] ^ g[6])
+	f[7] ^= b & (f[7] ^ g[7])
+	f[8] ^= b & (f[8] ^ g[8])
+	f[9] ^= b & (f[9] ^ g[9])
+}
+
+func load3(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	return r
+}
+
+func load4(in []byte) int64 {
+	var r int64
+	r = int64(in[0])
+	r |= int64(in[1]) << 8
+	r |= int64(in[2]) << 16
+	r |= int64(in[3]) << 24
+	return r
+}
+
+func FeFromBytes(dst *FieldElement, src *[32]byte) {
+	h0 := load4(src[:])
+	h1 := load3(src[4:]) << 6
+	h2 := load3(src[7:]) << 5
+	h3 := load3(src[10:]) << 3
+	h4 := load3(src[13:]) << 2
+	h5 := load4(src[16:])
+	h6 := load3(src[20:]) << 7
+	h7 := load3(src[23:]) << 5
+	h8 := load3(src[26:]) << 4
+	h9 := (load3(src[29:]) & 8388607) << 2
+
+	FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+// FeToBytes marshals h to s.
+// Preconditions:
+//   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Write p=2^255-19; q=floor(h/p).
+// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+//
+// Proof:
+//   Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+//   Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
+//
+//   Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+//   Then 0<y<1.
+//
+//   Write r=h-pq.
+//   Have 0<=r<=p-1=2^255-20.
+//   Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+//
+//   Write x=r+19(2^-255)r+y.
+//   Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+//
+//   Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+//   so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+func FeToBytes(s *[32]byte, h *FieldElement) {
+	var carry [10]int32
+
+	q := (19*h[9] + (1 << 24)) >> 25
+	q = (h[0] + q) >> 26
+	q = (h[1] + q) >> 25
+	q = (h[2] + q) >> 26
+	q = (h[3] + q) >> 25
+	q = (h[4] + q) >> 26
+	q = (h[5] + q) >> 25
+	q = (h[6] + q) >> 26
+	q = (h[7] + q) >> 25
+	q = (h[8] + q) >> 26
+	q = (h[9] + q) >> 25
+
+	// Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
+	h[0] += 19 * q
+	// Goal: Output h-2^255 q, which is between 0 and 2^255-20.
+
+	carry[0] = h[0] >> 26
+	h[1] += carry[0]
+	h[0] -= carry[0] << 26
+	carry[1] = h[1] >> 25
+	h[2] += carry[1]
+	h[1] -= carry[1] << 25
+	carry[2] = h[2] >> 26
+	h[3] += carry[2]
+	h[2] -= carry[2] << 26
+	carry[3] = h[3] >> 25
+	h[4] += carry[3]
+	h[3] -= carry[3] << 25
+	carry[4] = h[4] >> 26
+	h[5] += carry[4]
+	h[4] -= carry[4] << 26
+	carry[5] = h[5] >> 25
+	h[6] += carry[5]
+	h[5] -= carry[5] << 25
+	carry[6] = h[6] >> 26
+	h[7] += carry[6]
+	h[6] -= carry[6] << 26
+	carry[7] = h[7] >> 25
+	h[8] += carry[7]
+	h[7] -= carry[7] << 25
+	carry[8] = h[8] >> 26
+	h[9] += carry[8]
+	h[8] -= carry[8] << 26
+	carry[9] = h[9] >> 25
+	h[9] -= carry[9] << 25
+	// h10 = carry9
+
+	// Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+	// Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
+	// evidently 2^255 h10-2^255 q = 0.
+	// Goal: Output h[0]+...+2^230 h[9].
+
+	s[0] = byte(h[0] >> 0)
+	s[1] = byte(h[0] >> 8)
+	s[2] = byte(h[0] >> 16)
+	s[3] = byte((h[0] >> 24) | (h[1] << 2))
+	s[4] = byte(h[1] >> 6)
+	s[5] = byte(h[1] >> 14)
+	s[6] = byte((h[1] >> 22) | (h[2] << 3))
+	s[7] = byte(h[2] >> 5)
+	s[8] = byte(h[2] >> 13)
+	s[9] = byte((h[2] >> 21) | (h[3] << 5))
+	s[10] = byte(h[3] >> 3)
+	s[11] = byte(h[3] >> 11)
+	s[12] = byte((h[3] >> 19) | (h[4] << 6))
+	s[13] = byte(h[4] >> 2)
+	s[14] = byte(h[4] >> 10)
+	s[15] = byte(h[4] >> 18)
+	s[16] = byte(h[5] >> 0)
+	s[17] = byte(h[5] >> 8)
+	s[18] = byte(h[5] >> 16)
+	s[19] = byte((h[5] >> 24) | (h[6] << 1))
+	s[20] = byte(h[6] >> 7)
+	s[21] = byte(h[6] >> 15)
+	s[22] = byte((h[6] >> 23) | (h[7] << 3))
+	s[23] = byte(h[7] >> 5)
+	s[24] = byte(h[7] >> 13)
+	s[25] = byte((h[7] >> 21) | (h[8] << 4))
+	s[26] = byte(h[8] >> 4)
+	s[27] = byte(h[8] >> 12)
+	s[28] = byte((h[8] >> 20) | (h[9] << 6))
+	s[29] = byte(h[9] >> 2)
+	s[30] = byte(h[9] >> 10)
+	s[31] = byte(h[9] >> 18)
+}
+
+func FeIsNegative(f *FieldElement) byte {
+	var s [32]byte
+	FeToBytes(&s, f)
+	return s[0] & 1
+}
+
+func FeIsNonZero(f *FieldElement) int32 {
+	var s [32]byte
+	FeToBytes(&s, f)
+	var x uint8
+	for _, b := range s {
+		x |= b
+	}
+	x |= x >> 4
+	x |= x >> 2
+	x |= x >> 1
+	return int32(x & 1)
+}
+
+// FeNeg sets h = -f
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+func FeNeg(h, f *FieldElement) {
+	h[0] = -f[0]
+	h[1] = -f[1]
+	h[2] = -f[2]
+	h[3] = -f[3]
+	h[4] = -f[4]
+	h[5] = -f[5]
+	h[6] = -f[6]
+	h[7] = -f[7]
+	h[8] = -f[8]
+	h[9] = -f[9]
+}
+
+func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
+	var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64
+
+	/*
+	  |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
+	    i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
+	  |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
+	    i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
+	*/
+
+	c0 = (h0 + (1 << 25)) >> 26
+	h1 += c0
+	h0 -= c0 << 26
+	c4 = (h4 + (1 << 25)) >> 26
+	h5 += c4
+	h4 -= c4 << 26
+	/* |h0| <= 2^25 */
+	/* |h4| <= 2^25 */
+	/* |h1| <= 1.51*2^58 */
+	/* |h5| <= 1.51*2^58 */
+
+	c1 = (h1 + (1 << 24)) >> 25
+	h2 += c1
+	h1 -= c1 << 25
+	c5 = (h5 + (1 << 24)) >> 25
+	h6 += c5
+	h5 -= c5 << 25
+	/* |h1| <= 2^24; from now on fits into int32 */
+	/* |h5| <= 2^24; from now on fits into int32 */
+	/* |h2| <= 1.21*2^59 */
+	/* |h6| <= 1.21*2^59 */
+
+	c2 = (h2 + (1 << 25)) >> 26
+	h3 += c2
+	h2 -= c2 << 26
+	c6 = (h6 + (1 << 25)) >> 26
+	h7 += c6
+	h6 -= c6 << 26
+	/* |h2| <= 2^25; from now on fits into int32 unchanged */
+	/* |h6| <= 2^25; from now on fits into int32 unchanged */
+	/* |h3| <= 1.51*2^58 */
+	/* |h7| <= 1.51*2^58 */
+
+	c3 = (h3 + (1 << 24)) >> 25
+	h4 += c3
+	h3 -= c3 << 25
+	c7 = (h7 + (1 << 24)) >> 25
+	h8 += c7
+	h7 -= c7 << 25
+	/* |h3| <= 2^24; from now on fits into int32 unchanged */
+	/* |h7| <= 2^24; from now on fits into int32 unchanged */
+	/* |h4| <= 1.52*2^33 */
+	/* |h8| <= 1.52*2^33 */
+
+	c4 = (h4 + (1 << 25)) >> 26
+	h5 += c4
+	h4 -= c4 << 26
+	c8 = (h8 + (1 << 25)) >> 26
+	h9 += c8
+	h8 -= c8 << 26
+	/* |h4| <= 2^25; from now on fits into int32 unchanged */
+	/* |h8| <= 2^25; from now on fits into int32 unchanged */
+	/* |h5| <= 1.01*2^24 */
+	/* |h9| <= 1.51*2^58 */
+
+	c9 = (h9 + (1 << 24)) >> 25
+	h0 += c9 * 19
+	h9 -= c9 << 25
+	/* |h9| <= 2^24; from now on fits into int32 unchanged */
+	/* |h0| <= 1.8*2^37 */
+
+	c0 = (h0 + (1 << 25)) >> 26
+	h1 += c0
+	h0 -= c0 << 26
+	/* |h0| <= 2^25; from now on fits into int32 unchanged */
+	/* |h1| <= 1.01*2^24 */
+
+	h[0] = int32(h0)
+	h[1] = int32(h1)
+	h[2] = int32(h2)
+	h[3] = int32(h3)
+	h[4] = int32(h4)
+	h[5] = int32(h5)
+	h[6] = int32(h6)
+	h[7] = int32(h7)
+	h[8] = int32(h8)
+	h[9] = int32(h9)
+}
+
+// FeMul calculates h = f * g
+// Can overlap h with f or g.
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//    |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+//
+// Notes on implementation strategy:
+//
+// Using schoolbook multiplication.
+// Karatsuba would save a little in some cost models.
+//
+// Most multiplications by 2 and 19 are 32-bit precomputations;
+// cheaper than 64-bit postcomputations.
+//
+// There is one remaining multiplication by 19 in the carry chain;
+// one *19 precomputation can be merged into this,
+// but the resulting data flow is considerably less clean.
+//
+// There are 12 carries below.
+// 10 of them are 2-way parallelizable and vectorizable.
+// Can get away with 11 carries, but then data flow is much deeper.
+//
+// With tighter constraints on inputs, can squeeze carries into int32.
+func FeMul(h, f, g *FieldElement) {
+	f0 := int64(f[0])
+	f1 := int64(f[1])
+	f2 := int64(f[2])
+	f3 := int64(f[3])
+	f4 := int64(f[4])
+	f5 := int64(f[5])
+	f6 := int64(f[6])
+	f7 := int64(f[7])
+	f8 := int64(f[8])
+	f9 := int64(f[9])
+
+	f1_2 := int64(2 * f[1])
+	f3_2 := int64(2 * f[3])
+	f5_2 := int64(2 * f[5])
+	f7_2 := int64(2 * f[7])
+	f9_2 := int64(2 * f[9])
+
+	g0 := int64(g[0])
+	g1 := int64(g[1])
+	g2 := int64(g[2])
+	g3 := int64(g[3])
+	g4 := int64(g[4])
+	g5 := int64(g[5])
+	g6 := int64(g[6])
+	g7 := int64(g[7])
+	g8 := int64(g[8])
+	g9 := int64(g[9])
+
+	g1_19 := int64(19 * g[1]) /* 1.4*2^29 */
+	g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */
+	g3_19 := int64(19 * g[3])
+	g4_19 := int64(19 * g[4])
+	g5_19 := int64(19 * g[5])
+	g6_19 := int64(19 * g[6])
+	g7_19 := int64(19 * g[7])
+	g8_19 := int64(19 * g[8])
+	g9_19 := int64(19 * g[9])
+
+	h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19
+	h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19
+	h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19
+	h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19
+	h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19
+	h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19
+	h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19
+	h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19
+	h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19
+	h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0
+
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
+	f0 := int64(f[0])
+	f1 := int64(f[1])
+	f2 := int64(f[2])
+	f3 := int64(f[3])
+	f4 := int64(f[4])
+	f5 := int64(f[5])
+	f6 := int64(f[6])
+	f7 := int64(f[7])
+	f8 := int64(f[8])
+	f9 := int64(f[9])
+	f0_2 := int64(2 * f[0])
+	f1_2 := int64(2 * f[1])
+	f2_2 := int64(2 * f[2])
+	f3_2 := int64(2 * f[3])
+	f4_2 := int64(2 * f[4])
+	f5_2 := int64(2 * f[5])
+	f6_2 := int64(2 * f[6])
+	f7_2 := int64(2 * f[7])
+	f5_38 := 38 * f5 // 1.31*2^30
+	f6_19 := 19 * f6 // 1.31*2^30
+	f7_38 := 38 * f7 // 1.31*2^30
+	f8_19 := 19 * f8 // 1.31*2^30
+	f9_38 := 38 * f9 // 1.31*2^30
+
+	h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38
+	h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19
+	h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19
+	h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38
+	h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38
+	h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19
+	h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19
+	h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38
+	h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38
+	h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5
+
+	return
+}
+
+// FeSquare calculates h = f*f. Can overlap h with f.
+//
+// Preconditions:
+//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+func FeSquare(h, f *FieldElement) {
+	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+// FeSquare2 sets h = 2 * f * f
+//
+// Can overlap h with f.
+//
+// Preconditions:
+//    |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+//
+// Postconditions:
+//    |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+// See fe_mul.c for discussion of implementation strategy.
+func FeSquare2(h, f *FieldElement) {
+	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
+
+	h0 += h0
+	h1 += h1
+	h2 += h2
+	h3 += h3
+	h4 += h4
+	h5 += h5
+	h6 += h6
+	h7 += h7
+	h8 += h8
+	h9 += h9
+
+	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
+}
+
+func FeInvert(out, z *FieldElement) {
+	var t0, t1, t2, t3 FieldElement
+	var i int
+
+	FeSquare(&t0, z)        // 2^1
+	FeSquare(&t1, &t0)      // 2^2
+	for i = 1; i < 2; i++ { // 2^3
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, z, &t1)      // 2^3 + 2^0
+	FeMul(&t0, &t0, &t1)    // 2^3 + 2^1 + 2^0
+	FeSquare(&t2, &t0)      // 2^4 + 2^2 + 2^1
+	FeMul(&t1, &t1, &t2)    // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
+	FeSquare(&t2, &t1)      // 5,4,3,2,1
+	for i = 1; i < 5; i++ { // 9,8,7,6,5
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)     // 9,8,7,6,5,4,3,2,1,0
+	FeSquare(&t2, &t1)       // 10..1
+	for i = 1; i < 10; i++ { // 19..10
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t2, &t2, &t1)     // 19..0
+	FeSquare(&t3, &t2)       // 20..1
+	for i = 1; i < 20; i++ { // 39..20
+		FeSquare(&t3, &t3)
+	}
+	FeMul(&t2, &t3, &t2)     // 39..0
+	FeSquare(&t2, &t2)       // 40..1
+	for i = 1; i < 10; i++ { // 49..10
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)     // 49..0
+	FeSquare(&t2, &t1)       // 50..1
+	for i = 1; i < 50; i++ { // 99..50
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t2, &t2, &t1)      // 99..0
+	FeSquare(&t3, &t2)        // 100..1
+	for i = 1; i < 100; i++ { // 199..100
+		FeSquare(&t3, &t3)
+	}
+	FeMul(&t2, &t3, &t2)     // 199..0
+	FeSquare(&t2, &t2)       // 200..1
+	for i = 1; i < 50; i++ { // 249..50
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)    // 249..0
+	FeSquare(&t1, &t1)      // 250..1
+	for i = 1; i < 5; i++ { // 254..5
+		FeSquare(&t1, &t1)
+	}
+	FeMul(out, &t1, &t0) // 254..5,3,1,0
+}
+
+func fePow22523(out, z *FieldElement) {
+	var t0, t1, t2 FieldElement
+	var i int
+
+	FeSquare(&t0, z)
+	for i = 1; i < 1; i++ {
+		FeSquare(&t0, &t0)
+	}
+	FeSquare(&t1, &t0)
+	for i = 1; i < 2; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, z, &t1)
+	FeMul(&t0, &t0, &t1)
+	FeSquare(&t0, &t0)
+	for i = 1; i < 1; i++ {
+		FeSquare(&t0, &t0)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 5; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 10; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, &t1, &t0)
+	FeSquare(&t2, &t1)
+	for i = 1; i < 20; i++ {
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)
+	FeSquare(&t1, &t1)
+	for i = 1; i < 10; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t1, &t0)
+	for i = 1; i < 50; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t1, &t1, &t0)
+	FeSquare(&t2, &t1)
+	for i = 1; i < 100; i++ {
+		FeSquare(&t2, &t2)
+	}
+	FeMul(&t1, &t2, &t1)
+	FeSquare(&t1, &t1)
+	for i = 1; i < 50; i++ {
+		FeSquare(&t1, &t1)
+	}
+	FeMul(&t0, &t1, &t0)
+	FeSquare(&t0, &t0)
+	for i = 1; i < 2; i++ {
+		FeSquare(&t0, &t0)
+	}
+	FeMul(out, &t0, z)
+}
+
+// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 *
+// y^2 where d = -121665/121666.
+//
+// Several representations are used:
+//   ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z
+//   ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+//   CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+//   PreComputedGroupElement: (y+x,y-x,2dxy)
+
+type ProjectiveGroupElement struct {
+	X, Y, Z FieldElement
+}
+
+type ExtendedGroupElement struct {
+	X, Y, Z, T FieldElement
+}
+
+type CompletedGroupElement struct {
+	X, Y, Z, T FieldElement
+}
+
+type PreComputedGroupElement struct {
+	yPlusX, yMinusX, xy2d FieldElement
+}
+
+type CachedGroupElement struct {
+	yPlusX, yMinusX, Z, T2d FieldElement
+}
+
+func (p *ProjectiveGroupElement) Zero() {
+	FeZero(&p.X)
+	FeOne(&p.Y)
+	FeOne(&p.Z)
+}
+
+func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) {
+	var t0 FieldElement
+
+	FeSquare(&r.X, &p.X)
+	FeSquare(&r.Z, &p.Y)
+	FeSquare2(&r.T, &p.Z)
+	FeAdd(&r.Y, &p.X, &p.Y)
+	FeSquare(&t0, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.X)
+	FeSub(&r.Z, &r.Z, &r.X)
+	FeSub(&r.X, &t0, &r.Y)
+	FeSub(&r.T, &r.T, &r.Z)
+}
+
+func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) {
+	var recip, x, y FieldElement
+
+	FeInvert(&recip, &p.Z)
+	FeMul(&x, &p.X, &recip)
+	FeMul(&y, &p.Y, &recip)
+	FeToBytes(s, &y)
+	s[31] ^= FeIsNegative(&x) << 7
+}
+
+func (p *ExtendedGroupElement) Zero() {
+	FeZero(&p.X)
+	FeOne(&p.Y)
+	FeOne(&p.Z)
+	FeZero(&p.T)
+}
+
+func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) {
+	var q ProjectiveGroupElement
+	p.ToProjective(&q)
+	q.Double(r)
+}
+
+func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) {
+	FeAdd(&r.yPlusX, &p.Y, &p.X)
+	FeSub(&r.yMinusX, &p.Y, &p.X)
+	FeCopy(&r.Z, &p.Z)
+	FeMul(&r.T2d, &p.T, &d2)
+}
+
+func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) {
+	FeCopy(&r.X, &p.X)
+	FeCopy(&r.Y, &p.Y)
+	FeCopy(&r.Z, &p.Z)
+}
+
+func (p *ExtendedGroupElement) ToBytes(s *[32]byte) {
+	var recip, x, y FieldElement
+
+	FeInvert(&recip, &p.Z)
+	FeMul(&x, &p.X, &recip)
+	FeMul(&y, &p.Y, &recip)
+	FeToBytes(s, &y)
+	s[31] ^= FeIsNegative(&x) << 7
+}
+
+func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool {
+	var u, v, v3, vxx, check FieldElement
+
+	FeFromBytes(&p.Y, s)
+	FeOne(&p.Z)
+	FeSquare(&u, &p.Y)
+	FeMul(&v, &u, &d)
+	FeSub(&u, &u, &p.Z) // y = y^2-1
+	FeAdd(&v, &v, &p.Z) // v = dy^2+1
+
+	FeSquare(&v3, &v)
+	FeMul(&v3, &v3, &v) // v3 = v^3
+	FeSquare(&p.X, &v3)
+	FeMul(&p.X, &p.X, &v)
+	FeMul(&p.X, &p.X, &u) // x = uv^7
+
+	fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8)
+	FeMul(&p.X, &p.X, &v3)
+	FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8)
+
+	var tmpX, tmp2 [32]byte
+
+	FeSquare(&vxx, &p.X)
+	FeMul(&vxx, &vxx, &v)
+	FeSub(&check, &vxx, &u) // vx^2-u
+	if FeIsNonZero(&check) == 1 {
+		FeAdd(&check, &vxx, &u) // vx^2+u
+		if FeIsNonZero(&check) == 1 {
+			return false
+		}
+		FeMul(&p.X, &p.X, &SqrtM1)
+
+		FeToBytes(&tmpX, &p.X)
+		for i, v := range tmpX {
+			tmp2[31-i] = v
+		}
+	}
+
+	if FeIsNegative(&p.X) != (s[31] >> 7) {
+		FeNeg(&p.X, &p.X)
+	}
+
+	FeMul(&p.T, &p.X, &p.Y)
+	return true
+}
+
+func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) {
+	FeMul(&r.X, &p.X, &p.T)
+	FeMul(&r.Y, &p.Y, &p.Z)
+	FeMul(&r.Z, &p.Z, &p.T)
+}
+
+func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) {
+	FeMul(&r.X, &p.X, &p.T)
+	FeMul(&r.Y, &p.Y, &p.Z)
+	FeMul(&r.Z, &p.Z, &p.T)
+	FeMul(&r.T, &p.X, &p.Y)
+}
+
+func (p *PreComputedGroupElement) Zero() {
+	FeOne(&p.yPlusX)
+	FeOne(&p.yMinusX)
+	FeZero(&p.xy2d)
+}
+
+func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yPlusX)
+	FeMul(&r.Y, &r.Y, &q.yMinusX)
+	FeMul(&r.T, &q.T2d, &p.T)
+	FeMul(&r.X, &p.Z, &q.Z)
+	FeAdd(&t0, &r.X, &r.X)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeAdd(&r.Z, &t0, &r.T)
+	FeSub(&r.T, &t0, &r.T)
+}
+
+func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yMinusX)
+	FeMul(&r.Y, &r.Y, &q.yPlusX)
+	FeMul(&r.T, &q.T2d, &p.T)
+	FeMul(&r.X, &p.Z, &q.Z)
+	FeAdd(&t0, &r.X, &r.X)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeSub(&r.Z, &t0, &r.T)
+	FeAdd(&r.T, &t0, &r.T)
+}
+
+func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yPlusX)
+	FeMul(&r.Y, &r.Y, &q.yMinusX)
+	FeMul(&r.T, &q.xy2d, &p.T)
+	FeAdd(&t0, &p.Z, &p.Z)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeAdd(&r.Z, &t0, &r.T)
+	FeSub(&r.T, &t0, &r.T)
+}
+
+func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
+	var t0 FieldElement
+
+	FeAdd(&r.X, &p.Y, &p.X)
+	FeSub(&r.Y, &p.Y, &p.X)
+	FeMul(&r.Z, &r.X, &q.yMinusX)
+	FeMul(&r.Y, &r.Y, &q.yPlusX)
+	FeMul(&r.T, &q.xy2d, &p.T)
+	FeAdd(&t0, &p.Z, &p.Z)
+	FeSub(&r.X, &r.Z, &r.Y)
+	FeAdd(&r.Y, &r.Z, &r.Y)
+	FeSub(&r.Z, &t0, &r.T)
+	FeAdd(&r.T, &t0, &r.T)
+}
+
+func slide(r *[256]int8, a *[32]byte) {
+	for i := range r {
+		r[i] = int8(1 & (a[i>>3] >> uint(i&7)))
+	}
+
+	for i := range r {
+		if r[i] != 0 {
+			for b := 1; b <= 6 && i+b < 256; b++ {
+				if r[i+b] != 0 {
+					if r[i]+(r[i+b]<<uint(b)) <= 15 {
+						r[i] += r[i+b] << uint(b)
+						r[i+b] = 0
+					} else if r[i]-(r[i+b]<<uint(b)) >= -15 {
+						r[i] -= r[i+b] << uint(b)
+						for k := i + b; k < 256; k++ {
+							if r[k] == 0 {
+								r[k] = 1
+								break
+							}
+							r[k] = 0
+						}
+					} else {
+						break
+					}
+				}
+			}
+		}
+	}
+}
+
+// GeDoubleScalarMultVartime sets r = a*A + b*B
+// where a = a[0]+256*a[1]+...+256^31 a[31].
+// and b = b[0]+256*b[1]+...+256^31 b[31].
+// B is the Ed25519 base point (x,4/5) with x positive.
+func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) {
+	var aSlide, bSlide [256]int8
+	var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A
+	var t CompletedGroupElement
+	var u, A2 ExtendedGroupElement
+	var i int
+
+	slide(&aSlide, a)
+	slide(&bSlide, b)
+
+	A.ToCached(&Ai[0])
+	A.Double(&t)
+	t.ToExtended(&A2)
+
+	for i := 0; i < 7; i++ {
+		geAdd(&t, &A2, &Ai[i])
+		t.ToExtended(&u)
+		u.ToCached(&Ai[i+1])
+	}
+
+	r.Zero()
+
+	for i = 255; i >= 0; i-- {
+		if aSlide[i] != 0 || bSlide[i] != 0 {
+			break
+		}
+	}
+
+	for ; i >= 0; i-- {
+		r.Double(&t)
+
+		if aSlide[i] > 0 {
+			t.ToExtended(&u)
+			geAdd(&t, &u, &Ai[aSlide[i]/2])
+		} else if aSlide[i] < 0 {
+			t.ToExtended(&u)
+			geSub(&t, &u, &Ai[(-aSlide[i])/2])
+		}
+
+		if bSlide[i] > 0 {
+			t.ToExtended(&u)
+			geMixedAdd(&t, &u, &bi[bSlide[i]/2])
+		} else if bSlide[i] < 0 {
+			t.ToExtended(&u)
+			geMixedSub(&t, &u, &bi[(-bSlide[i])/2])
+		}
+
+		t.ToProjective(r)
+	}
+}
+
+// equal returns 1 if b == c and 0 otherwise, assuming that b and c are
+// non-negative.
+func equal(b, c int32) int32 {
+	x := uint32(b ^ c)
+	x--
+	return int32(x >> 31)
+}
+
+// negative returns 1 if b < 0 and 0 otherwise.
+func negative(b int32) int32 {
+	return (b >> 31) & 1
+}
+
+func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) {
+	FeCMove(&t.yPlusX, &u.yPlusX, b)
+	FeCMove(&t.yMinusX, &u.yMinusX, b)
+	FeCMove(&t.xy2d, &u.xy2d, b)
+}
+
+func selectPoint(t *PreComputedGroupElement, pos int32, b int32) {
+	var minusT PreComputedGroupElement
+	bNegative := negative(b)
+	bAbs := b - (((-bNegative) & b) << 1)
+
+	t.Zero()
+	for i := int32(0); i < 8; i++ {
+		PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1))
+	}
+	FeCopy(&minusT.yPlusX, &t.yMinusX)
+	FeCopy(&minusT.yMinusX, &t.yPlusX)
+	FeNeg(&minusT.xy2d, &t.xy2d)
+	PreComputedGroupElementCMove(t, &minusT, bNegative)
+}
+
+// GeScalarMultBase computes h = a*B, where
+//   a = a[0]+256*a[1]+...+256^31 a[31]
+//   B is the Ed25519 base point (x,4/5) with x positive.
+//
+// Preconditions:
+//   a[31] <= 127
+func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) {
+	var e [64]int8
+
+	for i, v := range a {
+		e[2*i] = int8(v & 15)
+		e[2*i+1] = int8((v >> 4) & 15)
+	}
+
+	// each e[i] is between 0 and 15 and e[63] is between 0 and 7.
+
+	carry := int8(0)
+	for i := 0; i < 63; i++ {
+		e[i] += carry
+		carry = (e[i] + 8) >> 4
+		e[i] -= carry << 4
+	}
+	e[63] += carry
+	// each e[i] is between -8 and 8.
+
+	h.Zero()
+	var t PreComputedGroupElement
+	var r CompletedGroupElement
+	for i := int32(1); i < 64; i += 2 {
+		selectPoint(&t, i/2, int32(e[i]))
+		geMixedAdd(&r, h, &t)
+		r.ToExtended(h)
+	}
+
+	var s ProjectiveGroupElement
+
+	h.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToProjective(&s)
+	s.Double(&r)
+	r.ToExtended(h)
+
+	for i := int32(0); i < 64; i += 2 {
+		selectPoint(&t, i/2, int32(e[i]))
+		geMixedAdd(&r, h, &t)
+		r.ToExtended(h)
+	}
+}
+
+// The scalars are GF(2^252 + 27742317777372353535851937790883648493).
+
+// Input:
+//   a[0]+256*a[1]+...+256^31*a[31] = a
+//   b[0]+256*b[1]+...+256^31*b[31] = b
+//   c[0]+256*c[1]+...+256^31*c[31] = c
+//
+// Output:
+//   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+//   where l = 2^252 + 27742317777372353535851937790883648493.
+func ScMulAdd(s, a, b, c *[32]byte) {
+	a0 := 2097151 & load3(a[:])
+	a1 := 2097151 & (load4(a[2:]) >> 5)
+	a2 := 2097151 & (load3(a[5:]) >> 2)
+	a3 := 2097151 & (load4(a[7:]) >> 7)
+	a4 := 2097151 & (load4(a[10:]) >> 4)
+	a5 := 2097151 & (load3(a[13:]) >> 1)
+	a6 := 2097151 & (load4(a[15:]) >> 6)
+	a7 := 2097151 & (load3(a[18:]) >> 3)
+	a8 := 2097151 & load3(a[21:])
+	a9 := 2097151 & (load4(a[23:]) >> 5)
+	a10 := 2097151 & (load3(a[26:]) >> 2)
+	a11 := (load4(a[28:]) >> 7)
+	b0 := 2097151 & load3(b[:])
+	b1 := 2097151 & (load4(b[2:]) >> 5)
+	b2 := 2097151 & (load3(b[5:]) >> 2)
+	b3 := 2097151 & (load4(b[7:]) >> 7)
+	b4 := 2097151 & (load4(b[10:]) >> 4)
+	b5 := 2097151 & (load3(b[13:]) >> 1)
+	b6 := 2097151 & (load4(b[15:]) >> 6)
+	b7 := 2097151 & (load3(b[18:]) >> 3)
+	b8 := 2097151 & load3(b[21:])
+	b9 := 2097151 & (load4(b[23:]) >> 5)
+	b10 := 2097151 & (load3(b[26:]) >> 2)
+	b11 := (load4(b[28:]) >> 7)
+	c0 := 2097151 & load3(c[:])
+	c1 := 2097151 & (load4(c[2:]) >> 5)
+	c2 := 2097151 & (load3(c[5:]) >> 2)
+	c3 := 2097151 & (load4(c[7:]) >> 7)
+	c4 := 2097151 & (load4(c[10:]) >> 4)
+	c5 := 2097151 & (load3(c[13:]) >> 1)
+	c6 := 2097151 & (load4(c[15:]) >> 6)
+	c7 := 2097151 & (load3(c[18:]) >> 3)
+	c8 := 2097151 & load3(c[21:])
+	c9 := 2097151 & (load4(c[23:]) >> 5)
+	c10 := 2097151 & (load3(c[26:]) >> 2)
+	c11 := (load4(c[28:]) >> 7)
+	var carry [23]int64
+
+	s0 := c0 + a0*b0
+	s1 := c1 + a0*b1 + a1*b0
+	s2 := c2 + a0*b2 + a1*b1 + a2*b0
+	s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0
+	s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0
+	s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0
+	s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0
+	s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0
+	s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0
+	s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0
+	s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0
+	s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0
+	s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1
+	s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2
+	s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3
+	s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4
+	s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5
+	s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6
+	s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7
+	s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8
+	s20 := a9*b11 + a10*b10 + a11*b9
+	s21 := a10*b11 + a11*b10
+	s22 := a11 * b11
+	s23 := int64(0)
+
+	carry[0] = (s0 + (1 << 20)) >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[2] = (s2 + (1 << 20)) >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[4] = (s4 + (1 << 20)) >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[6] = (s6 + (1 << 20)) >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[8] = (s8 + (1 << 20)) >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[10] = (s10 + (1 << 20)) >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+	carry[12] = (s12 + (1 << 20)) >> 21
+	s13 += carry[12]
+	s12 -= carry[12] << 21
+	carry[14] = (s14 + (1 << 20)) >> 21
+	s15 += carry[14]
+	s14 -= carry[14] << 21
+	carry[16] = (s16 + (1 << 20)) >> 21
+	s17 += carry[16]
+	s16 -= carry[16] << 21
+	carry[18] = (s18 + (1 << 20)) >> 21
+	s19 += carry[18]
+	s18 -= carry[18] << 21
+	carry[20] = (s20 + (1 << 20)) >> 21
+	s21 += carry[20]
+	s20 -= carry[20] << 21
+	carry[22] = (s22 + (1 << 20)) >> 21
+	s23 += carry[22]
+	s22 -= carry[22] << 21
+
+	carry[1] = (s1 + (1 << 20)) >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[3] = (s3 + (1 << 20)) >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[5] = (s5 + (1 << 20)) >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[7] = (s7 + (1 << 20)) >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[9] = (s9 + (1 << 20)) >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[11] = (s11 + (1 << 20)) >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+	carry[13] = (s13 + (1 << 20)) >> 21
+	s14 += carry[13]
+	s13 -= carry[13] << 21
+	carry[15] = (s15 + (1 << 20)) >> 21
+	s16 += carry[15]
+	s15 -= carry[15] << 21
+	carry[17] = (s17 + (1 << 20)) >> 21
+	s18 += carry[17]
+	s17 -= carry[17] << 21
+	carry[19] = (s19 + (1 << 20)) >> 21
+	s20 += carry[19]
+	s19 -= carry[19] << 21
+	carry[21] = (s21 + (1 << 20)) >> 21
+	s22 += carry[21]
+	s21 -= carry[21] << 21
+
+	s11 += s23 * 666643
+	s12 += s23 * 470296
+	s13 += s23 * 654183
+	s14 -= s23 * 997805
+	s15 += s23 * 136657
+	s16 -= s23 * 683901
+	s23 = 0
+
+	s10 += s22 * 666643
+	s11 += s22 * 470296
+	s12 += s22 * 654183
+	s13 -= s22 * 997805
+	s14 += s22 * 136657
+	s15 -= s22 * 683901
+	s22 = 0
+
+	s9 += s21 * 666643
+	s10 += s21 * 470296
+	s11 += s21 * 654183
+	s12 -= s21 * 997805
+	s13 += s21 * 136657
+	s14 -= s21 * 683901
+	s21 = 0
+
+	s8 += s20 * 666643
+	s9 += s20 * 470296
+	s10 += s20 * 654183
+	s11 -= s20 * 997805
+	s12 += s20 * 136657
+	s13 -= s20 * 683901
+	s20 = 0
+
+	s7 += s19 * 666643
+	s8 += s19 * 470296
+	s9 += s19 * 654183
+	s10 -= s19 * 997805
+	s11 += s19 * 136657
+	s12 -= s19 * 683901
+	s19 = 0
+
+	s6 += s18 * 666643
+	s7 += s18 * 470296
+	s8 += s18 * 654183
+	s9 -= s18 * 997805
+	s10 += s18 * 136657
+	s11 -= s18 * 683901
+	s18 = 0
+
+	carry[6] = (s6 + (1 << 20)) >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[8] = (s8 + (1 << 20)) >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[10] = (s10 + (1 << 20)) >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+	carry[12] = (s12 + (1 << 20)) >> 21
+	s13 += carry[12]
+	s12 -= carry[12] << 21
+	carry[14] = (s14 + (1 << 20)) >> 21
+	s15 += carry[14]
+	s14 -= carry[14] << 21
+	carry[16] = (s16 + (1 << 20)) >> 21
+	s17 += carry[16]
+	s16 -= carry[16] << 21
+
+	carry[7] = (s7 + (1 << 20)) >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[9] = (s9 + (1 << 20)) >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[11] = (s11 + (1 << 20)) >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+	carry[13] = (s13 + (1 << 20)) >> 21
+	s14 += carry[13]
+	s13 -= carry[13] << 21
+	carry[15] = (s15 + (1 << 20)) >> 21
+	s16 += carry[15]
+	s15 -= carry[15] << 21
+
+	s5 += s17 * 666643
+	s6 += s17 * 470296
+	s7 += s17 * 654183
+	s8 -= s17 * 997805
+	s9 += s17 * 136657
+	s10 -= s17 * 683901
+	s17 = 0
+
+	s4 += s16 * 666643
+	s5 += s16 * 470296
+	s6 += s16 * 654183
+	s7 -= s16 * 997805
+	s8 += s16 * 136657
+	s9 -= s16 * 683901
+	s16 = 0
+
+	s3 += s15 * 666643
+	s4 += s15 * 470296
+	s5 += s15 * 654183
+	s6 -= s15 * 997805
+	s7 += s15 * 136657
+	s8 -= s15 * 683901
+	s15 = 0
+
+	s2 += s14 * 666643
+	s3 += s14 * 470296
+	s4 += s14 * 654183
+	s5 -= s14 * 997805
+	s6 += s14 * 136657
+	s7 -= s14 * 683901
+	s14 = 0
+
+	s1 += s13 * 666643
+	s2 += s13 * 470296
+	s3 += s13 * 654183
+	s4 -= s13 * 997805
+	s5 += s13 * 136657
+	s6 -= s13 * 683901
+	s13 = 0
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = (s0 + (1 << 20)) >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[2] = (s2 + (1 << 20)) >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[4] = (s4 + (1 << 20)) >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[6] = (s6 + (1 << 20)) >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[8] = (s8 + (1 << 20)) >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[10] = (s10 + (1 << 20)) >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+
+	carry[1] = (s1 + (1 << 20)) >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[3] = (s3 + (1 << 20)) >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[5] = (s5 + (1 << 20)) >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[7] = (s7 + (1 << 20)) >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[9] = (s9 + (1 << 20)) >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[11] = (s11 + (1 << 20)) >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = s0 >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[1] = s1 >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[2] = s2 >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[3] = s3 >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[4] = s4 >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[5] = s5 >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[6] = s6 >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[7] = s7 >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[8] = s8 >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[9] = s9 >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[10] = s10 >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+	carry[11] = s11 >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = s0 >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[1] = s1 >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[2] = s2 >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[3] = s3 >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[4] = s4 >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[5] = s5 >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[6] = s6 >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[7] = s7 >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[8] = s8 >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[9] = s9 >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[10] = s10 >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+
+	s[0] = byte(s0 >> 0)
+	s[1] = byte(s0 >> 8)
+	s[2] = byte((s0 >> 16) | (s1 << 5))
+	s[3] = byte(s1 >> 3)
+	s[4] = byte(s1 >> 11)
+	s[5] = byte((s1 >> 19) | (s2 << 2))
+	s[6] = byte(s2 >> 6)
+	s[7] = byte((s2 >> 14) | (s3 << 7))
+	s[8] = byte(s3 >> 1)
+	s[9] = byte(s3 >> 9)
+	s[10] = byte((s3 >> 17) | (s4 << 4))
+	s[11] = byte(s4 >> 4)
+	s[12] = byte(s4 >> 12)
+	s[13] = byte((s4 >> 20) | (s5 << 1))
+	s[14] = byte(s5 >> 7)
+	s[15] = byte((s5 >> 15) | (s6 << 6))
+	s[16] = byte(s6 >> 2)
+	s[17] = byte(s6 >> 10)
+	s[18] = byte((s6 >> 18) | (s7 << 3))
+	s[19] = byte(s7 >> 5)
+	s[20] = byte(s7 >> 13)
+	s[21] = byte(s8 >> 0)
+	s[22] = byte(s8 >> 8)
+	s[23] = byte((s8 >> 16) | (s9 << 5))
+	s[24] = byte(s9 >> 3)
+	s[25] = byte(s9 >> 11)
+	s[26] = byte((s9 >> 19) | (s10 << 2))
+	s[27] = byte(s10 >> 6)
+	s[28] = byte((s10 >> 14) | (s11 << 7))
+	s[29] = byte(s11 >> 1)
+	s[30] = byte(s11 >> 9)
+	s[31] = byte(s11 >> 17)
+}
+
+// Input:
+//   s[0]+256*s[1]+...+256^63*s[63] = s
+//
+// Output:
+//   s[0]+256*s[1]+...+256^31*s[31] = s mod l
+//   where l = 2^252 + 27742317777372353535851937790883648493.
+func ScReduce(out *[32]byte, s *[64]byte) {
+	s0 := 2097151 & load3(s[:])
+	s1 := 2097151 & (load4(s[2:]) >> 5)
+	s2 := 2097151 & (load3(s[5:]) >> 2)
+	s3 := 2097151 & (load4(s[7:]) >> 7)
+	s4 := 2097151 & (load4(s[10:]) >> 4)
+	s5 := 2097151 & (load3(s[13:]) >> 1)
+	s6 := 2097151 & (load4(s[15:]) >> 6)
+	s7 := 2097151 & (load3(s[18:]) >> 3)
+	s8 := 2097151 & load3(s[21:])
+	s9 := 2097151 & (load4(s[23:]) >> 5)
+	s10 := 2097151 & (load3(s[26:]) >> 2)
+	s11 := 2097151 & (load4(s[28:]) >> 7)
+	s12 := 2097151 & (load4(s[31:]) >> 4)
+	s13 := 2097151 & (load3(s[34:]) >> 1)
+	s14 := 2097151 & (load4(s[36:]) >> 6)
+	s15 := 2097151 & (load3(s[39:]) >> 3)
+	s16 := 2097151 & load3(s[42:])
+	s17 := 2097151 & (load4(s[44:]) >> 5)
+	s18 := 2097151 & (load3(s[47:]) >> 2)
+	s19 := 2097151 & (load4(s[49:]) >> 7)
+	s20 := 2097151 & (load4(s[52:]) >> 4)
+	s21 := 2097151 & (load3(s[55:]) >> 1)
+	s22 := 2097151 & (load4(s[57:]) >> 6)
+	s23 := (load4(s[60:]) >> 3)
+
+	s11 += s23 * 666643
+	s12 += s23 * 470296
+	s13 += s23 * 654183
+	s14 -= s23 * 997805
+	s15 += s23 * 136657
+	s16 -= s23 * 683901
+	s23 = 0
+
+	s10 += s22 * 666643
+	s11 += s22 * 470296
+	s12 += s22 * 654183
+	s13 -= s22 * 997805
+	s14 += s22 * 136657
+	s15 -= s22 * 683901
+	s22 = 0
+
+	s9 += s21 * 666643
+	s10 += s21 * 470296
+	s11 += s21 * 654183
+	s12 -= s21 * 997805
+	s13 += s21 * 136657
+	s14 -= s21 * 683901
+	s21 = 0
+
+	s8 += s20 * 666643
+	s9 += s20 * 470296
+	s10 += s20 * 654183
+	s11 -= s20 * 997805
+	s12 += s20 * 136657
+	s13 -= s20 * 683901
+	s20 = 0
+
+	s7 += s19 * 666643
+	s8 += s19 * 470296
+	s9 += s19 * 654183
+	s10 -= s19 * 997805
+	s11 += s19 * 136657
+	s12 -= s19 * 683901
+	s19 = 0
+
+	s6 += s18 * 666643
+	s7 += s18 * 470296
+	s8 += s18 * 654183
+	s9 -= s18 * 997805
+	s10 += s18 * 136657
+	s11 -= s18 * 683901
+	s18 = 0
+
+	var carry [17]int64
+
+	carry[6] = (s6 + (1 << 20)) >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[8] = (s8 + (1 << 20)) >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[10] = (s10 + (1 << 20)) >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+	carry[12] = (s12 + (1 << 20)) >> 21
+	s13 += carry[12]
+	s12 -= carry[12] << 21
+	carry[14] = (s14 + (1 << 20)) >> 21
+	s15 += carry[14]
+	s14 -= carry[14] << 21
+	carry[16] = (s16 + (1 << 20)) >> 21
+	s17 += carry[16]
+	s16 -= carry[16] << 21
+
+	carry[7] = (s7 + (1 << 20)) >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[9] = (s9 + (1 << 20)) >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[11] = (s11 + (1 << 20)) >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+	carry[13] = (s13 + (1 << 20)) >> 21
+	s14 += carry[13]
+	s13 -= carry[13] << 21
+	carry[15] = (s15 + (1 << 20)) >> 21
+	s16 += carry[15]
+	s15 -= carry[15] << 21
+
+	s5 += s17 * 666643
+	s6 += s17 * 470296
+	s7 += s17 * 654183
+	s8 -= s17 * 997805
+	s9 += s17 * 136657
+	s10 -= s17 * 683901
+	s17 = 0
+
+	s4 += s16 * 666643
+	s5 += s16 * 470296
+	s6 += s16 * 654183
+	s7 -= s16 * 997805
+	s8 += s16 * 136657
+	s9 -= s16 * 683901
+	s16 = 0
+
+	s3 += s15 * 666643
+	s4 += s15 * 470296
+	s5 += s15 * 654183
+	s6 -= s15 * 997805
+	s7 += s15 * 136657
+	s8 -= s15 * 683901
+	s15 = 0
+
+	s2 += s14 * 666643
+	s3 += s14 * 470296
+	s4 += s14 * 654183
+	s5 -= s14 * 997805
+	s6 += s14 * 136657
+	s7 -= s14 * 683901
+	s14 = 0
+
+	s1 += s13 * 666643
+	s2 += s13 * 470296
+	s3 += s13 * 654183
+	s4 -= s13 * 997805
+	s5 += s13 * 136657
+	s6 -= s13 * 683901
+	s13 = 0
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = (s0 + (1 << 20)) >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[2] = (s2 + (1 << 20)) >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[4] = (s4 + (1 << 20)) >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[6] = (s6 + (1 << 20)) >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[8] = (s8 + (1 << 20)) >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[10] = (s10 + (1 << 20)) >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+
+	carry[1] = (s1 + (1 << 20)) >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[3] = (s3 + (1 << 20)) >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[5] = (s5 + (1 << 20)) >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[7] = (s7 + (1 << 20)) >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[9] = (s9 + (1 << 20)) >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[11] = (s11 + (1 << 20)) >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = s0 >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[1] = s1 >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[2] = s2 >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[3] = s3 >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[4] = s4 >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[5] = s5 >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[6] = s6 >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[7] = s7 >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[8] = s8 >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[9] = s9 >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[10] = s10 >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+	carry[11] = s11 >> 21
+	s12 += carry[11]
+	s11 -= carry[11] << 21
+
+	s0 += s12 * 666643
+	s1 += s12 * 470296
+	s2 += s12 * 654183
+	s3 -= s12 * 997805
+	s4 += s12 * 136657
+	s5 -= s12 * 683901
+	s12 = 0
+
+	carry[0] = s0 >> 21
+	s1 += carry[0]
+	s0 -= carry[0] << 21
+	carry[1] = s1 >> 21
+	s2 += carry[1]
+	s1 -= carry[1] << 21
+	carry[2] = s2 >> 21
+	s3 += carry[2]
+	s2 -= carry[2] << 21
+	carry[3] = s3 >> 21
+	s4 += carry[3]
+	s3 -= carry[3] << 21
+	carry[4] = s4 >> 21
+	s5 += carry[4]
+	s4 -= carry[4] << 21
+	carry[5] = s5 >> 21
+	s6 += carry[5]
+	s5 -= carry[5] << 21
+	carry[6] = s6 >> 21
+	s7 += carry[6]
+	s6 -= carry[6] << 21
+	carry[7] = s7 >> 21
+	s8 += carry[7]
+	s7 -= carry[7] << 21
+	carry[8] = s8 >> 21
+	s9 += carry[8]
+	s8 -= carry[8] << 21
+	carry[9] = s9 >> 21
+	s10 += carry[9]
+	s9 -= carry[9] << 21
+	carry[10] = s10 >> 21
+	s11 += carry[10]
+	s10 -= carry[10] << 21
+
+	out[0] = byte(s0 >> 0)
+	out[1] = byte(s0 >> 8)
+	out[2] = byte((s0 >> 16) | (s1 << 5))
+	out[3] = byte(s1 >> 3)
+	out[4] = byte(s1 >> 11)
+	out[5] = byte((s1 >> 19) | (s2 << 2))
+	out[6] = byte(s2 >> 6)
+	out[7] = byte((s2 >> 14) | (s3 << 7))
+	out[8] = byte(s3 >> 1)
+	out[9] = byte(s3 >> 9)
+	out[10] = byte((s3 >> 17) | (s4 << 4))
+	out[11] = byte(s4 >> 4)
+	out[12] = byte(s4 >> 12)
+	out[13] = byte((s4 >> 20) | (s5 << 1))
+	out[14] = byte(s5 >> 7)
+	out[15] = byte((s5 >> 15) | (s6 << 6))
+	out[16] = byte(s6 >> 2)
+	out[17] = byte(s6 >> 10)
+	out[18] = byte((s6 >> 18) | (s7 << 3))
+	out[19] = byte(s7 >> 5)
+	out[20] = byte(s7 >> 13)
+	out[21] = byte(s8 >> 0)
+	out[22] = byte(s8 >> 8)
+	out[23] = byte((s8 >> 16) | (s9 << 5))
+	out[24] = byte(s9 >> 3)
+	out[25] = byte(s9 >> 11)
+	out[26] = byte((s9 >> 19) | (s10 << 2))
+	out[27] = byte(s10 >> 6)
+	out[28] = byte((s10 >> 14) | (s11 << 7))
+	out[29] = byte(s11 >> 1)
+	out[30] = byte(s11 >> 9)
+	out[31] = byte(s11 >> 17)
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/armor/armor.go b/vendor/github.com/keybase/go-crypto/openpgp/armor/armor.go
similarity index 82%
rename from vendor/golang.org/x/crypto/openpgp/armor/armor.go
rename to vendor/github.com/keybase/go-crypto/openpgp/armor/armor.go
index 592d18643..9513a0905 100644
--- a/vendor/golang.org/x/crypto/openpgp/armor/armor.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/armor/armor.go
@@ -4,14 +4,17 @@
 
 // Package armor implements OpenPGP ASCII Armor, see RFC 4880. OpenPGP Armor is
 // very similar to PEM except that it has an additional CRC checksum.
-package armor // import "golang.org/x/crypto/openpgp/armor"
+package armor // import "github.com/keybase/go-crypto/openpgp/armor"
 
 import (
 	"bufio"
 	"bytes"
 	"encoding/base64"
-	"golang.org/x/crypto/openpgp/errors"
 	"io"
+	"strings"
+	"unicode"
+
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // A Block represents an OpenPGP armored structure.
@@ -65,7 +68,14 @@ type lineReader struct {
 	in  *bufio.Reader
 	buf []byte
 	eof bool
-	crc uint32
+	crc *uint32
+}
+
+// ourIsSpace checks if a rune is either space according to unicode
+// package, or ZeroWidthSpace (which is not a space according to
+// unicode module). Used to trim lines during header reading.
+func ourIsSpace(r rune) bool {
+	return r == '\u200b' || unicode.IsSpace(r)
 }
 
 func (l *lineReader) Read(p []byte) (n int, err error) {
@@ -79,13 +89,12 @@ func (l *lineReader) Read(p []byte) (n int, err error) {
 		return
 	}
 
-	line, isPrefix, err := l.in.ReadLine()
+	line, _, err := l.in.ReadLine()
 	if err != nil {
 		return
 	}
-	if isPrefix {
-		return 0, ArmorCorrupt
-	}
+
+	line = bytes.TrimFunc(line, ourIsSpace)
 
 	if len(line) == 5 && line[0] == '=' {
 		// This is the checksum line
@@ -95,13 +104,19 @@ func (l *lineReader) Read(p []byte) (n int, err error) {
 		if m != 3 || err != nil {
 			return
 		}
-		l.crc = uint32(expectedBytes[0])<<16 |
+		crc := uint32(expectedBytes[0])<<16 |
 			uint32(expectedBytes[1])<<8 |
 			uint32(expectedBytes[2])
+		l.crc = &crc
 
-		line, _, err = l.in.ReadLine()
-		if err != nil && err != io.EOF {
-			return
+		for {
+			line, _, err = l.in.ReadLine()
+			if err != nil && err != io.EOF {
+				return
+			}
+			if len(strings.TrimSpace(string(line))) > 0 {
+				break
+			}
 		}
 		if !bytes.HasPrefix(line, armorEnd) {
 			return 0, ArmorCorrupt
@@ -111,8 +126,11 @@ func (l *lineReader) Read(p []byte) (n int, err error) {
 		return 0, io.EOF
 	}
 
-	if len(line) > 96 {
-		return 0, ArmorCorrupt
+	if bytes.HasPrefix(line, armorEnd) {
+		// Unexpected ending, there was no checksum.
+		l.eof = true
+		l.crc = nil
+		return 0, io.EOF
 	}
 
 	n = copy(p, line)
@@ -142,7 +160,7 @@ func (r *openpgpReader) Read(p []byte) (n int, err error) {
 	r.currentCRC = crc24(r.currentCRC, p[:n])
 
 	if err == io.EOF {
-		if r.lReader.crc != uint32(r.currentCRC&crc24Mask) {
+		if r.lReader.crc != nil && *r.lReader.crc != uint32(r.currentCRC&crc24Mask) {
 			return 0, ArmorCorrupt
 		}
 	}
@@ -196,7 +214,7 @@ TryNextBlock:
 			p.Header[lastKey] += string(line)
 			continue
 		}
-		line = bytes.TrimSpace(line)
+		line = bytes.TrimFunc(line, ourIsSpace)
 		if len(line) == 0 {
 			break
 		}
diff --git a/vendor/golang.org/x/crypto/openpgp/armor/encode.go b/vendor/github.com/keybase/go-crypto/openpgp/armor/encode.go
similarity index 98%
rename from vendor/golang.org/x/crypto/openpgp/armor/encode.go
rename to vendor/github.com/keybase/go-crypto/openpgp/armor/encode.go
index 6f07582c3..075a1978e 100644
--- a/vendor/golang.org/x/crypto/openpgp/armor/encode.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/armor/encode.go
@@ -125,7 +125,7 @@ func (e *encoding) Close() (err error) {
 	var b64ChecksumBytes [4]byte
 	base64.StdEncoding.Encode(b64ChecksumBytes[:], checksumBytes[:])
 
-	return writeSlices(e.out, blockEnd, b64ChecksumBytes[:], newline, armorEnd, e.blockType, armorEndOfLine)
+	return writeSlices(e.out, blockEnd, b64ChecksumBytes[:], newline, armorEnd, e.blockType, armorEndOfLine, []byte{'\n'})
 }
 
 // Encode returns a WriteCloser which will encode the data written to it in
diff --git a/vendor/golang.org/x/crypto/openpgp/canonical_text.go b/vendor/github.com/keybase/go-crypto/openpgp/canonical_text.go
similarity index 100%
rename from vendor/golang.org/x/crypto/openpgp/canonical_text.go
rename to vendor/github.com/keybase/go-crypto/openpgp/canonical_text.go
diff --git a/vendor/github.com/keybase/go-crypto/openpgp/ecdh/ecdh.go b/vendor/github.com/keybase/go-crypto/openpgp/ecdh/ecdh.go
new file mode 100644
index 000000000..64c18d0b3
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/openpgp/ecdh/ecdh.go
@@ -0,0 +1,282 @@
+package ecdh
+
+import (
+	"bytes"
+	"crypto"
+	"crypto/aes"
+	"crypto/elliptic"
+	"encoding/binary"
+	"errors"
+	"github.com/keybase/go-crypto/curve25519"
+	"io"
+	"math/big"
+)
+
+type PublicKey struct {
+	elliptic.Curve
+	X, Y *big.Int
+}
+
+type PrivateKey struct {
+	PublicKey
+	X *big.Int
+}
+
+// KDF implements Key Derivation Function as described in
+// https://tools.ietf.org/html/rfc6637#section-7
+func (e *PublicKey) KDF(S []byte, kdfParams []byte, hash crypto.Hash) []byte {
+	sLen := (e.Curve.Params().P.BitLen() + 7) / 8
+	buf := new(bytes.Buffer)
+	buf.Write([]byte{0, 0, 0, 1})
+	if sLen > len(S) {
+		// zero-pad the S. If we got invalid S (bigger than curve's
+		// P), we are going to produce invalid key. Garbage in,
+		// garbage out.
+		buf.Write(make([]byte, sLen-len(S)))
+	}
+	buf.Write(S)
+	buf.Write(kdfParams)
+
+	hashw := hash.New()
+
+	hashw.Write(buf.Bytes())
+	key := hashw.Sum(nil)
+
+	return key
+}
+
+// AESKeyUnwrap implements RFC 3394 Key Unwrapping. See
+// http://tools.ietf.org/html/rfc3394#section-2.2.1
+// Note: The second described algorithm ("index-based") is implemented
+// here.
+func AESKeyUnwrap(key, cipherText []byte) ([]byte, error) {
+	if len(cipherText)%8 != 0 {
+		return nil, errors.New("cipherText must by a multiple of 64 bits")
+	}
+
+	cipher, err := aes.NewCipher(key)
+	if err != nil {
+		return nil, err
+	}
+
+	nblocks := len(cipherText)/8 - 1
+
+	// 1) Initialize variables.
+	// - Set A = C[0]
+	var A [aes.BlockSize]byte
+	copy(A[:8], cipherText[:8])
+
+	// For i = 1 to n
+	//   Set R[i] = C[i]
+	R := make([]byte, len(cipherText)-8)
+	copy(R, cipherText[8:])
+
+	// 2) Compute intermediate values.
+	for j := 5; j >= 0; j-- {
+		for i := nblocks - 1; i >= 0; i-- {
+			// B = AES-1(K, (A ^ t) | R[i]) where t = n*j+i
+			// A = MSB(64, B)
+			t := uint64(nblocks*j + i + 1)
+			At := binary.BigEndian.Uint64(A[:8]) ^ t
+			binary.BigEndian.PutUint64(A[:8], At)
+
+			copy(A[8:], R[i*8:i*8+8])
+			cipher.Decrypt(A[:], A[:])
+
+			// R[i] = LSB(B, 64)
+			copy(R[i*8:i*8+8], A[8:])
+		}
+	}
+
+	// 3) Output results.
+	// If A is an appropriate initial value (see 2.2.3),
+	for i := 0; i < 8; i++ {
+		if A[i] != 0xA6 {
+			return nil, errors.New("Failed to unwrap key (A is not IV)")
+		}
+	}
+
+	return R, nil
+}
+
+// AESKeyWrap implements RFC 3394 Key Wrapping. See
+// https://tools.ietf.org/html/rfc3394#section-2.2.2
+// Note: The second described algorithm ("index-based") is implemented
+// here.
+func AESKeyWrap(key, plainText []byte) ([]byte, error) {
+	if len(plainText)%8 != 0 {
+		return nil, errors.New("plainText must be a multiple of 64 bits")
+	}
+
+	cipher, err := aes.NewCipher(key) // NewCipher checks key size
+	if err != nil {
+		return nil, err
+	}
+
+	nblocks := len(plainText) / 8
+
+	// 1) Initialize variables.
+	var A [aes.BlockSize]byte
+	// Section 2.2.3.1 -- Initial Value
+	// http://tools.ietf.org/html/rfc3394#section-2.2.3.1
+	for i := 0; i < 8; i++ {
+		A[i] = 0xA6
+	}
+
+	// For i = 1 to n
+	//   Set R[i] = P[i]
+	R := make([]byte, len(plainText))
+	copy(R, plainText)
+
+	// 2) Calculate intermediate values.
+	for j := 0; j <= 5; j++ {
+		for i := 0; i < nblocks; i++ {
+			// B = AES(K, A | R[i])
+			copy(A[8:], R[i*8:i*8+8])
+			cipher.Encrypt(A[:], A[:])
+
+			// (Assume B = A)
+			// A = MSB(64, B) ^ t where t = (n*j)+1
+			t := uint64(j*nblocks + i + 1)
+			At := binary.BigEndian.Uint64(A[:8]) ^ t
+			binary.BigEndian.PutUint64(A[:8], At)
+
+			// R[i] = LSB(64, B)
+			copy(R[i*8:i*8+8], A[8:])
+		}
+	}
+
+	// 3) Output results.
+	// Set C[0] = A
+	// For i = 1 to n
+	//   C[i] = R[i]
+	return append(A[:8], R...), nil
+}
+
+// PadBuffer pads byte buffer buf to a length being multiple of
+// blockLen. Additional bytes appended to the buffer have value of the
+// number padded bytes. E.g. if the buffer is 3 bytes short of being
+// 40 bytes total, the appended bytes will be [03, 03, 03].
+func PadBuffer(buf []byte, blockLen int) []byte {
+	padding := blockLen - (len(buf) % blockLen)
+	if padding == 0 {
+		return buf
+	}
+
+	padBuf := make([]byte, padding)
+	for i := 0; i < padding; i++ {
+		padBuf[i] = byte(padding)
+	}
+
+	return append(buf, padBuf...)
+}
+
+// UnpadBuffer verifies that buffer contains proper padding and
+// returns buffer without the padding, or nil if the padding was
+// invalid.
+func UnpadBuffer(buf []byte, dataLen int) []byte {
+	padding := len(buf) - dataLen
+	outBuf := buf[:dataLen]
+
+	for i := dataLen; i < len(buf); i++ {
+		if buf[i] != byte(padding) {
+			// Invalid padding - bail out
+			return nil
+		}
+	}
+
+	return outBuf
+}
+
+func (e *PublicKey) Encrypt(random io.Reader, kdfParams []byte, plain []byte, hash crypto.Hash, kdfKeySize int) (Vx *big.Int, Vy *big.Int, C []byte, err error) {
+	// Vx, Vy - encryption key
+
+	// Note for Curve 25519 - curve25519 library already does key
+	// clamping in scalarMult, so we can use generic random scalar
+	// generation from elliptic.
+	priv, Vx, Vy, err := elliptic.GenerateKey(e.Curve, random)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+
+	// Sx, Sy - shared secret
+	Sx, _ := e.Curve.ScalarMult(e.X, e.Y, priv)
+
+	// Encrypt the payload with KDF-ed S as the encryption key. Pass
+	// the ciphertext along with V to the recipient. Recipient can
+	// generate S using V and their priv key, and then KDF(S), on
+	// their own, to get encryption key and decrypt the ciphertext,
+	// revealing encryption key for symmetric encryption later.
+
+	plain = PadBuffer(plain, 8)
+	key := e.KDF(Sx.Bytes(), kdfParams, hash)
+
+	// Take only as many bytes from key as the key length (the hash
+	// result might be bigger)
+	encrypted, err := AESKeyWrap(key[:kdfKeySize], plain)
+
+	return Vx, Vy, encrypted, nil
+}
+
+func (e *PrivateKey) DecryptShared(X, Y *big.Int) []byte {
+	Sx, _ := e.Curve.ScalarMult(X, Y, e.X.Bytes())
+	return Sx.Bytes()
+}
+
+func countBits(buffer []byte) int {
+	var headerLen int
+	switch buffer[0] {
+	case 0x4:
+		headerLen = 3
+	case 0x40:
+		headerLen = 7
+	default:
+		// Unexpected header - but we can still count the bits.
+		val := buffer[0]
+		headerLen = 0
+		for val > 0 {
+			val = val / 2
+			headerLen++
+		}
+	}
+
+	return headerLen + (len(buffer)-1)*8
+}
+
+// elliptic.Marshal and elliptic.Unmarshal only marshals uncompressed
+// 0x4 MPI types. These functions will check if the curve is cv25519,
+// and if so, use 0x40 compressed type to (un)marshal. Otherwise,
+// elliptic.(Un)marshal will be called.
+
+// Marshal encodes point into either 0x4 uncompressed point form, or
+// 0x40 compressed point for Curve 25519.
+func Marshal(curve elliptic.Curve, x, y *big.Int) (buf []byte, bitSize int) {
+	// NOTE: Read more about MPI encoding in the RFC:
+	// https://tools.ietf.org/html/rfc4880#section-3.2
+
+	// We are required to encode size in bits, counting from the most-
+	// significant non-zero bit. So assuming that the buffer never
+	// starts with 0x00, we only need to count bits in the first byte
+	// - and in current implentation it will always be 0x4 or 0x40.
+
+	cv, ok := curve25519.ToCurve25519(curve)
+	if ok {
+		buf = cv.MarshalType40(x, y)
+	} else {
+		buf = elliptic.Marshal(curve, x, y)
+	}
+
+	return buf, countBits(buf)
+}
+
+// Unmarshal converts point, serialized by Marshal, into x, y pair.
+// For 0x40 compressed points (for Curve 25519), y will always be 0.
+// It is an error if point is not on the curve, On error, x = nil.
+func Unmarshal(curve elliptic.Curve, data []byte) (x, y *big.Int) {
+	cv, ok := curve25519.ToCurve25519(curve)
+	if ok {
+		return cv.UnmarshalType40(data)
+	}
+
+	return elliptic.Unmarshal(curve, data)
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go b/vendor/github.com/keybase/go-crypto/openpgp/elgamal/elgamal.go
similarity index 97%
rename from vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go
rename to vendor/github.com/keybase/go-crypto/openpgp/elgamal/elgamal.go
index 73f4fe378..15dafc556 100644
--- a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/elgamal/elgamal.go
@@ -10,7 +10,7 @@
 // This form of ElGamal embeds PKCS#1 v1.5 padding, which may make it
 // unsuitable for other protocols. RSA should be used in preference in any
 // case.
-package elgamal // import "golang.org/x/crypto/openpgp/elgamal"
+package elgamal // import "github.com/keybase/go-crypto/openpgp/elgamal"
 
 import (
 	"crypto/rand"
diff --git a/vendor/golang.org/x/crypto/openpgp/errors/errors.go b/vendor/github.com/keybase/go-crypto/openpgp/errors/errors.go
similarity index 96%
rename from vendor/golang.org/x/crypto/openpgp/errors/errors.go
rename to vendor/github.com/keybase/go-crypto/openpgp/errors/errors.go
index eb0550b2d..d48c6c9b6 100644
--- a/vendor/golang.org/x/crypto/openpgp/errors/errors.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/errors/errors.go
@@ -3,7 +3,7 @@
 // license that can be found in the LICENSE file.
 
 // Package errors contains common error types for the OpenPGP packages.
-package errors // import "golang.org/x/crypto/openpgp/errors"
+package errors // import "github.com/keybase/go-crypto/openpgp/errors"
 
 import (
 	"strconv"
diff --git a/vendor/github.com/keybase/go-crypto/openpgp/keys.go b/vendor/github.com/keybase/go-crypto/openpgp/keys.go
new file mode 100644
index 000000000..e1a458879
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/openpgp/keys.go
@@ -0,0 +1,902 @@
+// Copyright 2011 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package openpgp
+
+import (
+	"crypto/hmac"
+	"encoding/binary"
+	"io"
+	"time"
+
+	"github.com/keybase/go-crypto/openpgp/armor"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/packet"
+	"github.com/keybase/go-crypto/rsa"
+)
+
+// PublicKeyType is the armor type for a PGP public key.
+var PublicKeyType = "PGP PUBLIC KEY BLOCK"
+
+// PrivateKeyType is the armor type for a PGP private key.
+var PrivateKeyType = "PGP PRIVATE KEY BLOCK"
+
+// An Entity represents the components of an OpenPGP key: a primary public key
+// (which must be a signing key), one or more identities claimed by that key,
+// and zero or more subkeys, which may be encryption keys.
+type Entity struct {
+	PrimaryKey  *packet.PublicKey
+	PrivateKey  *packet.PrivateKey
+	Identities  map[string]*Identity // indexed by Identity.Name
+	Revocations []*packet.Signature
+	// Revocations that are signed by designated revokers. Reading keys
+	// will not verify these revocations, because it won't have access to
+	// issuers' public keys, API consumers should do this instead (or
+	// not, and just assume that the key is probably revoked).
+	UnverifiedRevocations []*packet.Signature
+	Subkeys               []Subkey
+	BadSubkeys            []BadSubkey
+}
+
+// An Identity represents an identity claimed by an Entity and zero or more
+// assertions by other entities about that claim.
+type Identity struct {
+	Name          string // by convention, has the form "Full Name (comment) <email@example.com>"
+	UserId        *packet.UserId
+	SelfSignature *packet.Signature
+	Signatures    []*packet.Signature
+	Revocation    *packet.Signature
+}
+
+// A Subkey is an additional public key in an Entity. Subkeys can be used for
+// encryption.
+type Subkey struct {
+	PublicKey  *packet.PublicKey
+	PrivateKey *packet.PrivateKey
+	Sig        *packet.Signature
+	Revocation *packet.Signature
+}
+
+// BadSubkey is one that failed reconstruction, but we'll keep it around for
+// informational purposes.
+type BadSubkey struct {
+	Subkey
+	Err error
+}
+
+// A Key identifies a specific public key in an Entity. This is either the
+// Entity's primary key or a subkey.
+type Key struct {
+	Entity        *Entity
+	PublicKey     *packet.PublicKey
+	PrivateKey    *packet.PrivateKey
+	SelfSignature *packet.Signature
+	KeyFlags      packet.KeyFlagBits
+}
+
+// A KeyRing provides access to public and private keys.
+type KeyRing interface {
+
+	// KeysById returns the set of keys that have the given key id.
+	// fp can be optionally supplied, which is the full key fingerprint.
+	// If it's provided, then it must match. This comes up in the case
+	// of GPG subpacket 33.
+	KeysById(id uint64, fp []byte) []Key
+
+	// KeysByIdAndUsage returns the set of keys with the given id
+	// that also meet the key usage given by requiredUsage.
+	// The requiredUsage is expressed as the bitwise-OR of
+	// packet.KeyFlag* values.
+	// fp can be optionally supplied, which is the full key fingerprint.
+	// If it's provided, then it must match. This comes up in the case
+	// of GPG subpacket 33.
+	KeysByIdUsage(id uint64, fp []byte, requiredUsage byte) []Key
+
+	// DecryptionKeys returns all private keys that are valid for
+	// decryption.
+	DecryptionKeys() []Key
+}
+
+// primaryIdentity returns the Identity marked as primary or the first identity
+// if none are so marked.
+func (e *Entity) primaryIdentity() *Identity {
+	var firstIdentity *Identity
+	for _, ident := range e.Identities {
+		if firstIdentity == nil {
+			firstIdentity = ident
+		}
+		if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
+			return ident
+		}
+	}
+	return firstIdentity
+}
+
+// encryptionKey returns the best candidate Key for encrypting a message to the
+// given Entity.
+func (e *Entity) encryptionKey(now time.Time) (Key, bool) {
+	candidateSubkey := -1
+
+	// Iterate the keys to find the newest key
+	var maxTime time.Time
+	for i, subkey := range e.Subkeys {
+
+		// NOTE(maxtaco)
+		// If there is a Flags subpacket, then we have to follow it, and only
+		// use keys that are marked for Encryption of Communication.  If there
+		// isn't a Flags subpacket, and this is an Encrypt-Only key (right now only ElGamal
+		// suffices), then we implicitly use it. The check for primary below is a little
+		// more open-ended, but for now, let's be strict and potentially open up
+		// if we see bugs in the wild.
+		//
+		// One more note: old DSA/ElGamal keys tend not to have the Flags subpacket,
+		// so this sort of thing is pretty important for encrypting to older keys.
+		//
+		if ((subkey.Sig.FlagsValid && subkey.Sig.FlagEncryptCommunications) ||
+			(!subkey.Sig.FlagsValid && subkey.PublicKey.PubKeyAlgo == packet.PubKeyAlgoElGamal)) &&
+			subkey.PublicKey.PubKeyAlgo.CanEncrypt() &&
+			!subkey.Sig.KeyExpired(now) &&
+			subkey.Revocation == nil &&
+			(maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) {
+			candidateSubkey = i
+			maxTime = subkey.Sig.CreationTime
+		}
+	}
+
+	if candidateSubkey != -1 {
+		subkey := e.Subkeys[candidateSubkey]
+		return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Sig.GetKeyFlags()}, true
+	}
+
+	// If we don't have any candidate subkeys for encryption and
+	// the primary key doesn't have any usage metadata then we
+	// assume that the primary key is ok. Or, if the primary key is
+	// marked as ok to encrypt to, then we can obviously use it.
+	//
+	// NOTE(maxtaco) - see note above, how this policy is a little too open-ended
+	// for my liking, but leave it for now.
+	i := e.primaryIdentity()
+	if (!i.SelfSignature.FlagsValid || i.SelfSignature.FlagEncryptCommunications) &&
+		e.PrimaryKey.PubKeyAlgo.CanEncrypt() &&
+		!i.SelfSignature.KeyExpired(now) {
+		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, i.SelfSignature.GetKeyFlags()}, true
+	}
+
+	// This Entity appears to be signing only.
+	return Key{}, false
+}
+
+// signingKey return the best candidate Key for signing a message with this
+// Entity.
+func (e *Entity) signingKey(now time.Time) (Key, bool) {
+	candidateSubkey := -1
+
+	for i, subkey := range e.Subkeys {
+		if (!subkey.Sig.FlagsValid || subkey.Sig.FlagSign) &&
+			subkey.PrivateKey.PrivateKey != nil &&
+			subkey.PublicKey.PubKeyAlgo.CanSign() &&
+			subkey.Revocation == nil &&
+			!subkey.Sig.KeyExpired(now) {
+			candidateSubkey = i
+			break
+		}
+	}
+
+	if candidateSubkey != -1 {
+		subkey := e.Subkeys[candidateSubkey]
+		return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig, subkey.Sig.GetKeyFlags()}, true
+	}
+
+	// If we have no candidate subkey then we assume that it's ok to sign
+	// with the primary key.
+	i := e.primaryIdentity()
+	if (!i.SelfSignature.FlagsValid || i.SelfSignature.FlagSign) &&
+		e.PrimaryKey.PubKeyAlgo.CanSign() &&
+		!i.SelfSignature.KeyExpired(now) &&
+		e.PrivateKey.PrivateKey != nil {
+		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature, i.SelfSignature.GetKeyFlags()}, true
+	}
+
+	return Key{}, false
+}
+
+// An EntityList contains one or more Entities.
+type EntityList []*Entity
+
+func keyMatchesIdAndFingerprint(key *packet.PublicKey, id uint64, fp []byte) bool {
+	if key.KeyId != id {
+		return false
+	}
+	if fp == nil {
+		return true
+	}
+	return hmac.Equal(fp, key.Fingerprint[:])
+}
+
+// KeysById returns the set of keys that have the given key id.
+// fp can be optionally supplied, which is the full key fingerprint.
+// If it's provided, then it must match. This comes up in the case
+// of GPG subpacket 33.
+func (el EntityList) KeysById(id uint64, fp []byte) (keys []Key) {
+	for _, e := range el {
+		if keyMatchesIdAndFingerprint(e.PrimaryKey, id, fp) {
+			var selfSig *packet.Signature
+			for _, ident := range e.Identities {
+				if selfSig == nil {
+					selfSig = ident.SelfSignature
+				} else if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
+					selfSig = ident.SelfSignature
+					break
+				}
+			}
+
+			var keyFlags packet.KeyFlagBits
+			for _, ident := range e.Identities {
+				keyFlags.Merge(ident.SelfSignature.GetKeyFlags())
+			}
+
+			keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig, keyFlags})
+		}
+
+		for _, subKey := range e.Subkeys {
+			if keyMatchesIdAndFingerprint(subKey.PublicKey, id, fp) {
+
+				// If there's both a a revocation and a sig, then take the
+				// revocation. Otherwise, we can proceed with the sig.
+				sig := subKey.Revocation
+				if sig == nil {
+					sig = subKey.Sig
+				}
+
+				keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, sig, sig.GetKeyFlags()})
+			}
+		}
+	}
+	return
+}
+
+// KeysByIdAndUsage returns the set of keys with the given id that also meet
+// the key usage given by requiredUsage.  The requiredUsage is expressed as
+// the bitwise-OR of packet.KeyFlag* values.
+// fp can be optionally supplied, which is the full key fingerprint.
+// If it's provided, then it must match. This comes up in the case
+// of GPG subpacket 33.
+func (el EntityList) KeysByIdUsage(id uint64, fp []byte, requiredUsage byte) (keys []Key) {
+	for _, key := range el.KeysById(id, fp) {
+		if len(key.Entity.Revocations) > 0 {
+			continue
+		}
+
+		if key.SelfSignature.RevocationReason != nil {
+			continue
+		}
+
+		if requiredUsage != 0 {
+			var usage byte
+
+			switch {
+			case key.KeyFlags.Valid:
+				usage = key.KeyFlags.BitField
+
+			case key.PublicKey.PubKeyAlgo == packet.PubKeyAlgoElGamal:
+				// We also need to handle the case where, although the sig's
+				// flags aren't valid, the key can is implicitly usable for
+				// encryption by virtue of being ElGamal. See also the comment
+				// in encryptionKey() above.
+				usage |= packet.KeyFlagEncryptCommunications
+				usage |= packet.KeyFlagEncryptStorage
+
+			case key.PublicKey.PubKeyAlgo == packet.PubKeyAlgoDSA ||
+				key.PublicKey.PubKeyAlgo == packet.PubKeyAlgoECDSA ||
+				key.PublicKey.PubKeyAlgo == packet.PubKeyAlgoEdDSA:
+				usage |= packet.KeyFlagSign
+
+			// For a primary RSA key without any key flags, be as permissiable
+			// as possible.
+			case key.PublicKey.PubKeyAlgo == packet.PubKeyAlgoRSA &&
+				keyMatchesIdAndFingerprint(key.Entity.PrimaryKey, id, fp):
+				usage = (packet.KeyFlagCertify | packet.KeyFlagSign |
+					packet.KeyFlagEncryptCommunications | packet.KeyFlagEncryptStorage)
+			}
+
+			if usage&requiredUsage != requiredUsage {
+				continue
+			}
+		}
+
+		keys = append(keys, key)
+	}
+	return
+}
+
+// DecryptionKeys returns all private keys that are valid for decryption.
+func (el EntityList) DecryptionKeys() (keys []Key) {
+	for _, e := range el {
+		for _, subKey := range e.Subkeys {
+			if subKey.PrivateKey != nil && subKey.PrivateKey.PrivateKey != nil && (!subKey.Sig.FlagsValid || subKey.Sig.FlagEncryptStorage || subKey.Sig.FlagEncryptCommunications) {
+				keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig, subKey.Sig.GetKeyFlags()})
+			}
+		}
+	}
+	return
+}
+
+// ReadArmoredKeyRing reads one or more public/private keys from an armor keyring file.
+func ReadArmoredKeyRing(r io.Reader) (EntityList, error) {
+	block, err := armor.Decode(r)
+	if err == io.EOF {
+		return nil, errors.InvalidArgumentError("no armored data found")
+	}
+	if err != nil {
+		return nil, err
+	}
+	if block.Type != PublicKeyType && block.Type != PrivateKeyType {
+		return nil, errors.InvalidArgumentError("expected public or private key block, got: " + block.Type)
+	}
+
+	return ReadKeyRing(block.Body)
+}
+
+// ReadKeyRing reads one or more public/private keys. Unsupported keys are
+// ignored as long as at least a single valid key is found.
+func ReadKeyRing(r io.Reader) (el EntityList, err error) {
+	packets := packet.NewReader(r)
+	var lastUnsupportedError error
+
+	for {
+		var e *Entity
+		e, err = ReadEntity(packets)
+		if err != nil {
+			// TODO: warn about skipped unsupported/unreadable keys
+			if _, ok := err.(errors.UnsupportedError); ok {
+				lastUnsupportedError = err
+				err = readToNextPublicKey(packets)
+			} else if _, ok := err.(errors.StructuralError); ok {
+				// Skip unreadable, badly-formatted keys
+				lastUnsupportedError = err
+				err = readToNextPublicKey(packets)
+			}
+			if err == io.EOF {
+				err = nil
+				break
+			}
+			if err != nil {
+				el = nil
+				break
+			}
+		} else {
+			el = append(el, e)
+		}
+	}
+
+	if len(el) == 0 && err == nil {
+		err = lastUnsupportedError
+	}
+	return
+}
+
+// readToNextPublicKey reads packets until the start of the entity and leaves
+// the first packet of the new entity in the Reader.
+func readToNextPublicKey(packets *packet.Reader) (err error) {
+	var p packet.Packet
+	for {
+		p, err = packets.Next()
+		if err == io.EOF {
+			return
+		} else if err != nil {
+			if _, ok := err.(errors.UnsupportedError); ok {
+				err = nil
+				continue
+			}
+			return
+		}
+
+		if pk, ok := p.(*packet.PublicKey); ok && !pk.IsSubkey {
+			packets.Unread(p)
+			return
+		}
+	}
+
+	panic("unreachable")
+}
+
+// ReadEntity reads an entity (public key, identities, subkeys etc) from the
+// given Reader.
+func ReadEntity(packets *packet.Reader) (*Entity, error) {
+	e := new(Entity)
+	e.Identities = make(map[string]*Identity)
+
+	p, err := packets.Next()
+	if err != nil {
+		return nil, err
+	}
+
+	var ok bool
+	if e.PrimaryKey, ok = p.(*packet.PublicKey); !ok {
+		if e.PrivateKey, ok = p.(*packet.PrivateKey); !ok {
+			packets.Unread(p)
+			return nil, errors.StructuralError("first packet was not a public/private key")
+		} else {
+			e.PrimaryKey = &e.PrivateKey.PublicKey
+		}
+	}
+
+	if !e.PrimaryKey.PubKeyAlgo.CanSign() {
+		return nil, errors.StructuralError("primary key cannot be used for signatures")
+	}
+
+	var current *Identity
+	var revocations []*packet.Signature
+
+	designatedRevokers := make(map[uint64]bool)
+EachPacket:
+	for {
+		p, err := packets.Next()
+		if err == io.EOF {
+			break
+		} else if err != nil {
+			return nil, err
+		}
+		switch pkt := p.(type) {
+		case *packet.UserId:
+
+			// Make a new Identity object, that we might wind up throwing away.
+			// We'll only add it if we get a valid self-signature over this
+			// userID.
+			current = new(Identity)
+			current.Name = pkt.Id
+			current.UserId = pkt
+		case *packet.Signature:
+			if pkt.SigType == packet.SigTypeKeyRevocation {
+				// These revocations won't revoke UIDs (see
+				// SigTypeIdentityRevocation). Handle these first,
+				// because key might have revocation coming from
+				// another key (designated revoke).
+				revocations = append(revocations, pkt)
+				continue
+			}
+
+			// These are signatures by other people on this key. Let's just ignore them
+			// from the beginning, since they shouldn't affect our key decoding one way
+			// or the other.
+			if pkt.IssuerKeyId != nil && *pkt.IssuerKeyId != e.PrimaryKey.KeyId {
+				continue
+			}
+
+			// If this is a signature made by the keyholder, and the signature has stubbed out
+			// critical packets, then *now* we need to bail out.
+			if e := pkt.StubbedOutCriticalError; e != nil {
+				return nil, e
+			}
+
+			// Next handle the case of a self-signature. According to RFC8440,
+			// Section 5.2.3.3, if there are several self-signatures,
+			// we should take the newer one.  If they were both created
+			// at the same time, but one of them has keyflags specified and the
+			// other doesn't, keep the one with the keyflags. We have actually
+			// seen this in the wild (see the 'Yield' test in read_test.go).
+			// If there is a tie, and both have the same value for FlagsValid,
+			// then "last writer wins."
+			//
+			// HOWEVER! We have seen yet more keys in the wild (see the 'Spiros'
+			// test in read_test.go), in which the later self-signature is a bunch
+			// of junk, and doesn't even specify key flags. Does it really make
+			// sense to overwrite reasonable key flags with the empty set? I'm not
+			// sure what that would be trying to achieve, and plus GPG seems to be
+			// ok with this situation, and ignores the later (empty) keyflag set.
+			// So further tighten our overwrite rules, and only allow the later
+			// signature to overwrite the earlier signature if so doing won't
+			// trash the key flags.
+			if current != nil &&
+				(current.SelfSignature == nil ||
+					(!pkt.CreationTime.Before(current.SelfSignature.CreationTime) &&
+						(pkt.FlagsValid || !current.SelfSignature.FlagsValid))) &&
+				(pkt.SigType == packet.SigTypePositiveCert || pkt.SigType == packet.SigTypeGenericCert) &&
+				pkt.IssuerKeyId != nil &&
+				*pkt.IssuerKeyId == e.PrimaryKey.KeyId {
+
+				if err = e.PrimaryKey.VerifyUserIdSignature(current.Name, e.PrimaryKey, pkt); err == nil {
+
+					current.SelfSignature = pkt
+
+					// NOTE(maxtaco) 2016.01.11
+					// Only register an identity once we've gotten a valid self-signature.
+					// It's possible therefore for us to throw away `current` in the case
+					// no valid self-signatures were found. That's OK as long as there are
+					// other identies that make sense.
+					//
+					// NOTE! We might later see a revocation for this very same UID, and it
+					// won't be undone. We've preserved this feature from the original
+					// Google OpenPGP we forked from.
+					e.Identities[current.Name] = current
+				} else {
+					// We really should warn that there was a failure here. Not raise an error
+					// since this really shouldn't be a fail-stop error.
+				}
+			} else if current != nil && pkt.SigType == packet.SigTypeIdentityRevocation {
+				if err = e.PrimaryKey.VerifyUserIdSignature(current.Name, e.PrimaryKey, pkt); err == nil {
+					// Note: we are not removing the identity from
+					// e.Identities. Caller can always filter by Revocation
+					// field to ignore revoked identities.
+					current.Revocation = pkt
+				}
+			} else if pkt.SigType == packet.SigTypeDirectSignature {
+				if err = e.PrimaryKey.VerifyRevocationSignature(e.PrimaryKey, pkt); err == nil {
+					if desig := pkt.DesignatedRevoker; desig != nil {
+						// If it's a designated revoker signature, take last 8 octects
+						// of fingerprint as Key ID and save it to designatedRevokers
+						// map. We consult this map later to see if a foreign
+						// revocation should be added to UnverifiedRevocations.
+						keyID := binary.BigEndian.Uint64(desig.Fingerprint[len(desig.Fingerprint)-8:])
+						designatedRevokers[keyID] = true
+					}
+				}
+			} else if current == nil {
+				// NOTE(maxtaco)
+				//
+				// See https://github.com/keybase/client/issues/2666
+				//
+				// There might have been a user attribute picture before this signature,
+				// in which case this is still a valid PGP key. In the future we might
+				// not ignore user attributes (like picture). But either way, it doesn't
+				// make sense to bail out here. Keep looking for other valid signatures.
+				//
+				// Used to be:
+				//    return nil, errors.StructuralError("signature packet found before user id packet")
+			} else {
+				current.Signatures = append(current.Signatures, pkt)
+			}
+		case *packet.PrivateKey:
+			if pkt.IsSubkey == false {
+				packets.Unread(p)
+				break EachPacket
+			}
+			err = addSubkey(e, packets, &pkt.PublicKey, pkt)
+			if err != nil {
+				return nil, err
+			}
+		case *packet.PublicKey:
+			if pkt.IsSubkey == false {
+				packets.Unread(p)
+				break EachPacket
+			}
+			err = addSubkey(e, packets, pkt, nil)
+			if err != nil {
+				return nil, err
+			}
+		default:
+			// we ignore unknown packets
+		}
+	}
+
+	if len(e.Identities) == 0 {
+		return nil, errors.StructuralError("entity without any identities")
+	}
+
+	for _, revocation := range revocations {
+		if revocation.IssuerKeyId == nil || *revocation.IssuerKeyId == e.PrimaryKey.KeyId {
+			// Key revokes itself, something that we can verify.
+			err = e.PrimaryKey.VerifyRevocationSignature(e.PrimaryKey, revocation)
+			if err == nil {
+				e.Revocations = append(e.Revocations, revocation)
+			} else {
+				return nil, errors.StructuralError("revocation signature signed by alternate key")
+			}
+		} else if revocation.IssuerKeyId != nil {
+			if _, ok := designatedRevokers[*revocation.IssuerKeyId]; ok {
+				// Revocation is done by certified designated revoker,
+				// but we can't verify the revocation.
+				e.UnverifiedRevocations = append(e.UnverifiedRevocations, revocation)
+			}
+		}
+	}
+
+	return e, nil
+}
+
+func addSubkey(e *Entity, packets *packet.Reader, pub *packet.PublicKey, priv *packet.PrivateKey) error {
+	var subKey Subkey
+	subKey.PublicKey = pub
+	subKey.PrivateKey = priv
+	var lastErr error
+	for {
+		p, err := packets.Next()
+		if err == io.EOF {
+			break
+		}
+		if err != nil {
+			return errors.StructuralError("subkey signature invalid: " + err.Error())
+		}
+		sig, ok := p.(*packet.Signature)
+		if !ok {
+			// Hit a non-signature packet, so assume we're up to the next key
+			packets.Unread(p)
+			break
+		}
+		if st := sig.SigType; st != packet.SigTypeSubkeyBinding && st != packet.SigTypeSubkeyRevocation {
+
+			// Note(maxtaco):
+			// We used to error out here, but instead, let's fast-forward past
+			// packets that are in the wrong place (like misplaced 0x13 signatures)
+			// until we get to one that works.  For a test case,
+			// see TestWithBadSubkeySignaturePackets.
+
+			continue
+		}
+		err = e.PrimaryKey.VerifyKeySignature(subKey.PublicKey, sig)
+		if err != nil {
+			// Non valid signature, so again, no need to abandon all hope, just continue;
+			// make a note of the error we hit.
+			lastErr = errors.StructuralError("subkey signature invalid: " + err.Error())
+			continue
+		}
+		switch sig.SigType {
+		case packet.SigTypeSubkeyBinding:
+			// Does the "new" sig set expiration to later date than
+			// "previous" sig?
+			if subKey.Sig == nil || subKey.Sig.ExpiresBeforeOther(sig) {
+				subKey.Sig = sig
+			}
+		case packet.SigTypeSubkeyRevocation:
+			// First writer wins
+			if subKey.Revocation == nil {
+				subKey.Revocation = sig
+			}
+		}
+	}
+	if subKey.Sig != nil {
+		e.Subkeys = append(e.Subkeys, subKey)
+	} else {
+		if lastErr == nil {
+			lastErr = errors.StructuralError("Subkey wasn't signed; expected a 'binding' signature")
+		}
+		e.BadSubkeys = append(e.BadSubkeys, BadSubkey{Subkey: subKey, Err: lastErr})
+	}
+	return nil
+}
+
+const defaultRSAKeyBits = 2048
+
+// NewEntity returns an Entity that contains a fresh RSA/RSA keypair with a
+// single identity composed of the given full name, comment and email, any of
+// which may be empty but must not contain any of "()<>\x00".
+// If config is nil, sensible defaults will be used.
+func NewEntity(name, comment, email string, config *packet.Config) (*Entity, error) {
+	currentTime := config.Now()
+
+	bits := defaultRSAKeyBits
+	if config != nil && config.RSABits != 0 {
+		bits = config.RSABits
+	}
+
+	uid := packet.NewUserId(name, comment, email)
+	if uid == nil {
+		return nil, errors.InvalidArgumentError("user id field contained invalid characters")
+	}
+	signingPriv, err := rsa.GenerateKey(config.Random(), bits)
+	if err != nil {
+		return nil, err
+	}
+	encryptingPriv, err := rsa.GenerateKey(config.Random(), bits)
+	if err != nil {
+		return nil, err
+	}
+
+	e := &Entity{
+		PrimaryKey: packet.NewRSAPublicKey(currentTime, &signingPriv.PublicKey),
+		PrivateKey: packet.NewRSAPrivateKey(currentTime, signingPriv),
+		Identities: make(map[string]*Identity),
+	}
+	isPrimaryId := true
+	e.Identities[uid.Id] = &Identity{
+		Name:   uid.Name,
+		UserId: uid,
+		SelfSignature: &packet.Signature{
+			CreationTime: currentTime,
+			SigType:      packet.SigTypePositiveCert,
+			PubKeyAlgo:   packet.PubKeyAlgoRSA,
+			Hash:         config.Hash(),
+			IsPrimaryId:  &isPrimaryId,
+			FlagsValid:   true,
+			FlagSign:     true,
+			FlagCertify:  true,
+			IssuerKeyId:  &e.PrimaryKey.KeyId,
+		},
+	}
+
+	e.Subkeys = make([]Subkey, 1)
+	e.Subkeys[0] = Subkey{
+		PublicKey:  packet.NewRSAPublicKey(currentTime, &encryptingPriv.PublicKey),
+		PrivateKey: packet.NewRSAPrivateKey(currentTime, encryptingPriv),
+		Sig: &packet.Signature{
+			CreationTime:              currentTime,
+			SigType:                   packet.SigTypeSubkeyBinding,
+			PubKeyAlgo:                packet.PubKeyAlgoRSA,
+			Hash:                      config.Hash(),
+			FlagsValid:                true,
+			FlagEncryptStorage:        true,
+			FlagEncryptCommunications: true,
+			IssuerKeyId:               &e.PrimaryKey.KeyId,
+		},
+	}
+	e.Subkeys[0].PublicKey.IsSubkey = true
+	e.Subkeys[0].PrivateKey.IsSubkey = true
+
+	return e, nil
+}
+
+// SerializePrivate serializes an Entity, including private key material, to
+// the given Writer. For now, it must only be used on an Entity returned from
+// NewEntity.
+// If config is nil, sensible defaults will be used.
+func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error) {
+	err = e.PrivateKey.Serialize(w)
+	if err != nil {
+		return
+	}
+	for _, ident := range e.Identities {
+		err = ident.UserId.Serialize(w)
+		if err != nil {
+			return
+		}
+		if e.PrivateKey.PrivateKey != nil {
+			err = ident.SelfSignature.SignUserId(ident.UserId.Id, e.PrimaryKey, e.PrivateKey, config)
+			if err != nil {
+				return
+			}
+		}
+		err = ident.SelfSignature.Serialize(w)
+		if err != nil {
+			return
+		}
+	}
+	for _, subkey := range e.Subkeys {
+		err = subkey.PrivateKey.Serialize(w)
+		if err != nil {
+			return
+		}
+		// Workaround shortcoming of SignKey(), which doesn't work to reverse-sign
+		// sub-signing keys. So if requested, just reuse the signatures already
+		// available to us (if we read this key from a keyring).
+		if e.PrivateKey.PrivateKey != nil && !config.ReuseSignatures() {
+			err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
+			if err != nil {
+				return
+			}
+		}
+
+		if subkey.Revocation != nil {
+			err = subkey.Revocation.Serialize(w)
+			if err != nil {
+				return
+			}
+		}
+
+		err = subkey.Sig.Serialize(w)
+		if err != nil {
+			return
+		}
+	}
+	return nil
+}
+
+// Serialize writes the public part of the given Entity to w. (No private
+// key material will be output).
+func (e *Entity) Serialize(w io.Writer) error {
+	err := e.PrimaryKey.Serialize(w)
+	if err != nil {
+		return err
+	}
+	for _, ident := range e.Identities {
+		err = ident.UserId.Serialize(w)
+		if err != nil {
+			return err
+		}
+		err = ident.SelfSignature.Serialize(w)
+		if err != nil {
+			return err
+		}
+		for _, sig := range ident.Signatures {
+			err = sig.Serialize(w)
+			if err != nil {
+				return err
+			}
+		}
+	}
+	for _, subkey := range e.Subkeys {
+		err = subkey.PublicKey.Serialize(w)
+		if err != nil {
+			return err
+		}
+
+		if subkey.Revocation != nil {
+			err = subkey.Revocation.Serialize(w)
+			if err != nil {
+				return err
+			}
+		}
+		err = subkey.Sig.Serialize(w)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// SignIdentity adds a signature to e, from signer, attesting that identity is
+// associated with e. The provided identity must already be an element of
+// e.Identities and the private key of signer must have been decrypted if
+// necessary.
+// If config is nil, sensible defaults will be used.
+func (e *Entity) SignIdentity(identity string, signer *Entity, config *packet.Config) error {
+	if signer.PrivateKey == nil {
+		return errors.InvalidArgumentError("signing Entity must have a private key")
+	}
+	if signer.PrivateKey.Encrypted {
+		return errors.InvalidArgumentError("signing Entity's private key must be decrypted")
+	}
+	ident, ok := e.Identities[identity]
+	if !ok {
+		return errors.InvalidArgumentError("given identity string not found in Entity")
+	}
+
+	sig := &packet.Signature{
+		SigType:      packet.SigTypeGenericCert,
+		PubKeyAlgo:   signer.PrivateKey.PubKeyAlgo,
+		Hash:         config.Hash(),
+		CreationTime: config.Now(),
+		IssuerKeyId:  &signer.PrivateKey.KeyId,
+	}
+	if err := sig.SignUserId(identity, e.PrimaryKey, signer.PrivateKey, config); err != nil {
+		return err
+	}
+	ident.Signatures = append(ident.Signatures, sig)
+	return nil
+}
+
+// CopySubkeyRevocations copies subkey revocations from the src Entity over
+// to the receiver entity. We need this because `gpg --export-secret-key` does
+// not appear to output subkey revocations.  In this case we need to manually
+// merge with the output of `gpg --export`.
+func (e *Entity) CopySubkeyRevocations(src *Entity) {
+	m := make(map[[20]byte]*packet.Signature)
+	for _, subkey := range src.Subkeys {
+		if subkey.Revocation != nil {
+			m[subkey.PublicKey.Fingerprint] = subkey.Revocation
+		}
+	}
+	for i, subkey := range e.Subkeys {
+		if r := m[subkey.PublicKey.Fingerprint]; r != nil {
+			e.Subkeys[i].Revocation = r
+		}
+	}
+}
+
+// CheckDesignatedRevokers will try to confirm any of designated
+// revocation of entity. For this function to work, revocation
+// issuer's key should be found in keyring. First successfully
+// verified designated revocation is returned along with the key that
+// verified it.
+func FindVerifiedDesignatedRevoke(keyring KeyRing, entity *Entity) (*packet.Signature, *Key) {
+	for _, sig := range entity.UnverifiedRevocations {
+		if sig.IssuerKeyId == nil {
+			continue
+		}
+
+		issuerKeyId := *sig.IssuerKeyId
+		issuerFingerprint := sig.IssuerFingerprint
+		keys := keyring.KeysByIdUsage(issuerKeyId, issuerFingerprint, packet.KeyFlagSign)
+		if len(keys) == 0 {
+			continue
+		}
+		for _, key := range keys {
+			err := key.PublicKey.VerifyRevocationSignature(entity.PrimaryKey, sig)
+			if err == nil {
+				return sig, &key
+			}
+		}
+	}
+
+	return nil, nil
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/compressed.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/compressed.go
similarity index 98%
rename from vendor/golang.org/x/crypto/openpgp/packet/compressed.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/compressed.go
index e8f0b5caa..f023fe533 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/compressed.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/compressed.go
@@ -8,9 +8,10 @@ import (
 	"compress/bzip2"
 	"compress/flate"
 	"compress/zlib"
-	"golang.org/x/crypto/openpgp/errors"
 	"io"
 	"strconv"
+
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // Compressed represents a compressed OpenPGP packet. The decompressed contents
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/config.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/config.go
similarity index 92%
rename from vendor/golang.org/x/crypto/openpgp/packet/config.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/config.go
index c76eecc96..f4125e189 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/config.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/config.go
@@ -46,6 +46,9 @@ type Config struct {
 	// RSABits is the number of bits in new RSA keys made with NewEntity.
 	// If zero, then 2048 bit keys are created.
 	RSABits int
+	// ReuseSignatures tells us to reuse existing Signatures
+	// on serialized output.
+	ReuseSignaturesOnSerialize bool
 }
 
 func (c *Config) Random() io.Reader {
@@ -89,3 +92,7 @@ func (c *Config) PasswordHashIterations() int {
 	}
 	return c.S2KCount
 }
+
+func (c *Config) ReuseSignatures() bool {
+	return c != nil && c.ReuseSignaturesOnSerialize
+}
diff --git a/vendor/github.com/keybase/go-crypto/openpgp/packet/ecdh.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/ecdh.go
new file mode 100644
index 000000000..41de661d7
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/ecdh.go
@@ -0,0 +1,104 @@
+package packet
+
+import (
+	"bytes"
+	"io"
+	"math/big"
+
+	"github.com/keybase/go-crypto/openpgp/ecdh"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
+)
+
+// ECDHKdfParams generates KDF parameters sequence for given
+// PublicKey. See https://tools.ietf.org/html/rfc6637#section-8
+func ECDHKdfParams(pub *PublicKey) []byte {
+	buf := new(bytes.Buffer)
+	oid := pub.ec.oid
+	buf.WriteByte(byte(len(oid)))
+	buf.Write(oid)
+	buf.WriteByte(18) // ECDH TYPE
+	pub.ecdh.serialize(buf)
+	buf.WriteString("Anonymous Sender    ")
+	buf.Write(pub.Fingerprint[:])
+	return buf.Bytes()
+}
+
+func decryptKeyECDH(priv *PrivateKey, X, Y *big.Int, C []byte) (out []byte, err error) {
+	ecdhpriv, ok := priv.PrivateKey.(*ecdh.PrivateKey)
+	if !ok {
+		return nil, errors.InvalidArgumentError("bad internal ECDH key")
+	}
+
+	Sx := ecdhpriv.DecryptShared(X, Y)
+
+	kdfParams := ECDHKdfParams(&priv.PublicKey)
+	hash, ok := s2k.HashIdToHash(byte(priv.ecdh.KdfHash))
+	if !ok {
+		return nil, errors.InvalidArgumentError("invalid hash id in private key")
+	}
+
+	key := ecdhpriv.KDF(Sx, kdfParams, hash)
+	keySize := CipherFunction(priv.ecdh.KdfAlgo).KeySize()
+
+	decrypted, err := ecdh.AESKeyUnwrap(key[:keySize], C)
+	if err != nil {
+		return nil, err
+	}
+
+	// We have to "read ahead" to discover real length of the
+	// encryption key and properly unpad buffer.
+	cipherFunc := CipherFunction(decrypted[0])
+	// +3 bytes = 1-byte cipher id and checksum 2-byte checksum.
+	out = ecdh.UnpadBuffer(decrypted, cipherFunc.KeySize()+3)
+	if out == nil {
+		return nil, errors.InvalidArgumentError("invalid padding while ECDH")
+	}
+	return out, nil
+}
+
+func serializeEncryptedKeyECDH(w io.Writer, rand io.Reader, header [10]byte, pub *PublicKey, keyBlock []byte) error {
+	ecdhpub := pub.PublicKey.(*ecdh.PublicKey)
+	kdfParams := ECDHKdfParams(pub)
+
+	hash, ok := s2k.HashIdToHash(byte(pub.ecdh.KdfHash))
+	if !ok {
+		return errors.InvalidArgumentError("invalid hash id in private key")
+	}
+
+	kdfKeySize := CipherFunction(pub.ecdh.KdfAlgo).KeySize()
+	Vx, Vy, C, err := ecdhpub.Encrypt(rand, kdfParams, keyBlock, hash, kdfKeySize)
+	if err != nil {
+		return err
+	}
+
+	mpis, mpiBitLen := ecdh.Marshal(ecdhpub.Curve, Vx, Vy)
+
+	packetLen := len(header) /* header length in bytes */
+	packetLen += 2 /* mpi length in bits */ + len(mpis)
+	packetLen += 1 /* ciphertext size in bytes */ + len(C)
+
+	err = serializeHeader(w, packetTypeEncryptedKey, packetLen)
+	if err != nil {
+		return err
+	}
+
+	_, err = w.Write(header[:])
+	if err != nil {
+		return err
+	}
+
+	_, err = w.Write([]byte{byte(mpiBitLen >> 8), byte(mpiBitLen)})
+	if err != nil {
+		return err
+	}
+
+	_, err = w.Write(mpis[:])
+	if err != nil {
+		return err
+	}
+
+	w.Write([]byte{byte(len(C))})
+	w.Write(C[:])
+	return nil
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/encrypted_key.go
similarity index 86%
rename from vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/encrypted_key.go
index 266840d05..58692ec8b 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/encrypted_key.go
@@ -5,14 +5,15 @@
 package packet
 
 import (
-	"crypto/rsa"
 	"encoding/binary"
 	"io"
 	"math/big"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/elgamal"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/ecdh"
+	"github.com/keybase/go-crypto/openpgp/elgamal"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/rsa"
 )
 
 const encryptedKeyVersion = 3
@@ -26,6 +27,7 @@ type EncryptedKey struct {
 	Key        []byte         // only valid after a successful Decrypt
 
 	encryptedMPI1, encryptedMPI2 parsedMPI
+	ecdh_C                       []byte
 }
 
 func (e *EncryptedKey) parse(r io.Reader) (err error) {
@@ -48,9 +50,25 @@ func (e *EncryptedKey) parse(r io.Reader) (err error) {
 			return
 		}
 		e.encryptedMPI2.bytes, e.encryptedMPI2.bitLength, err = readMPI(r)
+	case PubKeyAlgoECDH:
+		e.encryptedMPI1.bytes, e.encryptedMPI1.bitLength, err = readMPI(r)
+		if err != nil {
+			return err
+		}
+		_, err = readFull(r, buf[:1]) // read C len (1 byte)
+		if err != nil {
+			return err
+		}
+		e.ecdh_C = make([]byte, int(buf[0]))
+		_, err = readFull(r, e.ecdh_C)
 	}
+
+	if err != nil {
+		return err
+	}
+
 	_, err = consumeAll(r)
-	return
+	return err
 }
 
 func checksumKeyMaterial(key []byte) uint16 {
@@ -77,6 +95,13 @@ func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error {
 		c1 := new(big.Int).SetBytes(e.encryptedMPI1.bytes)
 		c2 := new(big.Int).SetBytes(e.encryptedMPI2.bytes)
 		b, err = elgamal.Decrypt(priv.PrivateKey.(*elgamal.PrivateKey), c1, c2)
+	case PubKeyAlgoECDH:
+		// Note: Unmarshal checks if point is on the curve.
+		c1, c2 := ecdh.Unmarshal(priv.PrivateKey.(*ecdh.PrivateKey).Curve, e.encryptedMPI1.bytes)
+		if c1 == nil {
+			return errors.InvalidArgumentError("failed to parse EC point for encryption key")
+		}
+		b, err = decryptKeyECDH(priv, c1, c2, e.ecdh_C)
 	default:
 		err = errors.InvalidArgumentError("cannot decrypted encrypted session key with private key of type " + strconv.Itoa(int(priv.PubKeyAlgo)))
 	}
@@ -147,6 +172,8 @@ func SerializeEncryptedKey(w io.Writer, pub *PublicKey, cipherFunc CipherFunctio
 		return serializeEncryptedKeyRSA(w, config.Random(), buf, pub.PublicKey.(*rsa.PublicKey), keyBlock)
 	case PubKeyAlgoElGamal:
 		return serializeEncryptedKeyElGamal(w, config.Random(), buf, pub.PublicKey.(*elgamal.PublicKey), keyBlock)
+	case PubKeyAlgoECDH:
+		return serializeEncryptedKeyECDH(w, config.Random(), buf, pub, keyBlock)
 	case PubKeyAlgoDSA, PubKeyAlgoRSASignOnly:
 		return errors.InvalidArgumentError("cannot encrypt to public key of type " + strconv.Itoa(int(pub.PubKeyAlgo)))
 	}
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/literal.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/literal.go
similarity index 100%
rename from vendor/golang.org/x/crypto/openpgp/packet/literal.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/literal.go
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/ocfb.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/ocfb.go
similarity index 100%
rename from vendor/golang.org/x/crypto/openpgp/packet/ocfb.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/ocfb.go
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/one_pass_signature.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/one_pass_signature.go
similarity index 94%
rename from vendor/golang.org/x/crypto/openpgp/packet/one_pass_signature.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/one_pass_signature.go
index 171350339..af404bb10 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/one_pass_signature.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/one_pass_signature.go
@@ -7,10 +7,11 @@ package packet
 import (
 	"crypto"
 	"encoding/binary"
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
 	"io"
 	"strconv"
+
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
 )
 
 // OnePassSignature represents a one-pass signature packet. See RFC 4880,
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/opaque.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/opaque.go
similarity index 98%
rename from vendor/golang.org/x/crypto/openpgp/packet/opaque.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/opaque.go
index 456d807f2..cdeea012f 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/opaque.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/opaque.go
@@ -9,7 +9,7 @@ import (
 	"io"
 	"io/ioutil"
 
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // OpaquePacket represents an OpenPGP packet as raw, unparsed data. This is
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/packet.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/packet.go
similarity index 90%
rename from vendor/golang.org/x/crypto/openpgp/packet/packet.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/packet.go
index 3eded93f0..48854436f 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/packet.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/packet.go
@@ -4,17 +4,19 @@
 
 // Package packet implements parsing and serialization of OpenPGP packets, as
 // specified in RFC 4880.
-package packet // import "golang.org/x/crypto/openpgp/packet"
+package packet // import "github.com/keybase/go-crypto/openpgp/packet"
 
 import (
 	"bufio"
 	"crypto/aes"
 	"crypto/cipher"
 	"crypto/des"
-	"golang.org/x/crypto/cast5"
-	"golang.org/x/crypto/openpgp/errors"
+	"crypto/elliptic"
 	"io"
 	"math/big"
+
+	"github.com/keybase/go-crypto/cast5"
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // readFull is the same as io.ReadFull except that reading zero bytes returns
@@ -273,6 +275,8 @@ func consumeAll(r io.Reader) (n int64, err error) {
 			return
 		}
 	}
+
+	panic("unreachable")
 }
 
 // packetType represents the numeric ids of the different OpenPGP packet types. See
@@ -383,17 +387,18 @@ func Read(r io.Reader) (p Packet, err error) {
 type SignatureType uint8
 
 const (
-	SigTypeBinary            SignatureType = 0
-	SigTypeText                            = 1
-	SigTypeGenericCert                     = 0x10
-	SigTypePersonaCert                     = 0x11
-	SigTypeCasualCert                      = 0x12
-	SigTypePositiveCert                    = 0x13
-	SigTypeSubkeyBinding                   = 0x18
-	SigTypePrimaryKeyBinding               = 0x19
-	SigTypeDirectSignature                 = 0x1F
-	SigTypeKeyRevocation                   = 0x20
-	SigTypeSubkeyRevocation                = 0x28
+	SigTypeBinary             SignatureType = 0
+	SigTypeText                             = 1
+	SigTypeGenericCert                      = 0x10
+	SigTypePersonaCert                      = 0x11
+	SigTypeCasualCert                       = 0x12
+	SigTypePositiveCert                     = 0x13
+	SigTypeSubkeyBinding                    = 0x18
+	SigTypePrimaryKeyBinding                = 0x19
+	SigTypeDirectSignature                  = 0x1F
+	SigTypeKeyRevocation                    = 0x20
+	SigTypeSubkeyRevocation                 = 0x28
+	SigTypeIdentityRevocation               = 0x30
 )
 
 // PublicKeyAlgorithm represents the different public key system specified for
@@ -410,13 +415,15 @@ const (
 	// RFC 6637, Section 5.
 	PubKeyAlgoECDH  PublicKeyAlgorithm = 18
 	PubKeyAlgoECDSA PublicKeyAlgorithm = 19
+	// RFC -1
+	PubKeyAlgoEdDSA PublicKeyAlgorithm = 22
 )
 
 // CanEncrypt returns true if it's possible to encrypt a message to a public
 // key of the given type.
 func (pka PublicKeyAlgorithm) CanEncrypt() bool {
 	switch pka {
-	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoElGamal:
+	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoElGamal, PubKeyAlgoECDH:
 		return true
 	}
 	return false
@@ -426,7 +433,7 @@ func (pka PublicKeyAlgorithm) CanEncrypt() bool {
 // sign a message.
 func (pka PublicKeyAlgorithm) CanSign() bool {
 	switch pka {
-	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA:
+	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA:
 		return true
 	}
 	return false
@@ -520,6 +527,25 @@ func writeMPI(w io.Writer, bitLength uint16, mpiBytes []byte) (err error) {
 	return
 }
 
+func WritePaddedBigInt(w io.Writer, length int, X *big.Int) (n int, err error) {
+	bytes := X.Bytes()
+	n1, err := w.Write(make([]byte, length-len(bytes)))
+	if err != nil {
+		return n1, err
+	}
+	n2, err := w.Write(bytes)
+	if err != nil {
+		return n2, err
+	}
+	return (n1 + n2), err
+}
+
+// Minimum number of bytes to fit the curve coordinates. All
+// coordinates have to be 0-padded to this length.
+func mpiPointByteLength(curve elliptic.Curve) int {
+	return (curve.Params().P.BitLen() + 7) / 8
+}
+
 // writeBig serializes a *big.Int to w.
 func writeBig(w io.Writer, i *big.Int) error {
 	return writeMPI(w, uint16(i.BitLen()), i.Bytes())
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/private_key.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/private_key.go
similarity index 53%
rename from vendor/golang.org/x/crypto/openpgp/packet/private_key.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/private_key.go
index 34734cc63..27974e782 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/private_key.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/private_key.go
@@ -6,21 +6,23 @@ package packet
 
 import (
 	"bytes"
-	"crypto"
 	"crypto/cipher"
 	"crypto/dsa"
 	"crypto/ecdsa"
-	"crypto/rsa"
 	"crypto/sha1"
+	"fmt"
 	"io"
 	"io/ioutil"
 	"math/big"
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/elgamal"
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/ed25519"
+	"github.com/keybase/go-crypto/openpgp/ecdh"
+	"github.com/keybase/go-crypto/openpgp/elgamal"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/rsa"
 )
 
 // PrivateKey represents a possibly encrypted private key. See RFC 4880,
@@ -31,9 +33,32 @@ type PrivateKey struct {
 	encryptedData []byte
 	cipher        CipherFunction
 	s2k           func(out, in []byte)
-	PrivateKey    interface{} // An *{rsa|dsa|ecdsa}.PrivateKey or a crypto.Signer.
+	PrivateKey    interface{} // An *rsa.PrivateKey or *dsa.PrivateKey.
 	sha1Checksum  bool
 	iv            []byte
+	s2kHeader     []byte
+}
+
+type EdDSAPrivateKey struct {
+	PrivateKey
+	seed parsedMPI
+}
+
+func (e *EdDSAPrivateKey) Sign(digest []byte) (R, S []byte, err error) {
+	r := bytes.NewReader(e.seed.bytes)
+	publicKey, privateKey, err := ed25519.GenerateKey(r)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	if !bytes.Equal(publicKey, e.PublicKey.edk.p.bytes[1:]) { // [1:] because [0] is 0x40 mpi header
+		return nil, nil, errors.UnsupportedError("EdDSA: Private key does not match public key.")
+	}
+
+	sig := ed25519.Sign(privateKey, digest)
+
+	sigLen := ed25519.SignatureSize / 2
+	return sig[:sigLen], sig[sigLen:], nil
 }
 
 func NewRSAPrivateKey(currentTime time.Time, priv *rsa.PrivateKey) *PrivateKey {
@@ -64,23 +89,6 @@ func NewECDSAPrivateKey(currentTime time.Time, priv *ecdsa.PrivateKey) *PrivateK
 	return pk
 }
 
-// NewSignerPrivateKey creates a sign-only PrivateKey from a crypto.Signer that
-// implements RSA or ECDSA.
-func NewSignerPrivateKey(currentTime time.Time, signer crypto.Signer) *PrivateKey {
-	pk := new(PrivateKey)
-	switch pubkey := signer.Public().(type) {
-	case rsa.PublicKey:
-		pk.PublicKey = *NewRSAPublicKey(currentTime, &pubkey)
-		pk.PubKeyAlgo = PubKeyAlgoRSASignOnly
-	case ecdsa.PublicKey:
-		pk.PublicKey = *NewECDSAPublicKey(currentTime, &pubkey)
-	default:
-		panic("openpgp: unknown crypto.Signer type in NewSignerPrivateKey")
-	}
-	pk.PrivateKey = signer
-	return pk
-}
-
 func (pk *PrivateKey) parse(r io.Reader) (err error) {
 	err = (&pk.PublicKey).parse(r)
 	if err != nil {
@@ -112,10 +120,16 @@ func (pk *PrivateKey) parse(r io.Reader) (err error) {
 		if s2kType == 254 {
 			pk.sha1Checksum = true
 		}
+		// S2K == nil implies that we got a "GNU Dummy" S2K. For instance,
+		// because our master secret key is on a USB key in a vault somewhere.
+		// In that case, there is no further data to consume here.
+		if pk.s2k == nil {
+			pk.Encrypted = false
+			return
+		}
 	default:
 		return errors.UnsupportedError("deprecated s2k function in private key")
 	}
-
 	if pk.Encrypted {
 		blockSize := pk.cipher.blockSize()
 		if blockSize == 0 {
@@ -148,31 +162,105 @@ func mod64kHash(d []byte) uint16 {
 	return h
 }
 
+// Encrypt is the counterpart to the Decrypt() method below. It encrypts
+// the private key with the provided passphrase. If config is nil, then
+// the standard, and sensible, defaults apply.
+//
+// A key will be derived from the given passphrase using S2K Specifier
+// Type 3 (Iterated + Salted, see RFC-4880 Sec. 3.7.1.3). This choice
+// is hardcoded in s2k.Serialize(). S2KCount is hardcoded to 0, which is
+// equivalent to 65536. And the hash algorithm for key-derivation can be
+// set with config. The encrypted PrivateKey, using the algorithm specified
+// in config (if provided), is written out to the encryptedData member.
+// When Serialize() is called, this encryptedData member will be
+// serialized, using S2K Usage value of 254, and thus SHA1 checksum.
+func (pk *PrivateKey) Encrypt(passphrase []byte, config *Config) (err error) {
+	if pk.PrivateKey == nil {
+		return errors.InvalidArgumentError("there is no private key to encrypt")
+	}
+
+	pk.sha1Checksum = true
+	pk.cipher = config.Cipher()
+	s2kConfig := s2k.Config{
+		Hash:     config.Hash(),
+		S2KCount: 0,
+	}
+	s2kBuf := bytes.NewBuffer(nil)
+	derivedKey := make([]byte, pk.cipher.KeySize())
+	err = s2k.Serialize(s2kBuf, derivedKey, config.Random(), passphrase, &s2kConfig)
+	if err != nil {
+		return err
+	}
+
+	pk.s2kHeader = s2kBuf.Bytes()
+	// No good way to set pk.s2k but to call s2k.Parse(),
+	// even though we have all the information here, but
+	// most of the functions needed are private to s2k.
+	pk.s2k, err = s2k.Parse(s2kBuf)
+	pk.iv = make([]byte, pk.cipher.blockSize())
+	if _, err = config.Random().Read(pk.iv); err != nil {
+		return err
+	}
+
+	privateKeyBuf := bytes.NewBuffer(nil)
+	if err = pk.serializePrivateKey(privateKeyBuf); err != nil {
+		return err
+	}
+
+	checksum := sha1.Sum(privateKeyBuf.Bytes())
+	if _, err = privateKeyBuf.Write(checksum[:]); err != nil {
+		return err
+	}
+
+	pkData := privateKeyBuf.Bytes()
+	block := pk.cipher.new(derivedKey)
+	pk.encryptedData = make([]byte, len(pkData))
+	cfb := cipher.NewCFBEncrypter(block, pk.iv)
+	cfb.XORKeyStream(pk.encryptedData, pkData)
+	pk.Encrypted = true
+	return nil
+}
+
 func (pk *PrivateKey) Serialize(w io.Writer) (err error) {
-	// TODO(agl): support encrypted private keys
 	buf := bytes.NewBuffer(nil)
 	err = pk.PublicKey.serializeWithoutHeaders(buf)
 	if err != nil {
 		return
 	}
-	buf.WriteByte(0 /* no encryption */)
 
 	privateKeyBuf := bytes.NewBuffer(nil)
 
-	switch priv := pk.PrivateKey.(type) {
-	case *rsa.PrivateKey:
-		err = serializeRSAPrivateKey(privateKeyBuf, priv)
-	case *dsa.PrivateKey:
-		err = serializeDSAPrivateKey(privateKeyBuf, priv)
-	case *elgamal.PrivateKey:
-		err = serializeElGamalPrivateKey(privateKeyBuf, priv)
-	case *ecdsa.PrivateKey:
-		err = serializeECDSAPrivateKey(privateKeyBuf, priv)
-	default:
-		err = errors.InvalidArgumentError("unknown private key type")
-	}
-	if err != nil {
-		return
+	if pk.PrivateKey == nil {
+		_, err = buf.Write([]byte{
+			254,           // SHA-1 Convention
+			9,             // Encryption scheme (AES256)
+			101,           // GNU Extensions
+			2,             // Hash value (SHA1)
+			'G', 'N', 'U', // "GNU" as a string
+			1, // Extension type 1001 (minus 1000)
+		})
+	} else if pk.Encrypted {
+		_, err = buf.Write([]byte{
+			254,             // SHA-1 Convention
+			byte(pk.cipher), // Encryption scheme
+		})
+		if err != nil {
+			return err
+		}
+		if _, err = buf.Write(pk.s2kHeader); err != nil {
+			return err
+		}
+		if _, err = buf.Write(pk.iv); err != nil {
+			return err
+		}
+		if _, err = privateKeyBuf.Write(pk.encryptedData); err != nil {
+			return err
+		}
+	} else {
+		buf.WriteByte(0 /* no encryption */)
+		if err = pk.serializePrivateKey(privateKeyBuf); err != nil {
+			return err
+		}
 	}
 
 	ptype := packetTypePrivateKey
@@ -181,7 +269,11 @@ func (pk *PrivateKey) Serialize(w io.Writer) (err error) {
 	if pk.IsSubkey {
 		ptype = packetTypePrivateSubkey
 	}
-	err = serializeHeader(w, ptype, len(contents)+len(privateKeyBytes)+2)
+	totalLen := len(contents) + len(privateKeyBytes)
+	if !pk.Encrypted {
+		totalLen += 2
+	}
+	err = serializeHeader(w, ptype, totalLen)
 	if err != nil {
 		return
 	}
@@ -194,15 +286,38 @@ func (pk *PrivateKey) Serialize(w io.Writer) (err error) {
 		return
 	}
 
-	checksum := mod64kHash(privateKeyBytes)
-	var checksumBytes [2]byte
-	checksumBytes[0] = byte(checksum >> 8)
-	checksumBytes[1] = byte(checksum)
-	_, err = w.Write(checksumBytes[:])
+	if len(privateKeyBytes) > 0 && !pk.Encrypted {
+		checksum := mod64kHash(privateKeyBytes)
+		var checksumBytes [2]byte
+		checksumBytes[0] = byte(checksum >> 8)
+		checksumBytes[1] = byte(checksum)
+		_, err = w.Write(checksumBytes[:])
+	}
 
 	return
 }
 
+func (pk *PrivateKey) serializePrivateKey(w io.Writer) (err error) {
+	switch priv := pk.PrivateKey.(type) {
+	case *rsa.PrivateKey:
+		err = serializeRSAPrivateKey(w, priv)
+	case *dsa.PrivateKey:
+		err = serializeDSAPrivateKey(w, priv)
+	case *elgamal.PrivateKey:
+		err = serializeElGamalPrivateKey(w, priv)
+	case *ecdsa.PrivateKey:
+		err = serializeECDSAPrivateKey(w, priv)
+	case *ecdh.PrivateKey:
+		err = serializeECDHPrivateKey(w, priv)
+	case *EdDSAPrivateKey:
+		err = serializeEdDSAPrivateKey(w, priv)
+	default:
+		err = errors.InvalidArgumentError("unknown private key type")
+	}
+
+	return err
+}
+
 func serializeRSAPrivateKey(w io.Writer, priv *rsa.PrivateKey) error {
 	err := writeBig(w, priv.D)
 	if err != nil {
@@ -231,11 +346,23 @@ func serializeECDSAPrivateKey(w io.Writer, priv *ecdsa.PrivateKey) error {
 	return writeBig(w, priv.D)
 }
 
+func serializeECDHPrivateKey(w io.Writer, priv *ecdh.PrivateKey) error {
+	return writeBig(w, priv.X)
+}
+
+func serializeEdDSAPrivateKey(w io.Writer, priv *EdDSAPrivateKey) error {
+	return writeMPI(w, priv.seed.bitLength, priv.seed.bytes)
+}
+
 // Decrypt decrypts an encrypted private key using a passphrase.
 func (pk *PrivateKey) Decrypt(passphrase []byte) error {
 	if !pk.Encrypted {
 		return nil
 	}
+	// For GNU Dummy S2K, there's no key here, so don't do anything.
+	if pk.s2k == nil {
+		return nil
+	}
 
 	key := make([]byte, pk.cipher.KeySize())
 	pk.s2k(key, passphrase)
@@ -284,6 +411,10 @@ func (pk *PrivateKey) parsePrivateKey(data []byte) (err error) {
 		return pk.parseElGamalPrivateKey(data)
 	case PubKeyAlgoECDSA:
 		return pk.parseECDSAPrivateKey(data)
+	case PubKeyAlgoECDH:
+		return pk.parseECDHPrivateKey(data)
+	case PubKeyAlgoEdDSA:
+		return pk.parseEdDSAPrivateKey(data)
 	}
 	panic("impossible")
 }
@@ -360,8 +491,10 @@ func (pk *PrivateKey) parseElGamalPrivateKey(data []byte) (err error) {
 	return nil
 }
 
-func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) {
-	ecdsaPub := pk.PublicKey.PublicKey.(*ecdsa.PublicKey)
+func (pk *PrivateKey) parseECDHPrivateKey(data []byte) (err error) {
+	pub := pk.PublicKey.PublicKey.(*ecdh.PublicKey)
+	priv := new(ecdh.PrivateKey)
+	priv.PublicKey = *pub
 
 	buf := bytes.NewBuffer(data)
 	d, _, err := readMPI(buf)
@@ -369,10 +502,47 @@ func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) {
 		return
 	}
 
-	pk.PrivateKey = &ecdsa.PrivateKey{
-		PublicKey: *ecdsaPub,
-		D:         new(big.Int).SetBytes(d),
+	priv.X = new(big.Int).SetBytes(d)
+	pk.PrivateKey = priv
+	pk.Encrypted = false
+	pk.encryptedData = nil
+	return nil
+}
+
+func (pk *PrivateKey) parseECDSAPrivateKey(data []byte) (err error) {
+	ecdsaPub := pk.PublicKey.PublicKey.(*ecdsa.PublicKey)
+	ecdsaPriv := new(ecdsa.PrivateKey)
+	ecdsaPriv.PublicKey = *ecdsaPub
+
+	buf := bytes.NewBuffer(data)
+	d, _, err := readMPI(buf)
+	if err != nil {
+		return
 	}
+
+	ecdsaPriv.D = new(big.Int).SetBytes(d)
+	pk.PrivateKey = ecdsaPriv
+	pk.Encrypted = false
+	pk.encryptedData = nil
+
+	return nil
+}
+
+func (pk *PrivateKey) parseEdDSAPrivateKey(data []byte) (err error) {
+	eddsaPriv := new(EdDSAPrivateKey)
+	eddsaPriv.PublicKey = pk.PublicKey
+
+	buf := bytes.NewBuffer(data)
+	eddsaPriv.seed.bytes, eddsaPriv.seed.bitLength, err = readMPI(buf)
+	if err != nil {
+		return err
+	}
+
+	if bLen := len(eddsaPriv.seed.bytes); bLen != 32 { // 32 bytes private part of ed25519 key.
+		return errors.UnsupportedError(fmt.Sprintf("Unexpected EdDSA private key length: %d", bLen))
+	}
+
+	pk.PrivateKey = eddsaPriv
 	pk.Encrypted = false
 	pk.encryptedData = nil
 
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/public_key.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/public_key.go
similarity index 73%
rename from vendor/golang.org/x/crypto/openpgp/packet/public_key.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/public_key.go
index ead26233d..f9760177e 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/public_key.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/public_key.go
@@ -10,7 +10,6 @@ import (
 	"crypto/dsa"
 	"crypto/ecdsa"
 	"crypto/elliptic"
-	"crypto/rsa"
 	"crypto/sha1"
 	_ "crypto/sha256"
 	_ "crypto/sha512"
@@ -22,8 +21,13 @@ import (
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/elgamal"
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/brainpool"
+	"github.com/keybase/go-crypto/curve25519"
+	"github.com/keybase/go-crypto/ed25519"
+	"github.com/keybase/go-crypto/openpgp/ecdh"
+	"github.com/keybase/go-crypto/openpgp/elgamal"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/rsa"
 )
 
 var (
@@ -33,9 +37,19 @@ var (
 	oidCurveP384 []byte = []byte{0x2B, 0x81, 0x04, 0x00, 0x22}
 	// NIST curve P-521
 	oidCurveP521 []byte = []byte{0x2B, 0x81, 0x04, 0x00, 0x23}
+	// Brainpool curve P-256r1
+	oidCurveP256r1 []byte = []byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x07}
+	// Brainpool curve P-384r1
+	oidCurveP384r1 []byte = []byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0B}
+	// Brainpool curve P-512r1
+	oidCurveP512r1 []byte = []byte{0x2B, 0x24, 0x03, 0x03, 0x02, 0x08, 0x01, 0x01, 0x0D}
+	// EdDSA
+	oidEdDSA []byte = []byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0xDA, 0x47, 0x0F, 0x01}
+	// cv25519
+	oidCurve25519 []byte = []byte{0x2B, 0x06, 0x01, 0x04, 0x01, 0x97, 0x55, 0x01, 0x05, 0x01}
 )
 
-const maxOIDLength = 8
+const maxOIDLength = 10
 
 // ecdsaKey stores the algorithm-specific fields for ECDSA keys.
 // as defined in RFC 6637, Section 9.
@@ -46,6 +60,38 @@ type ecdsaKey struct {
 	p parsedMPI
 }
 
+type edDSAkey struct {
+	ecdsaKey
+}
+
+func copyFrontFill(dst, src []byte, length int) int {
+	if srcLen := len(src); srcLen < length {
+		return copy(dst[length-srcLen:], src[:])
+	} else {
+		return copy(dst[:], src[:])
+	}
+}
+
+func (e *edDSAkey) Verify(payload []byte, r parsedMPI, s parsedMPI) bool {
+	const halfSigSize = ed25519.SignatureSize / 2
+	var sig [ed25519.SignatureSize]byte
+
+	// NOTE: The first byte is 0x40 - MPI header
+	// TODO: Maybe clean the code up and use 0x40 as a header when
+	// reading and keep only actual number in p field. Find out how
+	// other MPIs are stored.
+	key := e.p.bytes[1:]
+
+	// Note: it may happen that R + S do not form 64-byte signature buffer that
+	// ed25519 expects, but because we copy it over to an array of exact size,
+	// we will always pass correctly sized slice to Verify. Slice too short
+	// would make ed25519 panic().
+	copyFrontFill(sig[:halfSigSize], r.bytes, halfSigSize)
+	copyFrontFill(sig[halfSigSize:], s.bytes, halfSigSize)
+
+	return ed25519.Verify(key, payload, sig[:])
+}
+
 // parseOID reads the OID for the curve as defined in RFC 6637, Section 9.
 func parseOID(r io.Reader) (oid []byte, err error) {
 	buf := make([]byte, maxOIDLength)
@@ -67,7 +113,7 @@ func (f *ecdsaKey) parse(r io.Reader) (err error) {
 		return err
 	}
 	f.p.bytes, f.p.bitLength, err = readMPI(r)
-	return
+	return err
 }
 
 func (f *ecdsaKey) serialize(w io.Writer) (err error) {
@@ -80,17 +126,34 @@ func (f *ecdsaKey) serialize(w io.Writer) (err error) {
 	return writeMPIs(w, f.p)
 }
 
+func getCurveByOid(oid []byte) elliptic.Curve {
+	switch {
+	case bytes.Equal(oid, oidCurveP256):
+		return elliptic.P256()
+	case bytes.Equal(oid, oidCurveP384):
+		return elliptic.P384()
+	case bytes.Equal(oid, oidCurveP521):
+		return elliptic.P521()
+	case bytes.Equal(oid, oidCurveP256r1):
+		return brainpool.P256r1()
+	case bytes.Equal(oid, oidCurveP384r1):
+		return brainpool.P384r1()
+	case bytes.Equal(oid, oidCurveP512r1):
+		return brainpool.P512r1()
+	case bytes.Equal(oid, oidCurve25519):
+		return curve25519.Cv25519()
+	default:
+		return nil
+	}
+}
+
 func (f *ecdsaKey) newECDSA() (*ecdsa.PublicKey, error) {
-	var c elliptic.Curve
-	if bytes.Equal(f.oid, oidCurveP256) {
-		c = elliptic.P256()
-	} else if bytes.Equal(f.oid, oidCurveP384) {
-		c = elliptic.P384()
-	} else if bytes.Equal(f.oid, oidCurveP521) {
-		c = elliptic.P521()
-	} else {
+	var c = getCurveByOid(f.oid)
+	// Curve25519 should not be used in ECDSA.
+	if c == nil || bytes.Equal(f.oid, oidCurve25519) {
 		return nil, errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", f.oid))
 	}
+	// Note: Unmarshal already checks if point is on curve.
 	x, y := elliptic.Unmarshal(c, f.p.bytes)
 	if x == nil {
 		return nil, errors.UnsupportedError("failed to parse EC point")
@@ -98,6 +161,20 @@ func (f *ecdsaKey) newECDSA() (*ecdsa.PublicKey, error) {
 	return &ecdsa.PublicKey{Curve: c, X: x, Y: y}, nil
 }
 
+func (f *ecdsaKey) newECDH() (*ecdh.PublicKey, error) {
+	var c = getCurveByOid(f.oid)
+	if c == nil {
+		return nil, errors.UnsupportedError(fmt.Sprintf("unsupported oid: %x", f.oid))
+	}
+	// ecdh.Unmarshal handles unmarshaling for all curve types. It
+	// also checks if point is on curve.
+	x, y := ecdh.Unmarshal(c, f.p.bytes)
+	if x == nil {
+		return nil, errors.UnsupportedError("failed to parse EC point")
+	}
+	return &ecdh.PublicKey{Curve: c, X: x, Y: y}, nil
+}
+
 func (f *ecdsaKey) byteLen() int {
 	return 1 + len(f.oid) + 2 + len(f.p.bytes)
 }
@@ -163,6 +240,9 @@ type PublicKey struct {
 	// RFC 6637 fields
 	ec   *ecdsaKey
 	ecdh *ecdhKdf
+
+	// EdDSA fields (no RFC available), uses ecdsa scaffolding
+	edk *edDSAkey
 }
 
 // signingKey provides a convenient abstraction over signature verification
@@ -172,21 +252,28 @@ type signingKey interface {
 	serializeWithoutHeaders(io.Writer) error
 }
 
-func fromBig(n *big.Int) parsedMPI {
+func FromBig(n *big.Int) parsedMPI {
 	return parsedMPI{
 		bytes:     n.Bytes(),
 		bitLength: uint16(n.BitLen()),
 	}
 }
 
+func FromBytes(bytes []byte) parsedMPI {
+	return parsedMPI{
+		bytes:     bytes,
+		bitLength: uint16(8 * len(bytes)),
+	}
+}
+
 // NewRSAPublicKey returns a PublicKey that wraps the given rsa.PublicKey.
 func NewRSAPublicKey(creationTime time.Time, pub *rsa.PublicKey) *PublicKey {
 	pk := &PublicKey{
 		CreationTime: creationTime,
 		PubKeyAlgo:   PubKeyAlgoRSA,
 		PublicKey:    pub,
-		n:            fromBig(pub.N),
-		e:            fromBig(big.NewInt(int64(pub.E))),
+		n:            FromBig(pub.N),
+		e:            FromBig(big.NewInt(int64(pub.E))),
 	}
 
 	pk.setFingerPrintAndKeyId()
@@ -199,25 +286,38 @@ func NewDSAPublicKey(creationTime time.Time, pub *dsa.PublicKey) *PublicKey {
 		CreationTime: creationTime,
 		PubKeyAlgo:   PubKeyAlgoDSA,
 		PublicKey:    pub,
-		p:            fromBig(pub.P),
-		q:            fromBig(pub.Q),
-		g:            fromBig(pub.G),
-		y:            fromBig(pub.Y),
+		p:            FromBig(pub.P),
+		q:            FromBig(pub.Q),
+		g:            FromBig(pub.G),
+		y:            FromBig(pub.Y),
 	}
 
 	pk.setFingerPrintAndKeyId()
 	return pk
 }
 
+// check EdDSA public key material.
+// There is currently no RFC for it, but it doesn't mean it's not
+// implemented or in use.
+func (e *edDSAkey) check() error {
+	if !bytes.Equal(e.oid, oidEdDSA) {
+		return errors.UnsupportedError(fmt.Sprintf("Bad OID for EdDSA key: %v", e.oid))
+	}
+	if bLen := len(e.p.bytes); bLen != 33 { // 32 bytes for ed25519 key and 1 byte for 0x40 header
+		return errors.UnsupportedError(fmt.Sprintf("Unexpected EdDSA public key length: %d", bLen))
+	}
+	return nil
+}
+
 // NewElGamalPublicKey returns a PublicKey that wraps the given elgamal.PublicKey.
 func NewElGamalPublicKey(creationTime time.Time, pub *elgamal.PublicKey) *PublicKey {
 	pk := &PublicKey{
 		CreationTime: creationTime,
 		PubKeyAlgo:   PubKeyAlgoElGamal,
 		PublicKey:    pub,
-		p:            fromBig(pub.P),
-		g:            fromBig(pub.G),
-		y:            fromBig(pub.Y),
+		p:            FromBig(pub.P),
+		g:            FromBig(pub.G),
+		y:            FromBig(pub.Y),
 	}
 
 	pk.setFingerPrintAndKeyId()
@@ -231,7 +331,6 @@ func NewECDSAPublicKey(creationTime time.Time, pub *ecdsa.PublicKey) *PublicKey
 		PublicKey:    pub,
 		ec:           new(ecdsaKey),
 	}
-
 	switch pub.Curve {
 	case elliptic.P256():
 		pk.ec.oid = oidCurveP256
@@ -239,10 +338,13 @@ func NewECDSAPublicKey(creationTime time.Time, pub *ecdsa.PublicKey) *PublicKey
 		pk.ec.oid = oidCurveP384
 	case elliptic.P521():
 		pk.ec.oid = oidCurveP521
-	default:
-		panic("unknown elliptic curve")
+	case brainpool.P256r1():
+		pk.ec.oid = oidCurveP256r1
+	case brainpool.P384r1():
+		pk.ec.oid = oidCurveP384r1
+	case brainpool.P512r1():
+		pk.ec.oid = oidCurveP512r1
 	}
-
 	pk.ec.p.bytes = elliptic.Marshal(pub.Curve, pub.X, pub.Y)
 	pk.ec.p.bitLength = uint16(8 * len(pk.ec.p.bytes))
 
@@ -269,6 +371,12 @@ func (pk *PublicKey) parse(r io.Reader) (err error) {
 		err = pk.parseDSA(r)
 	case PubKeyAlgoElGamal:
 		err = pk.parseElGamal(r)
+	case PubKeyAlgoEdDSA:
+		pk.edk = new(edDSAkey)
+		if err = pk.edk.parse(r); err != nil {
+			return err
+		}
+		err = pk.edk.check()
 	case PubKeyAlgoECDSA:
 		pk.ec = new(ecdsaKey)
 		if err = pk.ec.parse(r); err != nil {
@@ -284,8 +392,7 @@ func (pk *PublicKey) parse(r io.Reader) (err error) {
 		if err = pk.ecdh.parse(r); err != nil {
 			return
 		}
-		// The ECDH key is stored in an ecdsa.PublicKey for convenience.
-		pk.PublicKey, err = pk.ec.newECDSA()
+		pk.PublicKey, err = pk.ec.newECDH()
 	default:
 		err = errors.UnsupportedError("public key type: " + strconv.Itoa(int(pk.PubKeyAlgo)))
 	}
@@ -318,7 +425,7 @@ func (pk *PublicKey) parseRSA(r io.Reader) (err error) {
 		return
 	}
 
-	if len(pk.e.bytes) > 3 {
+	if len(pk.e.bytes) > 7 {
 		err = errors.UnsupportedError("large public exponent")
 		return
 	}
@@ -328,7 +435,7 @@ func (pk *PublicKey) parseRSA(r io.Reader) (err error) {
 	}
 	for i := 0; i < len(pk.e.bytes); i++ {
 		rsa.E <<= 8
-		rsa.E |= int(pk.e.bytes[i])
+		rsa.E |= int64(pk.e.bytes[i])
 	}
 	pk.PublicKey = rsa
 	return
@@ -410,6 +517,8 @@ func (pk *PublicKey) SerializeSignaturePrefix(h io.Writer) {
 	case PubKeyAlgoECDH:
 		pLength += uint16(pk.ec.byteLen())
 		pLength += uint16(pk.ecdh.byteLen())
+	case PubKeyAlgoEdDSA:
+		pLength += uint16(pk.edk.byteLen())
 	default:
 		panic("unknown public key algorithm")
 	}
@@ -439,6 +548,8 @@ func (pk *PublicKey) Serialize(w io.Writer) (err error) {
 	case PubKeyAlgoECDH:
 		length += pk.ec.byteLen()
 		length += pk.ecdh.byteLen()
+	case PubKeyAlgoEdDSA:
+		length += pk.edk.byteLen()
 	default:
 		panic("unknown public key algorithm")
 	}
@@ -480,6 +591,8 @@ func (pk *PublicKey) serializeWithoutHeaders(w io.Writer) (err error) {
 		return writeMPIs(w, pk.p, pk.g, pk.y)
 	case PubKeyAlgoECDSA:
 		return pk.ec.serialize(w)
+	case PubKeyAlgoEdDSA:
+		return pk.edk.serialize(w)
 	case PubKeyAlgoECDH:
 		if err = pk.ec.serialize(w); err != nil {
 			return
@@ -504,9 +617,18 @@ func (pk *PublicKey) VerifySignature(signed hash.Hash, sig *Signature) (err erro
 	signed.Write(sig.HashSuffix)
 	hashBytes := signed.Sum(nil)
 
-	if hashBytes[0] != sig.HashTag[0] || hashBytes[1] != sig.HashTag[1] {
-		return errors.SignatureError("hash tag doesn't match")
-	}
+	// NOTE(maxtaco) 2016-08-22
+	//
+	// We used to do this:
+	//
+	// if hashBytes[0] != sig.HashTag[0] || hashBytes[1] != sig.HashTag[1] {
+	//	  return errors.SignatureError("hash tag doesn't match")
+	// }
+	//
+	// But don't do anything in this case. Some GPGs generate bad
+	// 2-byte hash prefixes, but GPG also doesn't seem to care on
+	// import. See BrentMaxwell's key. I think it's safe to disable
+	// this check!
 
 	if pk.PubKeyAlgo != sig.PubKeyAlgo {
 		return errors.InvalidArgumentError("public key and signature use different algorithms")
@@ -537,9 +659,15 @@ func (pk *PublicKey) VerifySignature(signed hash.Hash, sig *Signature) (err erro
 			return errors.SignatureError("ECDSA verification failure")
 		}
 		return nil
+	case PubKeyAlgoEdDSA:
+		if !pk.edk.Verify(hashBytes, sig.EdDSASigR, sig.EdDSASigS) {
+			return errors.SignatureError("EdDSA verification failure")
+		}
+		return nil
 	default:
 		return errors.SignatureError("Unsupported public key algorithm used in signature")
 	}
+	panic("unreachable")
 }
 
 // VerifySignatureV3 returns nil iff sig is a valid signature, made by this
@@ -584,6 +712,7 @@ func (pk *PublicKey) VerifySignatureV3(signed hash.Hash, sig *SignatureV3) (err
 	default:
 		panic("shouldn't happen")
 	}
+	panic("unreachable")
 }
 
 // keySignatureHash returns a Hash of the message that needs to be signed for
@@ -594,12 +723,18 @@ func keySignatureHash(pk, signed signingKey, hashFunc crypto.Hash) (h hash.Hash,
 	}
 	h = hashFunc.New()
 
+	updateKeySignatureHash(pk, signed, h)
+
+	return
+}
+
+// updateKeySignatureHash does the actual hash updates for keySignatureHash.
+func updateKeySignatureHash(pk, signed signingKey, h hash.Hash) {
 	// RFC 4880, section 5.2.4
 	pk.SerializeSignaturePrefix(h)
 	pk.serializeWithoutHeaders(h)
 	signed.SerializeSignaturePrefix(h)
 	signed.serializeWithoutHeaders(h)
-	return
 }
 
 // VerifyKeySignature returns nil iff sig is a valid signature, made by this
@@ -614,6 +749,19 @@ func (pk *PublicKey) VerifyKeySignature(signed *PublicKey, sig *Signature) error
 	}
 
 	if sig.FlagSign {
+
+		// BUG(maxtaco)
+		//
+		// We should check for more than FlagsSign here, because if
+		// you read keys.go, we can sometimes use signing subkeys even if they're
+		// not explicitly flagged as such. However, so doing fails lots of currently
+		// working tests, so I'm not going to do much here.
+		//
+		// In other words, we should have this disjunction in the condition above:
+		//
+		//    || (!sig.FlagsValid && pk.PubKeyAlgo.CanSign()) {
+		//
+
 		// Signing subkeys must be cross-signed. See
 		// https://www.gnupg.org/faq/subkey-cross-certify.html.
 		if sig.EmbeddedSignature == nil {
@@ -648,14 +796,27 @@ func keyRevocationHash(pk signingKey, hashFunc crypto.Hash) (h hash.Hash, err er
 
 // VerifyRevocationSignature returns nil iff sig is a valid signature, made by this
 // public key.
-func (pk *PublicKey) VerifyRevocationSignature(sig *Signature) (err error) {
-	h, err := keyRevocationHash(pk, sig.Hash)
+func (pk *PublicKey) VerifyRevocationSignature(revokedKey *PublicKey, sig *Signature) (err error) {
+	h, err := keyRevocationHash(revokedKey, sig.Hash)
 	if err != nil {
 		return err
 	}
 	return pk.VerifySignature(h, sig)
 }
 
+type teeHash struct {
+	h hash.Hash
+}
+
+func (t teeHash) Write(b []byte) (n int, err error) {
+	fmt.Printf("hash -> %s %+v\n", string(b), b)
+	return t.h.Write(b)
+}
+func (t teeHash) Sum(b []byte) []byte { return t.h.Sum(b) }
+func (t teeHash) Reset()              { t.h.Reset() }
+func (t teeHash) Size() int           { return t.h.Size() }
+func (t teeHash) BlockSize() int      { return t.h.BlockSize() }
+
 // userIdSignatureHash returns a Hash of the message that needs to be signed
 // to assert that pk is a valid key for id.
 func userIdSignatureHash(id string, pk *PublicKey, hashFunc crypto.Hash) (h hash.Hash, err error) {
@@ -664,6 +825,14 @@ func userIdSignatureHash(id string, pk *PublicKey, hashFunc crypto.Hash) (h hash
 	}
 	h = hashFunc.New()
 
+	updateUserIdSignatureHash(id, pk, h)
+
+	return
+}
+
+// updateUserIdSignatureHash does the actual hash updates for
+// userIdSignatureHash.
+func updateUserIdSignatureHash(id string, pk *PublicKey, h hash.Hash) {
 	// RFC 4880, section 5.2.4
 	pk.SerializeSignaturePrefix(h)
 	pk.serializeWithoutHeaders(h)
@@ -732,7 +901,9 @@ func writeMPIs(w io.Writer, mpis ...parsedMPI) (err error) {
 	return
 }
 
-// BitLength returns the bit length for the given public key.
+// BitLength returns the bit length for the given public key. Used for
+// displaying key information, actual buffers and BigInts inside may
+// have non-matching different size if the key is invalid.
 func (pk *PublicKey) BitLength() (bitLength uint16, err error) {
 	switch pk.PubKeyAlgo {
 	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly, PubKeyAlgoRSASignOnly:
@@ -741,6 +912,17 @@ func (pk *PublicKey) BitLength() (bitLength uint16, err error) {
 		bitLength = pk.p.bitLength
 	case PubKeyAlgoElGamal:
 		bitLength = pk.p.bitLength
+	case PubKeyAlgoECDH:
+		ecdhPublicKey := pk.PublicKey.(*ecdh.PublicKey)
+		bitLength = uint16(ecdhPublicKey.Curve.Params().BitSize)
+	case PubKeyAlgoECDSA:
+		ecdsaPublicKey := pk.PublicKey.(*ecdsa.PublicKey)
+		bitLength = uint16(ecdsaPublicKey.Curve.Params().BitSize)
+	case PubKeyAlgoEdDSA:
+		// EdDSA only support ed25519 curves right now, just return
+		// the length. Also, we don't have any PublicKey.Curve object
+		// to look the size up from.
+		bitLength = 256
 	default:
 		err = errors.InvalidArgumentError("bad public-key algorithm")
 	}
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/public_key_v3.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/public_key_v3.go
similarity index 97%
rename from vendor/golang.org/x/crypto/openpgp/packet/public_key_v3.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/public_key_v3.go
index 5daf7b6cf..52474677b 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/public_key_v3.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/public_key_v3.go
@@ -7,7 +7,6 @@ package packet
 import (
 	"crypto"
 	"crypto/md5"
-	"crypto/rsa"
 	"encoding/binary"
 	"fmt"
 	"hash"
@@ -16,7 +15,8 @@ import (
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/rsa"
 )
 
 // PublicKeyV3 represents older, version 3 public keys. These keys are less secure and
@@ -42,8 +42,8 @@ func newRSAPublicKeyV3(creationTime time.Time, pub *rsa.PublicKey) *PublicKeyV3
 	pk := &PublicKeyV3{
 		CreationTime: creationTime,
 		PublicKey:    pub,
-		n:            fromBig(pub.N),
-		e:            fromBig(big.NewInt(int64(pub.E))),
+		n:            FromBig(pub.N),
+		e:            FromBig(big.NewInt(int64(pub.E))),
 	}
 
 	pk.setFingerPrintAndKeyId()
@@ -100,14 +100,14 @@ func (pk *PublicKeyV3) parseRSA(r io.Reader) (err error) {
 	if len(pk.n.bytes) < 8 {
 		return errors.StructuralError("v3 public key modulus is too short")
 	}
-	if len(pk.e.bytes) > 3 {
+	if len(pk.e.bytes) > 7 {
 		err = errors.UnsupportedError("large public exponent")
 		return
 	}
 	rsa := &rsa.PublicKey{N: new(big.Int).SetBytes(pk.n.bytes)}
 	for i := 0; i < len(pk.e.bytes); i++ {
 		rsa.E <<= 8
-		rsa.E |= int(pk.e.bytes[i])
+		rsa.E |= int64(pk.e.bytes[i])
 	}
 	pk.PublicKey = rsa
 	return
@@ -216,6 +216,7 @@ func (pk *PublicKeyV3) VerifySignatureV3(signed hash.Hash, sig *SignatureV3) (er
 		// V3 public keys only support RSA.
 		panic("shouldn't happen")
 	}
+	panic("unreachable")
 }
 
 // VerifyUserIdSignatureV3 returns nil iff sig is a valid signature, made by this
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/reader.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/reader.go
similarity index 97%
rename from vendor/golang.org/x/crypto/openpgp/packet/reader.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/reader.go
index 34bc7c613..957b3b897 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/reader.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/reader.go
@@ -5,8 +5,9 @@
 package packet
 
 import (
-	"golang.org/x/crypto/openpgp/errors"
 	"io"
+
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // Reader reads packets from an io.Reader and allows packets to be 'unread' so
@@ -46,7 +47,6 @@ func (r *Reader) Next() (p Packet, err error) {
 			return nil, err
 		}
 	}
-
 	return nil, io.EOF
 }
 
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/signature.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/signature.go
similarity index 76%
rename from vendor/golang.org/x/crypto/openpgp/packet/signature.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/signature.go
index 6ce0cbedb..46224ad66 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/signature.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/signature.go
@@ -9,16 +9,15 @@ import (
 	"crypto"
 	"crypto/dsa"
 	"crypto/ecdsa"
-	"encoding/asn1"
 	"encoding/binary"
 	"hash"
 	"io"
-	"math/big"
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/rsa"
 )
 
 const (
@@ -29,6 +28,29 @@ const (
 	KeyFlagEncryptStorage
 )
 
+// Signer can be implemented by application code to do actual signing.
+type Signer interface {
+	hash.Hash
+	Sign(sig *Signature) error
+	KeyId() uint64
+	PublicKeyAlgo() PublicKeyAlgorithm
+}
+
+// RevocationKey represents designated revoker packet. See RFC 4880
+// section 5.2.3.15 for details.
+type RevocationKey struct {
+	Class         byte
+	PublicKeyAlgo PublicKeyAlgorithm
+	Fingerprint   []byte
+}
+
+// KeyFlagBits holds boolean whether any usage flags were provided in
+// the signature and BitField with KeyFlag* flags.
+type KeyFlagBits struct {
+	Valid    bool
+	BitField byte
+}
+
 // Signature represents a signature. See RFC 4880, section 5.2.
 type Signature struct {
 	SigType    SignatureType
@@ -45,6 +67,7 @@ type Signature struct {
 	RSASignature         parsedMPI
 	DSASigR, DSASigS     parsedMPI
 	ECDSASigR, ECDSASigS parsedMPI
+	EdDSASigR, EdDSASigS parsedMPI
 
 	// rawSubpackets contains the unparsed subpackets, in order.
 	rawSubpackets []outputSubpacket
@@ -54,8 +77,10 @@ type Signature struct {
 
 	SigLifetimeSecs, KeyLifetimeSecs                        *uint32
 	PreferredSymmetric, PreferredHash, PreferredCompression []uint8
+	PreferredKeyServer                                      string
 	IssuerKeyId                                             *uint64
 	IsPrimaryId                                             *bool
+	IssuerFingerprint                                       []byte
 
 	// FlagsValid is set if any flags were given. See RFC 4880, section
 	// 5.2.3.21 for details.
@@ -67,6 +92,12 @@ type Signature struct {
 	RevocationReason     *uint8
 	RevocationReasonText string
 
+	// PolicyURI is optional. See RFC 4880, Section 5.2.3.20 for details
+	PolicyURI string
+
+	// Regex is a regex that can match a PGP UID. See RFC 4880, 5.2.3.14 for details
+	Regex string
+
 	// MDC is set if this signature has a feature packet that indicates
 	// support for MDC subpackets.
 	MDC bool
@@ -76,6 +107,16 @@ type Signature struct {
 	// subkey as their own.
 	EmbeddedSignature *Signature
 
+	// StubbedOutCriticalError is not fail-stop, since it shouldn't break key parsing
+	// when appearing in WoT-style cross signatures. But it should prevent a signature
+	// from being applied to a primary or subkey.
+	StubbedOutCriticalError error
+
+	// DesignaterRevoker will be present if this signature certifies a
+	// designated revoking key id (3rd party key that can sign
+	// revocation for this key).
+	DesignatedRevoker *RevocationKey
+
 	outSubpackets []outputSubpacket
 }
 
@@ -98,7 +139,7 @@ func (sig *Signature) parse(r io.Reader) (err error) {
 	sig.SigType = SignatureType(buf[0])
 	sig.PubKeyAlgo = PublicKeyAlgorithm(buf[1])
 	switch sig.PubKeyAlgo {
-	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA:
+	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly, PubKeyAlgoDSA, PubKeyAlgoECDSA, PubKeyAlgoEdDSA:
 	default:
 		err = errors.UnsupportedError("public key algorithm " + strconv.Itoa(int(sig.PubKeyAlgo)))
 		return
@@ -162,6 +203,11 @@ func (sig *Signature) parse(r io.Reader) (err error) {
 		if err == nil {
 			sig.DSASigS.bytes, sig.DSASigS.bitLength, err = readMPI(r)
 		}
+	case PubKeyAlgoEdDSA:
+		sig.EdDSASigR.bytes, sig.EdDSASigR.bitLength, err = readMPI(r)
+		if err == nil {
+			sig.EdDSASigS.bytes, sig.EdDSASigS.bitLength, err = readMPI(r)
+		}
 	case PubKeyAlgoECDSA:
 		sig.ECDSASigR.bytes, sig.ECDSASigR.bitLength, err = readMPI(r)
 		if err == nil {
@@ -195,16 +241,21 @@ type signatureSubpacketType uint8
 const (
 	creationTimeSubpacket        signatureSubpacketType = 2
 	signatureExpirationSubpacket signatureSubpacketType = 3
+	regularExpressionSubpacket   signatureSubpacketType = 6
 	keyExpirationSubpacket       signatureSubpacketType = 9
 	prefSymmetricAlgosSubpacket  signatureSubpacketType = 11
+	revocationKey                signatureSubpacketType = 12
 	issuerSubpacket              signatureSubpacketType = 16
 	prefHashAlgosSubpacket       signatureSubpacketType = 21
 	prefCompressionSubpacket     signatureSubpacketType = 22
+	prefKeyServerSubpacket       signatureSubpacketType = 24
 	primaryUserIdSubpacket       signatureSubpacketType = 25
+	policyURISubpacket           signatureSubpacketType = 26
 	keyFlagsSubpacket            signatureSubpacketType = 27
 	reasonForRevocationSubpacket signatureSubpacketType = 29
 	featuresSubpacket            signatureSubpacketType = 30
 	embeddedSignatureSubpacket   signatureSubpacketType = 32
+	issuerFingerprint            signatureSubpacketType = 33
 )
 
 // parseSignatureSubpacket parses a single subpacket. len(subpacket) is >= 1.
@@ -382,6 +433,32 @@ func parseSignatureSubpacket(sig *Signature, subpacket []byte, isHashed bool) (r
 		if sigType := sig.EmbeddedSignature.SigType; sigType != SigTypePrimaryKeyBinding {
 			return nil, errors.StructuralError("cross-signature has unexpected type " + strconv.Itoa(int(sigType)))
 		}
+	case policyURISubpacket:
+		// See RFC 4880, Section 5.2.3.20
+		sig.PolicyURI = string(subpacket[:])
+	case regularExpressionSubpacket:
+		sig.Regex = string(subpacket[:])
+		if isCritical {
+			sig.StubbedOutCriticalError = errors.UnsupportedError("regex support is stubbed out")
+		}
+	case prefKeyServerSubpacket:
+		sig.PreferredKeyServer = string(subpacket[:])
+	case issuerFingerprint:
+		// The first byte is how many bytes the fingerprint is, but we'll just
+		// read until the end of the subpacket, so we'll ignore it.
+		sig.IssuerFingerprint = append([]byte{}, subpacket[1:]...)
+	case revocationKey:
+		// Authorizes the specified key to issue revocation signatures
+		// for a key.
+
+		// TODO: Class octet must have bit 0x80 set. If the bit 0x40
+		// is set, then this means that the revocation information is
+		// sensitive.
+		sig.DesignatedRevoker = &RevocationKey{
+			Class:         subpacket[0],
+			PublicKeyAlgo: PublicKeyAlgorithm(subpacket[1]),
+			Fingerprint:   append([]byte{}, subpacket[2:]...),
+		}
 	default:
 		if isCritical {
 			err = errors.UnsupportedError("unknown critical signature subpacket type " + strconv.Itoa(int(packetType)))
@@ -464,6 +541,26 @@ func (sig *Signature) KeyExpired(currentTime time.Time) bool {
 	return currentTime.After(expiry)
 }
 
+// ExpiresBeforeOther checks if other signature has expiration at
+// later date than sig.
+func (sig *Signature) ExpiresBeforeOther(other *Signature) bool {
+	if sig.KeyLifetimeSecs == nil {
+		// This sig never expires, or has infinitely long expiration
+		// time.
+		return false
+	} else if other.KeyLifetimeSecs == nil {
+		// This sig expires at some non-infinite point, but the other
+		// sig never expires.
+		return true
+	}
+
+	getExpiryDate := func(s *Signature) time.Time {
+		return s.CreationTime.Add(time.Duration(*s.KeyLifetimeSecs) * time.Second)
+	}
+
+	return getExpiryDate(other).After(getExpiryDate(sig))
+}
+
 // buildHashSuffix constructs the HashSuffix member of sig in preparation for signing.
 func (sig *Signature) buildHashSuffix() (err error) {
 	hashedSubpacketsLen := subpacketsLength(sig.outSubpackets, true)
@@ -509,16 +606,27 @@ func (sig *Signature) signPrepareHash(h hash.Hash) (digest []byte, err error) {
 // On success, the signature is stored in sig. Call Serialize to write it out.
 // If config is nil, sensible defaults will be used.
 func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err error) {
+	signer, hashIsSigner := h.(Signer)
+
+	if !hashIsSigner && (priv == nil || priv.PrivateKey == nil) {
+		err = errors.InvalidArgumentError("attempting to sign with nil PrivateKey")
+		return
+	}
+
 	sig.outSubpackets = sig.buildSubpackets()
 	digest, err := sig.signPrepareHash(h)
 	if err != nil {
 		return
 	}
 
+	if hashIsSigner {
+		err = signer.Sign(sig)
+		return
+	}
+
 	switch priv.PubKeyAlgo {
 	case PubKeyAlgoRSA, PubKeyAlgoRSASignOnly:
-		// supports both *rsa.PrivateKey and crypto.Signer
-		sig.RSASignature.bytes, err = priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, sig.Hash)
+		sig.RSASignature.bytes, err = rsa.SignPKCS1v15(config.Random(), priv.PrivateKey.(*rsa.PrivateKey), sig.Hash, digest)
 		sig.RSASignature.bitLength = uint16(8 * len(sig.RSASignature.bytes))
 	case PubKeyAlgoDSA:
 		dsaPriv := priv.PrivateKey.(*dsa.PrivateKey)
@@ -536,20 +644,16 @@ func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err e
 			sig.DSASigS.bitLength = uint16(8 * len(sig.DSASigS.bytes))
 		}
 	case PubKeyAlgoECDSA:
-		var r, s *big.Int
-		if pk, ok := priv.PrivateKey.(*ecdsa.PrivateKey); ok {
-			// direct support, avoid asn1 wrapping/unwrapping
-			r, s, err = ecdsa.Sign(config.Random(), pk, digest)
-		} else {
-			var b []byte
-			b, err = priv.PrivateKey.(crypto.Signer).Sign(config.Random(), digest, nil)
-			if err == nil {
-				r, s, err = unwrapECDSASig(b)
-			}
-		}
+		r, s, err := ecdsa.Sign(config.Random(), priv.PrivateKey.(*ecdsa.PrivateKey), digest)
 		if err == nil {
-			sig.ECDSASigR = fromBig(r)
-			sig.ECDSASigS = fromBig(s)
+			sig.ECDSASigR = FromBig(r)
+			sig.ECDSASigS = FromBig(s)
+		}
+	case PubKeyAlgoEdDSA:
+		r, s, err := priv.PrivateKey.(*EdDSAPrivateKey).Sign(digest)
+		if err == nil {
+			sig.EdDSASigR = FromBytes(r)
+			sig.EdDSASigS = FromBytes(s)
 		}
 	default:
 		err = errors.UnsupportedError("public key algorithm: " + strconv.Itoa(int(sig.PubKeyAlgo)))
@@ -558,19 +662,6 @@ func (sig *Signature) Sign(h hash.Hash, priv *PrivateKey, config *Config) (err e
 	return
 }
 
-// unwrapECDSASig parses the two integer components of an ASN.1-encoded ECDSA
-// signature.
-func unwrapECDSASig(b []byte) (r, s *big.Int, err error) {
-	var ecsdaSig struct {
-		R, S *big.Int
-	}
-	_, err = asn1.Unmarshal(b, &ecsdaSig)
-	if err != nil {
-		return
-	}
-	return ecsdaSig.R, ecsdaSig.S, nil
-}
-
 // SignUserId computes a signature from priv, asserting that pub is a valid
 // key for the identity id.  On success, the signature is stored in sig. Call
 // Serialize to write it out.
@@ -583,6 +674,16 @@ func (sig *Signature) SignUserId(id string, pub *PublicKey, priv *PrivateKey, co
 	return sig.Sign(h, priv, config)
 }
 
+// SignUserIdWithSigner computes a signature from priv, asserting that pub is a
+// valid key for the identity id.  On success, the signature is stored in sig.
+// Call Serialize to write it out.
+// If config is nil, sensible defaults will be used.
+func (sig *Signature) SignUserIdWithSigner(id string, pub *PublicKey, s Signer, config *Config) error {
+	updateUserIdSignatureHash(id, pub, s)
+
+	return sig.Sign(s, nil, config)
+}
+
 // SignKey computes a signature from priv, asserting that pub is a subkey. On
 // success, the signature is stored in sig. Call Serialize to write it out.
 // If config is nil, sensible defaults will be used.
@@ -594,13 +695,25 @@ func (sig *Signature) SignKey(pub *PublicKey, priv *PrivateKey, config *Config)
 	return sig.Sign(h, priv, config)
 }
 
+// SignKeyWithSigner computes a signature using s, asserting that
+// signeePubKey is a subkey. On success, the signature is stored in sig. Call
+// Serialize to write it out. If config is nil, sensible defaults will be used.
+func (sig *Signature) SignKeyWithSigner(signeePubKey *PublicKey, signerPubKey *PublicKey, s Signer, config *Config) error {
+	updateKeySignatureHash(signerPubKey, signeePubKey, s)
+
+	return sig.Sign(s, nil, config)
+}
+
 // Serialize marshals sig to w. Sign, SignUserId or SignKey must have been
 // called first.
 func (sig *Signature) Serialize(w io.Writer) (err error) {
 	if len(sig.outSubpackets) == 0 {
 		sig.outSubpackets = sig.rawSubpackets
 	}
-	if sig.RSASignature.bytes == nil && sig.DSASigR.bytes == nil && sig.ECDSASigR.bytes == nil {
+	if sig.RSASignature.bytes == nil &&
+		sig.DSASigR.bytes == nil &&
+		sig.ECDSASigR.bytes == nil &&
+		sig.EdDSASigR.bytes == nil {
 		return errors.InvalidArgumentError("Signature: need to call Sign, SignUserId or SignKey before Serialize")
 	}
 
@@ -611,6 +724,9 @@ func (sig *Signature) Serialize(w io.Writer) (err error) {
 	case PubKeyAlgoDSA:
 		sigLength = 2 + len(sig.DSASigR.bytes)
 		sigLength += 2 + len(sig.DSASigS.bytes)
+	case PubKeyAlgoEdDSA:
+		sigLength = 2 + len(sig.EdDSASigR.bytes)
+		sigLength += 2 + len(sig.EdDSASigS.bytes)
 	case PubKeyAlgoECDSA:
 		sigLength = 2 + len(sig.ECDSASigR.bytes)
 		sigLength += 2 + len(sig.ECDSASigS.bytes)
@@ -651,6 +767,8 @@ func (sig *Signature) Serialize(w io.Writer) (err error) {
 		err = writeMPIs(w, sig.RSASignature)
 	case PubKeyAlgoDSA:
 		err = writeMPIs(w, sig.DSASigR, sig.DSASigS)
+	case PubKeyAlgoEdDSA:
+		err = writeMPIs(w, sig.EdDSASigR, sig.EdDSASigS)
 	case PubKeyAlgoECDSA:
 		err = writeMPIs(w, sig.ECDSASigR, sig.ECDSASigS)
 	default:
@@ -687,20 +805,7 @@ func (sig *Signature) buildSubpackets() (subpackets []outputSubpacket) {
 	// Key flags may only appear in self-signatures or certification signatures.
 
 	if sig.FlagsValid {
-		var flags byte
-		if sig.FlagCertify {
-			flags |= KeyFlagCertify
-		}
-		if sig.FlagSign {
-			flags |= KeyFlagSign
-		}
-		if sig.FlagEncryptCommunications {
-			flags |= KeyFlagEncryptCommunications
-		}
-		if sig.FlagEncryptStorage {
-			flags |= KeyFlagEncryptStorage
-		}
-		subpackets = append(subpackets, outputSubpacket{true, keyFlagsSubpacket, false, []byte{flags}})
+		subpackets = append(subpackets, outputSubpacket{true, keyFlagsSubpacket, false, []byte{sig.GetKeyFlags().BitField}})
 	}
 
 	// The following subpackets may only appear in self-signatures
@@ -729,3 +834,47 @@ func (sig *Signature) buildSubpackets() (subpackets []outputSubpacket) {
 
 	return
 }
+
+func (sig *Signature) GetKeyFlags() (ret KeyFlagBits) {
+	if !sig.FlagsValid {
+		return ret
+	}
+
+	ret.Valid = true
+	if sig.FlagCertify {
+		ret.BitField |= KeyFlagCertify
+	}
+	if sig.FlagSign {
+		ret.BitField |= KeyFlagSign
+	}
+	if sig.FlagEncryptCommunications {
+		ret.BitField |= KeyFlagEncryptCommunications
+	}
+	if sig.FlagEncryptStorage {
+		ret.BitField |= KeyFlagEncryptStorage
+	}
+	return ret
+}
+
+func (f *KeyFlagBits) HasFlagCertify() bool {
+	return f.BitField&KeyFlagCertify != 0
+}
+
+func (f *KeyFlagBits) HasFlagSign() bool {
+	return f.BitField&KeyFlagSign != 0
+}
+
+func (f *KeyFlagBits) HasFlagEncryptCommunications() bool {
+	return f.BitField&KeyFlagEncryptCommunications != 0
+}
+
+func (f *KeyFlagBits) HasFlagEncryptStorage() bool {
+	return f.BitField&KeyFlagEncryptStorage != 0
+}
+
+func (f *KeyFlagBits) Merge(other KeyFlagBits) {
+	if other.Valid {
+		f.Valid = true
+		f.BitField |= other.BitField
+	}
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/signature_v3.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/signature_v3.go
similarity index 97%
rename from vendor/golang.org/x/crypto/openpgp/packet/signature_v3.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/signature_v3.go
index 6edff8893..dfca651be 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/signature_v3.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/signature_v3.go
@@ -12,8 +12,8 @@ import (
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
 )
 
 // SignatureV3 represents older version 3 signatures. These signatures are less secure
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/symmetric_key_encrypted.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/symmetric_key_encrypted.go
similarity index 95%
rename from vendor/golang.org/x/crypto/openpgp/packet/symmetric_key_encrypted.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/symmetric_key_encrypted.go
index 4b1105b6f..d2bef0ce5 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/symmetric_key_encrypted.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/symmetric_key_encrypted.go
@@ -10,8 +10,8 @@ import (
 	"io"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/s2k"
 )
 
 // This is the largest session key that we'll support. Since no 512-bit cipher
@@ -48,6 +48,9 @@ func (ske *SymmetricKeyEncrypted) parse(r io.Reader) error {
 	if err != nil {
 		return err
 	}
+	if ske.s2k == nil {
+		return errors.UnsupportedError("can't use dummy S2K for symmetric key encryption")
+	}
 
 	encryptedKey := make([]byte, maxSessionKeySizeInBytes)
 	// The session key may follow. We just have to try and read to find
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/symmetrically_encrypted.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/symmetrically_encrypted.go
similarity index 99%
rename from vendor/golang.org/x/crypto/openpgp/packet/symmetrically_encrypted.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/symmetrically_encrypted.go
index 6126030eb..fd4f8f015 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/symmetrically_encrypted.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/packet/symmetrically_encrypted.go
@@ -8,10 +8,11 @@ import (
 	"crypto/cipher"
 	"crypto/sha1"
 	"crypto/subtle"
-	"golang.org/x/crypto/openpgp/errors"
 	"hash"
 	"io"
 	"strconv"
+
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // SymmetricallyEncrypted represents a symmetrically encrypted byte string. The
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/userattribute.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/userattribute.go
similarity index 100%
rename from vendor/golang.org/x/crypto/openpgp/packet/userattribute.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/userattribute.go
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/userid.go b/vendor/github.com/keybase/go-crypto/openpgp/packet/userid.go
similarity index 100%
rename from vendor/golang.org/x/crypto/openpgp/packet/userid.go
rename to vendor/github.com/keybase/go-crypto/openpgp/packet/userid.go
diff --git a/vendor/github.com/keybase/go-crypto/openpgp/patch.sh b/vendor/github.com/keybase/go-crypto/openpgp/patch.sh
new file mode 100644
index 000000000..23cacc83d
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/openpgp/patch.sh
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+patch < sig-v3.patch
+patch < s2k-gnu-dummy.patch
+find . -type f -name '*.go' -exec sed -i'' -e 's/golang.org\/x\/crypto\/openpgp/github.com\/keybase\/go-crypto\/openpgp/' {} \;
+find . -type f -name '*.go-e' -exec rm {} \;
+go test ./...
diff --git a/vendor/golang.org/x/crypto/openpgp/read.go b/vendor/github.com/keybase/go-crypto/openpgp/read.go
similarity index 87%
rename from vendor/golang.org/x/crypto/openpgp/read.go
rename to vendor/github.com/keybase/go-crypto/openpgp/read.go
index 6ec664f44..cde27cba0 100644
--- a/vendor/golang.org/x/crypto/openpgp/read.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/read.go
@@ -3,18 +3,19 @@
 // license that can be found in the LICENSE file.
 
 // Package openpgp implements high level operations on OpenPGP messages.
-package openpgp // import "golang.org/x/crypto/openpgp"
+package openpgp // import "github.com/keybase/go-crypto/openpgp"
 
 import (
 	"crypto"
+	"crypto/hmac"
 	_ "crypto/sha256"
 	"hash"
 	"io"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
+	"github.com/keybase/go-crypto/openpgp/armor"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/packet"
 )
 
 // SignatureType is the armor type for a PGP signature.
@@ -50,7 +51,7 @@ type MessageDetails struct {
 	// If IsSigned is true and SignedBy is non-zero then the signature will
 	// be verified as UnverifiedBody is read. The signature cannot be
 	// checked until the whole of UnverifiedBody is read so UnverifiedBody
-	// must be consumed until EOF before the data can be trusted. Even if a
+	// must be consumed until EOF before the data can trusted. Even if a
 	// message isn't signed (or the signer is unknown) the data may contain
 	// an authentication code that is only checked once UnverifiedBody has
 	// been consumed. Once EOF has been seen, the following fields are
@@ -113,7 +114,7 @@ ParsePackets:
 			// This packet contains the decryption key encrypted to a public key.
 			md.EncryptedToKeyIds = append(md.EncryptedToKeyIds, p.KeyId)
 			switch p.Algo {
-			case packet.PubKeyAlgoRSA, packet.PubKeyAlgoRSAEncryptOnly, packet.PubKeyAlgoElGamal:
+			case packet.PubKeyAlgoRSA, packet.PubKeyAlgoRSAEncryptOnly, packet.PubKeyAlgoElGamal, packet.PubKeyAlgoECDH:
 				break
 			default:
 				continue
@@ -122,7 +123,7 @@ ParsePackets:
 			if p.KeyId == 0 {
 				keys = keyring.DecryptionKeys()
 			} else {
-				keys = keyring.KeysById(p.KeyId)
+				keys = keyring.KeysById(p.KeyId, nil)
 			}
 			for _, k := range keys {
 				pubKeys = append(pubKeys, keyEnvelopePair{k, p})
@@ -255,7 +256,7 @@ FindLiteralData:
 
 			md.IsSigned = true
 			md.SignedByKeyId = p.KeyId
-			keys := keyring.KeysByIdUsage(p.KeyId, packet.KeyFlagSign)
+			keys := keyring.KeysByIdUsage(p.KeyId, nil, packet.KeyFlagSign)
 			if len(keys) > 0 {
 				md.SignedBy = &keys[0]
 			}
@@ -336,7 +337,16 @@ func (scr *signatureCheckReader) Read(buf []byte) (n int, err error) {
 
 		var ok bool
 		if scr.md.Signature, ok = p.(*packet.Signature); ok {
-			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
+			var err error
+			if fingerprint := scr.md.Signature.IssuerFingerprint; fingerprint != nil {
+				if !hmac.Equal(fingerprint, scr.md.SignedBy.PublicKey.Fingerprint[:]) {
+					err = errors.StructuralError("bad key fingerprint")
+				}
+			}
+			if err == nil {
+				err = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
+			}
+			scr.md.SignatureError = err
 		} else if scr.md.SignatureV3, ok = p.(*packet.SignatureV3); ok {
 			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignatureV3(scr.h, scr.md.SignatureV3)
 		} else {
@@ -361,7 +371,13 @@ func (scr *signatureCheckReader) Read(buf []byte) (n int, err error) {
 // returns the signer if the signature is valid. If the signer isn't known,
 // ErrUnknownIssuer is returned.
 func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, err error) {
+	signer, _, err = checkDetachedSignature(keyring, signed, signature)
+	return signer, err
+}
+
+func checkDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, issuer *uint64, err error) {
 	var issuerKeyId uint64
+	var issuerFingerprint []byte
 	var hashFunc crypto.Hash
 	var sigType packet.SignatureType
 	var keys []Key
@@ -371,29 +387,30 @@ func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signe
 	for {
 		p, err = packets.Next()
 		if err == io.EOF {
-			return nil, errors.ErrUnknownIssuer
+			return nil, nil, errors.ErrUnknownIssuer
 		}
 		if err != nil {
-			return nil, err
+			return nil, nil, err
 		}
 
 		switch sig := p.(type) {
 		case *packet.Signature:
 			if sig.IssuerKeyId == nil {
-				return nil, errors.StructuralError("signature doesn't have an issuer")
+				return nil, nil, errors.StructuralError("signature doesn't have an issuer")
 			}
 			issuerKeyId = *sig.IssuerKeyId
 			hashFunc = sig.Hash
 			sigType = sig.SigType
+			issuerFingerprint = sig.IssuerFingerprint
 		case *packet.SignatureV3:
 			issuerKeyId = sig.IssuerKeyId
 			hashFunc = sig.Hash
 			sigType = sig.SigType
 		default:
-			return nil, errors.StructuralError("non signature packet found")
+			return nil, nil, errors.StructuralError("non signature packet found")
 		}
 
-		keys = keyring.KeysByIdUsage(issuerKeyId, packet.KeyFlagSign)
+		keys = keyring.KeysByIdUsage(issuerKeyId, issuerFingerprint, packet.KeyFlagSign)
 		if len(keys) > 0 {
 			break
 		}
@@ -405,11 +422,11 @@ func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signe
 
 	h, wrappedHash, err := hashForSignature(hashFunc, sigType)
 	if err != nil {
-		return nil, err
+		return nil, nil, err
 	}
 
 	if _, err := io.Copy(wrappedHash, signed); err != nil && err != io.EOF {
-		return nil, err
+		return nil, nil, err
 	}
 
 	for _, key := range keys {
@@ -423,20 +440,24 @@ func CheckDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signe
 		}
 
 		if err == nil {
-			return key.Entity, nil
+			return key.Entity, &issuerKeyId, nil
 		}
 	}
 
-	return nil, err
+	return nil, nil, err
 }
 
 // CheckArmoredDetachedSignature performs the same actions as
 // CheckDetachedSignature but expects the signature to be armored.
 func CheckArmoredDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, err error) {
+	signer, _, err = checkArmoredDetachedSignature(keyring, signed, signature)
+	return signer, err
+}
+
+func checkArmoredDetachedSignature(keyring KeyRing, signed, signature io.Reader) (signer *Entity, issuer *uint64, err error) {
 	body, err := readArmored(signature, SignatureType)
 	if err != nil {
 		return
 	}
-
-	return CheckDetachedSignature(keyring, signed, body)
+	return checkDetachedSignature(keyring, signed, body)
 }
diff --git a/vendor/golang.org/x/crypto/openpgp/s2k/s2k.go b/vendor/github.com/keybase/go-crypto/openpgp/s2k/s2k.go
similarity index 83%
rename from vendor/golang.org/x/crypto/openpgp/s2k/s2k.go
rename to vendor/github.com/keybase/go-crypto/openpgp/s2k/s2k.go
index 4b9a44ca2..01bb67852 100644
--- a/vendor/golang.org/x/crypto/openpgp/s2k/s2k.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/s2k/s2k.go
@@ -4,7 +4,7 @@
 
 // Package s2k implements the various OpenPGP string-to-key transforms as
 // specified in RFC 4800 section 3.7.1.
-package s2k // import "golang.org/x/crypto/openpgp/s2k"
+package s2k // import "github.com/keybase/go-crypto/openpgp/s2k"
 
 import (
 	"crypto"
@@ -12,7 +12,7 @@ import (
 	"io"
 	"strconv"
 
-	"golang.org/x/crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/errors"
 )
 
 // Config collects configuration parameters for s2k key-stretching
@@ -151,6 +151,53 @@ func Iterated(out []byte, h hash.Hash, in []byte, salt []byte, count int) {
 	}
 }
 
+func parseGNUExtensions(r io.Reader) (f func(out, in []byte), err error) {
+	var buf [9]byte
+
+	// A three-byte string identifier
+	_, err = io.ReadFull(r, buf[:3])
+	if err != nil {
+		return
+	}
+	gnuExt := string(buf[:3])
+
+	if gnuExt != "GNU" {
+		return nil, errors.UnsupportedError("Malformed GNU extension: " + gnuExt)
+	}
+	_, err = io.ReadFull(r, buf[:1])
+	if err != nil {
+		return
+	}
+	gnuExtType := int(buf[0])
+	switch gnuExtType {
+	case 1:
+		return nil, nil
+	case 2:
+		// Read a serial number, which is prefixed by a 1-byte length.
+		// The maximum length is 16.
+		var lenBuf [1]byte
+		_, err = io.ReadFull(r, lenBuf[:])
+		if err != nil {
+			return
+		}
+
+		maxLen := 16
+		ivLen := int(lenBuf[0])
+		if ivLen > maxLen {
+			ivLen = maxLen
+		}
+		ivBuf := make([]byte, ivLen)
+		// For now we simply discard the IV
+		_, err = io.ReadFull(r, ivBuf)
+		if err != nil {
+			return
+		}
+		return nil, nil
+	default:
+		return nil, errors.UnsupportedError("unknown S2K GNU protection mode: " + strconv.Itoa(int(gnuExtType)))
+	}
+}
+
 // Parse reads a binary specification for a string-to-key transformation from r
 // and returns a function which performs that transform.
 func Parse(r io.Reader) (f func(out, in []byte), err error) {
@@ -161,6 +208,12 @@ func Parse(r io.Reader) (f func(out, in []byte), err error) {
 		return
 	}
 
+	// GNU Extensions; handle them before we try to look for a hash, which won't
+	// be needed in most cases anyway.
+	if buf[0] == 101 {
+		return parseGNUExtensions(r)
+	}
+
 	hash, ok := HashIdToHash(buf[1])
 	if !ok {
 		return nil, errors.UnsupportedError("hash for S2K function: " + strconv.Itoa(int(buf[1])))
@@ -251,7 +304,7 @@ func HashIdToHash(id byte) (h crypto.Hash, ok bool) {
 }
 
 // HashIdToString returns the name of the hash function corresponding to the
-// given OpenPGP hash id.
+// given OpenPGP hash id, or panics if id is unknown.
 func HashIdToString(id byte) (name string, ok bool) {
 	for _, m := range hashToHashIdMapping {
 		if m.id == id {
diff --git a/vendor/github.com/keybase/go-crypto/openpgp/sig-v3.patch b/vendor/github.com/keybase/go-crypto/openpgp/sig-v3.patch
new file mode 100644
index 000000000..bfd764afe
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/openpgp/sig-v3.patch
@@ -0,0 +1,135 @@
+diff --git a/openpgp/read.go b/openpgp/read.go
+index a6cecc5..0c9397b 100644
+--- a/openpgp/read.go
++++ b/openpgp/read.go
+@@ -56,8 +56,9 @@ type MessageDetails struct {
+ 	// been consumed. Once EOF has been seen, the following fields are
+ 	// valid. (An authentication code failure is reported as a
+ 	// SignatureError error when reading from UnverifiedBody.)
+-	SignatureError error             // nil if the signature is good.
+-	Signature      *packet.Signature // the signature packet itself.
++	SignatureError error               // nil if the signature is good.
++	Signature      *packet.Signature   // the signature packet itself, if v4 (default)
++	SignatureV3    *packet.SignatureV3 // the signature packet if it is a v2 or v3 signature
+ 
+ 	decrypted io.ReadCloser
+ }
+@@ -334,13 +335,15 @@ func (scr *signatureCheckReader) Read(buf []byte) (n int, err error) {
+ 		}
+ 
+ 		var ok bool
+-		if scr.md.Signature, ok = p.(*packet.Signature); !ok {
++		if scr.md.Signature, ok = p.(*packet.Signature); ok {
++			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
++		} else if scr.md.SignatureV3, ok = p.(*packet.SignatureV3); ok {
++			scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignatureV3(scr.h, scr.md.SignatureV3)
++		} else {
+ 			scr.md.SignatureError = errors.StructuralError("LiteralData not followed by Signature")
+ 			return
+ 		}
+ 
+-		scr.md.SignatureError = scr.md.SignedBy.PublicKey.VerifySignature(scr.h, scr.md.Signature)
+-
+ 		// The SymmetricallyEncrypted packet, if any, might have an
+ 		// unsigned hash of its own. In order to check this we need to
+ 		// close that Reader.
+diff --git a/openpgp/read_test.go b/openpgp/read_test.go
+index 52f942c..abe8d7b 100644
+--- a/openpgp/read_test.go
++++ b/openpgp/read_test.go
+@@ -13,6 +13,7 @@ import (
+ 	"strings"
+ 	"testing"
+ 
++	"golang.org/x/crypto/openpgp/armor"
+ 	"golang.org/x/crypto/openpgp/errors"
+ )
+ 
+@@ -411,6 +412,50 @@ func TestIssue11504(t *testing.T) {
+ 	testReadMessageError(t, "9303000130303030303030303030983002303030303030030000000130")
+ }
+ 
++// TestSignatureV3Message tests the verification of V3 signature, generated
++// with a modern V4-style key.  Some people have their clients set to generate
++// V3 signatures, so it's useful to be able to verify them.
++func TestSignatureV3Message(t *testing.T) {
++	sig, err := armor.Decode(strings.NewReader(signedMessageV3))
++	if err != nil {
++		t.Error(err)
++		return
++	}
++	key, err := ReadArmoredKeyRing(strings.NewReader(keyV4forVerifyingSignedMessageV3))
++	if err != nil {
++		t.Error(err)
++		return
++	}
++	md, err := ReadMessage(sig.Body, key, nil, nil)
++	if err != nil {
++		t.Error(err)
++		return
++	}
++
++	_, err = ioutil.ReadAll(md.UnverifiedBody)
++	if err != nil {
++		t.Error(err)
++		return
++	}
++
++	// We'll see a sig error here after reading in the UnverifiedBody above,
++	// if there was one to see.
++	if err = md.SignatureError; err != nil {
++		t.Error(err)
++		return
++	}
++
++	if md.SignatureV3 == nil {
++		t.Errorf("No available signature after checking signature")
++		return
++	}
++	if md.Signature != nil {
++		t.Errorf("Did not expect a signature V4 back")
++		return
++	}
++	return
++}
++
+ const testKey1KeyId = 0xA34D7E18C20C31BB
+ const testKey3KeyId = 0x338934250CCC0360
+ 
+@@ -504,3 +549,36 @@ const unknownHashFunctionHex = `8a00000040040001990006050253863c24000a09103b4fe6
+ const missingHashFunctionHex = `8a00000040040001030006050253863c24000a09103b4fe6acc0b21f32ffff0101010101010101010101010101010101010101010101010101010101010101010101010101`
+ 
+ const campbellQuine = `a0b001000300fcffa0b001000d00f2ff000300fcffa0b001000d00f2ff8270a01c00000500faff8270a01c00000500faff000500faff001400ebff8270a01c00000500faff000500faff001400ebff428821c400001400ebff428821c400001400ebff428821c400001400ebff428821c400001400ebff428821c400000000ffff000000ffff000b00f4ff428821c400000000ffff000000ffff000b00f4ff0233214c40000100feff000233214c40000100feff0000`
++
++const keyV4forVerifyingSignedMessageV3 = `-----BEGIN PGP PUBLIC KEY BLOCK-----
++Comment: GPGTools - https://gpgtools.org
++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RZia
++-----END PGP PUBLIC KEY BLOCK-----
++`
++
++const signedMessageV3 = `-----BEGIN PGP MESSAGE-----
++Comment: GPGTools - https://gpgtools.org
++
++owGbwMvMwMVYWXlhlrhb9GXG03JJDKF/MtxDMjKLFYAoUaEktbhEITe1uDgxPVWP
++q5NhKjMrWAVcC9evD8z/bF/uWNjqtk/X3y5/38XGRQHm/57rrDRYuGnTw597Xqka
++uM3137/hH3Os+Jf2dc0fXOITKwJvXJvecPVs0ta+Vg7ZO1MLn8w58Xx+6L58mbka
++DGHyU9yTueZE8D+QF/Tz28Y78dqtF56R1VPn9Xw4uJqrWYdd7b3vIZ1V6R4Nh05d
++iT57d/OhWwA=
++=hG7R
++-----END PGP MESSAGE-----
++`
diff --git a/vendor/golang.org/x/crypto/openpgp/write.go b/vendor/github.com/keybase/go-crypto/openpgp/write.go
similarity index 74%
rename from vendor/golang.org/x/crypto/openpgp/write.go
rename to vendor/github.com/keybase/go-crypto/openpgp/write.go
index 65a304cc8..03b019e78 100644
--- a/vendor/golang.org/x/crypto/openpgp/write.go
+++ b/vendor/github.com/keybase/go-crypto/openpgp/write.go
@@ -11,10 +11,10 @@ import (
 	"strconv"
 	"time"
 
-	"golang.org/x/crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
-	"golang.org/x/crypto/openpgp/s2k"
+	"github.com/keybase/go-crypto/openpgp/armor"
+	"github.com/keybase/go-crypto/openpgp/errors"
+	"github.com/keybase/go-crypto/openpgp/packet"
+	"github.com/keybase/go-crypto/openpgp/s2k"
 )
 
 // DetachSign signs message with the private key from signer (which must
@@ -59,20 +59,57 @@ func armoredDetachSign(w io.Writer, signer *Entity, message io.Reader, sigType p
 	return out.Close()
 }
 
+// SignWithSigner signs the message of type sigType with s and writes the
+// signature to w.
+// If config is nil, sensible defaults will be used.
+func SignWithSigner(s packet.Signer, w io.Writer, message io.Reader, sigType packet.SignatureType, config *packet.Config) (err error) {
+	keyId := s.KeyId()
+	sig := new(packet.Signature)
+	sig.SigType = sigType
+	sig.PubKeyAlgo = s.PublicKeyAlgo()
+	sig.Hash = config.Hash()
+	sig.CreationTime = config.Now()
+	sig.IssuerKeyId = &keyId
+
+	s.Reset()
+
+	wrapped := s.(hash.Hash)
+
+	if sigType == packet.SigTypeText {
+		wrapped = NewCanonicalTextHash(s)
+	}
+
+	io.Copy(wrapped, message)
+
+	err = sig.Sign(s, nil, config)
+	if err != nil {
+		return
+	}
+
+	err = sig.Serialize(w)
+
+	return
+}
+
 func detachSign(w io.Writer, signer *Entity, message io.Reader, sigType packet.SignatureType, config *packet.Config) (err error) {
-	if signer.PrivateKey == nil {
+	signerSubkey, ok := signer.signingKey(config.Now())
+	if !ok {
+		err = errors.InvalidArgumentError("no valid signing keys")
+		return
+	}
+	if signerSubkey.PrivateKey == nil {
 		return errors.InvalidArgumentError("signing key doesn't have a private key")
 	}
-	if signer.PrivateKey.Encrypted {
+	if signerSubkey.PrivateKey.Encrypted {
 		return errors.InvalidArgumentError("signing key is encrypted")
 	}
 
 	sig := new(packet.Signature)
 	sig.SigType = sigType
-	sig.PubKeyAlgo = signer.PrivateKey.PubKeyAlgo
+	sig.PubKeyAlgo = signerSubkey.PrivateKey.PubKeyAlgo
 	sig.Hash = config.Hash()
 	sig.CreationTime = config.Now()
-	sig.IssuerKeyId = &signer.PrivateKey.KeyId
+	sig.IssuerKeyId = &signerSubkey.PrivateKey.KeyId
 
 	h, wrappedHash, err := hashForSignature(sig.Hash, sig.SigType)
 	if err != nil {
@@ -80,7 +117,7 @@ func detachSign(w io.Writer, signer *Entity, message io.Reader, sigType packet.S
 	}
 	io.Copy(wrappedHash, message)
 
-	err = sig.Sign(h, signer.PrivateKey, config)
+	err = sig.Sign(h, signerSubkey.PrivateKey, config)
 	if err != nil {
 		return
 	}
@@ -198,11 +235,20 @@ func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHint
 		hashToHashId(crypto.SHA1),
 		hashToHashId(crypto.RIPEMD160),
 	}
-	// In the event that a recipient doesn't specify any supported ciphers
-	// or hash functions, these are the ones that we assume that every
-	// implementation supports.
-	defaultCiphers := candidateCiphers[len(candidateCiphers)-1:]
-	defaultHashes := candidateHashes[len(candidateHashes)-1:]
+
+	// If no preferences were specified, assume something safe and reasonable.
+	defaultCiphers := []uint8{
+		uint8(packet.CipherAES128),
+		uint8(packet.CipherAES192),
+		uint8(packet.CipherAES256),
+		uint8(packet.CipherCAST5),
+	}
+
+	defaultHashes := []uint8{
+		hashToHashId(crypto.SHA256),
+		hashToHashId(crypto.SHA512),
+		hashToHashId(crypto.RIPEMD160),
+	}
 
 	encryptKeys := make([]Key, len(to))
 	for i := range to {
@@ -226,12 +272,15 @@ func Encrypt(ciphertext io.Writer, to []*Entity, signed *Entity, hints *FileHint
 		candidateHashes = intersectPreferences(candidateHashes, preferredHashes)
 	}
 
-	if len(candidateCiphers) == 0 || len(candidateHashes) == 0 {
-		return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common algorithms")
+	if len(candidateCiphers) == 0 {
+		return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common ciphers")
+	}
+	if len(candidateHashes) == 0 {
+		return nil, errors.InvalidArgumentError("cannot encrypt because recipient set shares no common hashes")
 	}
 
 	cipher := packet.CipherFunction(candidateCiphers[0])
-	// If the cipher specified by config is a candidate, we'll use that.
+	// If the cipher specifed by config is a candidate, we'll use that.
 	configuredCipher := config.Cipher()
 	for _, c := range candidateCiphers {
 		cipherFunc := packet.CipherFunction(c)
@@ -376,3 +425,71 @@ func (c noOpCloser) Write(data []byte) (n int, err error) {
 func (c noOpCloser) Close() error {
 	return nil
 }
+
+// AttachedSign is like openpgp.Encrypt (as in p.crypto/openpgp/write.go), but
+// don't encrypt at all, just sign the literal unencrypted data.
+// Unfortunately we need to duplicate some code here that's already
+// in write.go
+func AttachedSign(out io.WriteCloser, signed Entity, hints *FileHints,
+	config *packet.Config) (in io.WriteCloser, err error) {
+
+	if hints == nil {
+		hints = &FileHints{}
+	}
+
+	if config == nil {
+		config = &packet.Config{}
+	}
+
+	var signer *packet.PrivateKey
+
+	signKey, ok := signed.signingKey(config.Now())
+	if !ok {
+		err = errors.InvalidArgumentError("no valid signing keys")
+		return
+	}
+	signer = signKey.PrivateKey
+	if signer == nil {
+		err = errors.InvalidArgumentError("no valid signing keys")
+		return
+	}
+	if signer.Encrypted {
+		err = errors.InvalidArgumentError("signing key must be decrypted")
+		return
+	}
+
+	hasher := crypto.SHA512
+
+	ops := &packet.OnePassSignature{
+		SigType:    packet.SigTypeBinary,
+		Hash:       hasher,
+		PubKeyAlgo: signer.PubKeyAlgo,
+		KeyId:      signer.KeyId,
+		IsLast:     true,
+	}
+
+	if err = ops.Serialize(out); err != nil {
+		return
+	}
+
+	var epochSeconds uint32
+	if !hints.ModTime.IsZero() {
+		epochSeconds = uint32(hints.ModTime.Unix())
+	}
+
+	// We don't want the literal serializer to closer the output stream
+	// since we're going to need to write to it when we finish up the
+	// signature stuff.
+	in, err = packet.SerializeLiteral(noOpCloser{out}, hints.IsBinary, hints.FileName, epochSeconds)
+
+	if err != nil {
+		return
+	}
+
+	// If we need to write a signature packet after the literal
+	// data then we need to stop literalData from closing
+	// encryptedData.
+	in = signatureWriter{out, in, hasher, hasher.New(), signer, config}
+
+	return
+}
diff --git a/vendor/github.com/keybase/go-crypto/rsa/pkcs1v15.go b/vendor/github.com/keybase/go-crypto/rsa/pkcs1v15.go
new file mode 100644
index 000000000..5c5f415c8
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/rsa/pkcs1v15.go
@@ -0,0 +1,325 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package rsa
+
+import (
+	"crypto"
+	"crypto/subtle"
+	"errors"
+	"io"
+	"math/big"
+)
+
+// This file implements encryption and decryption using PKCS#1 v1.5 padding.
+
+// PKCS1v15DecrypterOpts is for passing options to PKCS#1 v1.5 decryption using
+// the crypto.Decrypter interface.
+type PKCS1v15DecryptOptions struct {
+	// SessionKeyLen is the length of the session key that is being
+	// decrypted. If not zero, then a padding error during decryption will
+	// cause a random plaintext of this length to be returned rather than
+	// an error. These alternatives happen in constant time.
+	SessionKeyLen int
+}
+
+// EncryptPKCS1v15 encrypts the given message with RSA and the padding scheme from PKCS#1 v1.5.
+// The message must be no longer than the length of the public modulus minus 11 bytes.
+//
+// The rand parameter is used as a source of entropy to ensure that encrypting
+// the same message twice doesn't result in the same ciphertext.
+//
+// WARNING: use of this function to encrypt plaintexts other than session keys
+// is dangerous. Use RSA OAEP in new protocols.
+func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) (out []byte, err error) {
+	if err := checkPub(pub); err != nil {
+		return nil, err
+	}
+	k := (pub.N.BitLen() + 7) / 8
+	if len(msg) > k-11 {
+		err = ErrMessageTooLong
+		return
+	}
+
+	// EM = 0x00 || 0x02 || PS || 0x00 || M
+	em := make([]byte, k)
+	em[1] = 2
+	ps, mm := em[2:len(em)-len(msg)-1], em[len(em)-len(msg):]
+	err = nonZeroRandomBytes(ps, rand)
+	if err != nil {
+		return
+	}
+	em[len(em)-len(msg)-1] = 0
+	copy(mm, msg)
+
+	m := new(big.Int).SetBytes(em)
+	c := encrypt(new(big.Int), pub, m)
+
+	copyWithLeftPad(em, c.Bytes())
+	out = em
+	return
+}
+
+// DecryptPKCS1v15 decrypts a plaintext using RSA and the padding scheme from PKCS#1 v1.5.
+// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
+//
+// Note that whether this function returns an error or not discloses secret
+// information. If an attacker can cause this function to run repeatedly and
+// learn whether each instance returned an error then they can decrypt and
+// forge signatures as if they had the private key. See
+// DecryptPKCS1v15SessionKey for a way of solving this problem.
+func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (out []byte, err error) {
+	if err := checkPub(&priv.PublicKey); err != nil {
+		return nil, err
+	}
+	valid, out, index, err := decryptPKCS1v15(rand, priv, ciphertext)
+	if err != nil {
+		return
+	}
+	if valid == 0 {
+		return nil, ErrDecryption
+	}
+	out = out[index:]
+	return
+}
+
+// DecryptPKCS1v15SessionKey decrypts a session key using RSA and the padding scheme from PKCS#1 v1.5.
+// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
+// It returns an error if the ciphertext is the wrong length or if the
+// ciphertext is greater than the public modulus. Otherwise, no error is
+// returned. If the padding is valid, the resulting plaintext message is copied
+// into key. Otherwise, key is unchanged. These alternatives occur in constant
+// time. It is intended that the user of this function generate a random
+// session key beforehand and continue the protocol with the resulting value.
+// This will remove any possibility that an attacker can learn any information
+// about the plaintext.
+// See ``Chosen Ciphertext Attacks Against Protocols Based on the RSA
+// Encryption Standard PKCS #1'', Daniel Bleichenbacher, Advances in Cryptology
+// (Crypto '98).
+//
+// Note that if the session key is too small then it may be possible for an
+// attacker to brute-force it. If they can do that then they can learn whether
+// a random value was used (because it'll be different for the same ciphertext)
+// and thus whether the padding was correct. This defeats the point of this
+// function. Using at least a 16-byte key will protect against this attack.
+func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) (err error) {
+	if err := checkPub(&priv.PublicKey); err != nil {
+		return err
+	}
+	k := (priv.N.BitLen() + 7) / 8
+	if k-(len(key)+3+8) < 0 {
+		return ErrDecryption
+	}
+
+	valid, em, index, err := decryptPKCS1v15(rand, priv, ciphertext)
+	if err != nil {
+		return
+	}
+
+	if len(em) != k {
+		// This should be impossible because decryptPKCS1v15 always
+		// returns the full slice.
+		return ErrDecryption
+	}
+
+	valid &= subtle.ConstantTimeEq(int32(len(em)-index), int32(len(key)))
+	subtle.ConstantTimeCopy(valid, key, em[len(em)-len(key):])
+	return
+}
+
+// decryptPKCS1v15 decrypts ciphertext using priv and blinds the operation if
+// rand is not nil. It returns one or zero in valid that indicates whether the
+// plaintext was correctly structured. In either case, the plaintext is
+// returned in em so that it may be read independently of whether it was valid
+// in order to maintain constant memory access patterns. If the plaintext was
+// valid then index contains the index of the original message in em.
+func decryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (valid int, em []byte, index int, err error) {
+	k := (priv.N.BitLen() + 7) / 8
+	if k < 11 {
+		err = ErrDecryption
+		return
+	}
+
+	c := new(big.Int).SetBytes(ciphertext)
+	m, err := decrypt(rand, priv, c)
+	if err != nil {
+		return
+	}
+
+	em = leftPad(m.Bytes(), k)
+	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
+	secondByteIsTwo := subtle.ConstantTimeByteEq(em[1], 2)
+
+	// The remainder of the plaintext must be a string of non-zero random
+	// octets, followed by a 0, followed by the message.
+	//   lookingForIndex: 1 iff we are still looking for the zero.
+	//   index: the offset of the first zero byte.
+	lookingForIndex := 1
+
+	for i := 2; i < len(em); i++ {
+		equals0 := subtle.ConstantTimeByteEq(em[i], 0)
+		index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index)
+		lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex)
+	}
+
+	// The PS padding must be at least 8 bytes long, and it starts two
+	// bytes into em.
+	validPS := subtle.ConstantTimeLessOrEq(2+8, index)
+
+	valid = firstByteIsZero & secondByteIsTwo & (^lookingForIndex & 1) & validPS
+	index = subtle.ConstantTimeSelect(valid, index+1, 0)
+	return valid, em, index, nil
+}
+
+// nonZeroRandomBytes fills the given slice with non-zero random octets.
+func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) {
+	_, err = io.ReadFull(rand, s)
+	if err != nil {
+		return
+	}
+
+	for i := 0; i < len(s); i++ {
+		for s[i] == 0 {
+			_, err = io.ReadFull(rand, s[i:i+1])
+			if err != nil {
+				return
+			}
+			// In tests, the PRNG may return all zeros so we do
+			// this to break the loop.
+			s[i] ^= 0x42
+		}
+	}
+
+	return
+}
+
+// These are ASN1 DER structures:
+//   DigestInfo ::= SEQUENCE {
+//     digestAlgorithm AlgorithmIdentifier,
+//     digest OCTET STRING
+//   }
+// For performance, we don't use the generic ASN1 encoder. Rather, we
+// precompute a prefix of the digest value that makes a valid ASN1 DER string
+// with the correct contents.
+var hashPrefixes = map[crypto.Hash][]byte{
+	crypto.MD5:       {0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10},
+	crypto.SHA1:      {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14},
+	crypto.SHA224:    {0x30, 0x2d, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04, 0x05, 0x00, 0x04, 0x1c},
+	crypto.SHA256:    {0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20},
+	crypto.SHA384:    {0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30},
+	crypto.SHA512:    {0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40},
+	crypto.MD5SHA1:   {}, // A special TLS case which doesn't use an ASN1 prefix.
+	crypto.RIPEMD160: {0x30, 0x20, 0x30, 0x08, 0x06, 0x06, 0x28, 0xcf, 0x06, 0x03, 0x00, 0x31, 0x04, 0x14},
+}
+
+// SignPKCS1v15 calculates the signature of hashed using RSASSA-PKCS1-V1_5-SIGN from RSA PKCS#1 v1.5.
+// Note that hashed must be the result of hashing the input message using the
+// given hash function. If hash is zero, hashed is signed directly. This isn't
+// advisable except for interoperability.
+//
+// If rand is not nil then RSA blinding will be used to avoid timing side-channel attacks.
+//
+// This function is deterministic. Thus, if the set of possible messages is
+// small, an attacker may be able to build a map from messages to signatures
+// and identify the signed messages. As ever, signatures provide authenticity,
+// not confidentiality.
+func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []byte) (s []byte, err error) {
+	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
+	if err != nil {
+		return
+	}
+
+	tLen := len(prefix) + hashLen
+	k := (priv.N.BitLen() + 7) / 8
+	if k < tLen+11 {
+		return nil, ErrMessageTooLong
+	}
+
+	// EM = 0x00 || 0x01 || PS || 0x00 || T
+	em := make([]byte, k)
+	em[1] = 1
+	for i := 2; i < k-tLen-1; i++ {
+		em[i] = 0xff
+	}
+	copy(em[k-tLen:k-hashLen], prefix)
+	copy(em[k-hashLen:k], hashed)
+
+	m := new(big.Int).SetBytes(em)
+	c, err := decryptAndCheck(rand, priv, m)
+	if err != nil {
+		return
+	}
+
+	copyWithLeftPad(em, c.Bytes())
+	s = em
+	return
+}
+
+// VerifyPKCS1v15 verifies an RSA PKCS#1 v1.5 signature.
+// hashed is the result of hashing the input message using the given hash
+// function and sig is the signature. A valid signature is indicated by
+// returning a nil error. If hash is zero then hashed is used directly. This
+// isn't advisable except for interoperability.
+func VerifyPKCS1v15(pub *PublicKey, hash crypto.Hash, hashed []byte, sig []byte) (err error) {
+	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
+	if err != nil {
+		return
+	}
+
+	tLen := len(prefix) + hashLen
+	k := (pub.N.BitLen() + 7) / 8
+	if k < tLen+11 {
+		err = ErrVerification
+		return
+	}
+
+	c := new(big.Int).SetBytes(sig)
+	m := encrypt(new(big.Int), pub, c)
+	em := leftPad(m.Bytes(), k)
+	// EM = 0x00 || 0x01 || PS || 0x00 || T
+
+	ok := subtle.ConstantTimeByteEq(em[0], 0)
+	ok &= subtle.ConstantTimeByteEq(em[1], 1)
+	ok &= subtle.ConstantTimeCompare(em[k-hashLen:k], hashed)
+	ok &= subtle.ConstantTimeCompare(em[k-tLen:k-hashLen], prefix)
+	ok &= subtle.ConstantTimeByteEq(em[k-tLen-1], 0)
+
+	for i := 2; i < k-tLen-1; i++ {
+		ok &= subtle.ConstantTimeByteEq(em[i], 0xff)
+	}
+
+	if ok != 1 {
+		return ErrVerification
+	}
+
+	return nil
+}
+
+func pkcs1v15HashInfo(hash crypto.Hash, inLen int) (hashLen int, prefix []byte, err error) {
+	// Special case: crypto.Hash(0) is used to indicate that the data is
+	// signed directly.
+	if hash == 0 {
+		return inLen, nil, nil
+	}
+
+	hashLen = hash.Size()
+	if inLen != hashLen {
+		return 0, nil, errors.New("crypto/rsa: input must be hashed message")
+	}
+	prefix, ok := hashPrefixes[hash]
+	if !ok {
+		return 0, nil, errors.New("crypto/rsa: unsupported hash function")
+	}
+	return
+}
+
+// copyWithLeftPad copies src to the end of dest, padding with zero bytes as
+// needed.
+func copyWithLeftPad(dest, src []byte) {
+	numPaddingBytes := len(dest) - len(src)
+	for i := 0; i < numPaddingBytes; i++ {
+		dest[i] = 0
+	}
+	copy(dest[numPaddingBytes:], src)
+}
diff --git a/vendor/github.com/keybase/go-crypto/rsa/pss.go b/vendor/github.com/keybase/go-crypto/rsa/pss.go
new file mode 100644
index 000000000..8a94589b1
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/rsa/pss.go
@@ -0,0 +1,297 @@
+// Copyright 2013 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package rsa
+
+// This file implements the PSS signature scheme [1].
+//
+// [1] http://www.rsa.com/rsalabs/pkcs/files/h11300-wp-pkcs-1v2-2-rsa-cryptography-standard.pdf
+
+import (
+	"bytes"
+	"crypto"
+	"errors"
+	"hash"
+	"io"
+	"math/big"
+)
+
+func emsaPSSEncode(mHash []byte, emBits int, salt []byte, hash hash.Hash) ([]byte, error) {
+	// See [1], section 9.1.1
+	hLen := hash.Size()
+	sLen := len(salt)
+	emLen := (emBits + 7) / 8
+
+	// 1.  If the length of M is greater than the input limitation for the
+	//     hash function (2^61 - 1 octets for SHA-1), output "message too
+	//     long" and stop.
+	//
+	// 2.  Let mHash = Hash(M), an octet string of length hLen.
+
+	if len(mHash) != hLen {
+		return nil, errors.New("crypto/rsa: input must be hashed message")
+	}
+
+	// 3.  If emLen < hLen + sLen + 2, output "encoding error" and stop.
+
+	if emLen < hLen+sLen+2 {
+		return nil, errors.New("crypto/rsa: encoding error")
+	}
+
+	em := make([]byte, emLen)
+	db := em[:emLen-sLen-hLen-2+1+sLen]
+	h := em[emLen-sLen-hLen-2+1+sLen : emLen-1]
+
+	// 4.  Generate a random octet string salt of length sLen; if sLen = 0,
+	//     then salt is the empty string.
+	//
+	// 5.  Let
+	//       M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt;
+	//
+	//     M' is an octet string of length 8 + hLen + sLen with eight
+	//     initial zero octets.
+	//
+	// 6.  Let H = Hash(M'), an octet string of length hLen.
+
+	var prefix [8]byte
+
+	hash.Write(prefix[:])
+	hash.Write(mHash)
+	hash.Write(salt)
+
+	h = hash.Sum(h[:0])
+	hash.Reset()
+
+	// 7.  Generate an octet string PS consisting of emLen - sLen - hLen - 2
+	//     zero octets.  The length of PS may be 0.
+	//
+	// 8.  Let DB = PS || 0x01 || salt; DB is an octet string of length
+	//     emLen - hLen - 1.
+
+	db[emLen-sLen-hLen-2] = 0x01
+	copy(db[emLen-sLen-hLen-1:], salt)
+
+	// 9.  Let dbMask = MGF(H, emLen - hLen - 1).
+	//
+	// 10. Let maskedDB = DB \xor dbMask.
+
+	mgf1XOR(db, hash, h)
+
+	// 11. Set the leftmost 8 * emLen - emBits bits of the leftmost octet in
+	//     maskedDB to zero.
+
+	db[0] &= (0xFF >> uint(8*emLen-emBits))
+
+	// 12. Let EM = maskedDB || H || 0xbc.
+	em[emLen-1] = 0xBC
+
+	// 13. Output EM.
+	return em, nil
+}
+
+func emsaPSSVerify(mHash, em []byte, emBits, sLen int, hash hash.Hash) error {
+	// 1.  If the length of M is greater than the input limitation for the
+	//     hash function (2^61 - 1 octets for SHA-1), output "inconsistent"
+	//     and stop.
+	//
+	// 2.  Let mHash = Hash(M), an octet string of length hLen.
+	hLen := hash.Size()
+	if hLen != len(mHash) {
+		return ErrVerification
+	}
+
+	// 3.  If emLen < hLen + sLen + 2, output "inconsistent" and stop.
+	emLen := (emBits + 7) / 8
+	if emLen < hLen+sLen+2 {
+		return ErrVerification
+	}
+
+	// 4.  If the rightmost octet of EM does not have hexadecimal value
+	//     0xbc, output "inconsistent" and stop.
+	if em[len(em)-1] != 0xBC {
+		return ErrVerification
+	}
+
+	// 5.  Let maskedDB be the leftmost emLen - hLen - 1 octets of EM, and
+	//     let H be the next hLen octets.
+	db := em[:emLen-hLen-1]
+	h := em[emLen-hLen-1 : len(em)-1]
+
+	// 6.  If the leftmost 8 * emLen - emBits bits of the leftmost octet in
+	//     maskedDB are not all equal to zero, output "inconsistent" and
+	//     stop.
+	if em[0]&(0xFF<<uint(8-(8*emLen-emBits))) != 0 {
+		return ErrVerification
+	}
+
+	// 7.  Let dbMask = MGF(H, emLen - hLen - 1).
+	//
+	// 8.  Let DB = maskedDB \xor dbMask.
+	mgf1XOR(db, hash, h)
+
+	// 9.  Set the leftmost 8 * emLen - emBits bits of the leftmost octet in DB
+	//     to zero.
+	db[0] &= (0xFF >> uint(8*emLen-emBits))
+
+	if sLen == PSSSaltLengthAuto {
+	FindSaltLength:
+		for sLen = emLen - (hLen + 2); sLen >= 0; sLen-- {
+			switch db[emLen-hLen-sLen-2] {
+			case 1:
+				break FindSaltLength
+			case 0:
+				continue
+			default:
+				return ErrVerification
+			}
+		}
+		if sLen < 0 {
+			return ErrVerification
+		}
+	} else {
+		// 10. If the emLen - hLen - sLen - 2 leftmost octets of DB are not zero
+		//     or if the octet at position emLen - hLen - sLen - 1 (the leftmost
+		//     position is "position 1") does not have hexadecimal value 0x01,
+		//     output "inconsistent" and stop.
+		for _, e := range db[:emLen-hLen-sLen-2] {
+			if e != 0x00 {
+				return ErrVerification
+			}
+		}
+		if db[emLen-hLen-sLen-2] != 0x01 {
+			return ErrVerification
+		}
+	}
+
+	// 11.  Let salt be the last sLen octets of DB.
+	salt := db[len(db)-sLen:]
+
+	// 12.  Let
+	//          M' = (0x)00 00 00 00 00 00 00 00 || mHash || salt ;
+	//     M' is an octet string of length 8 + hLen + sLen with eight
+	//     initial zero octets.
+	//
+	// 13. Let H' = Hash(M'), an octet string of length hLen.
+	var prefix [8]byte
+	hash.Write(prefix[:])
+	hash.Write(mHash)
+	hash.Write(salt)
+
+	h0 := hash.Sum(nil)
+
+	// 14. If H = H', output "consistent." Otherwise, output "inconsistent."
+	if !bytes.Equal(h0, h) {
+		return ErrVerification
+	}
+	return nil
+}
+
+// signPSSWithSalt calculates the signature of hashed using PSS [1] with specified salt.
+// Note that hashed must be the result of hashing the input message using the
+// given hash function. salt is a random sequence of bytes whose length will be
+// later used to verify the signature.
+func signPSSWithSalt(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed, salt []byte) (s []byte, err error) {
+	nBits := priv.N.BitLen()
+	em, err := emsaPSSEncode(hashed, nBits-1, salt, hash.New())
+	if err != nil {
+		return
+	}
+	m := new(big.Int).SetBytes(em)
+	c, err := decryptAndCheck(rand, priv, m)
+	if err != nil {
+		return
+	}
+	s = make([]byte, (nBits+7)/8)
+	copyWithLeftPad(s, c.Bytes())
+	return
+}
+
+const (
+	// PSSSaltLengthAuto causes the salt in a PSS signature to be as large
+	// as possible when signing, and to be auto-detected when verifying.
+	PSSSaltLengthAuto = 0
+	// PSSSaltLengthEqualsHash causes the salt length to equal the length
+	// of the hash used in the signature.
+	PSSSaltLengthEqualsHash = -1
+)
+
+// PSSOptions contains options for creating and verifying PSS signatures.
+type PSSOptions struct {
+	// SaltLength controls the length of the salt used in the PSS
+	// signature. It can either be a number of bytes, or one of the special
+	// PSSSaltLength constants.
+	SaltLength int
+
+	// Hash, if not zero, overrides the hash function passed to SignPSS.
+	// This is the only way to specify the hash function when using the
+	// crypto.Signer interface.
+	Hash crypto.Hash
+}
+
+// HashFunc returns pssOpts.Hash so that PSSOptions implements
+// crypto.SignerOpts.
+func (pssOpts *PSSOptions) HashFunc() crypto.Hash {
+	return pssOpts.Hash
+}
+
+func (opts *PSSOptions) saltLength() int {
+	if opts == nil {
+		return PSSSaltLengthAuto
+	}
+	return opts.SaltLength
+}
+
+// SignPSS calculates the signature of hashed using RSASSA-PSS [1].
+// Note that hashed must be the result of hashing the input message using the
+// given hash function. The opts argument may be nil, in which case sensible
+// defaults are used.
+func SignPSS(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []byte, opts *PSSOptions) (s []byte, err error) {
+	saltLength := opts.saltLength()
+	switch saltLength {
+	case PSSSaltLengthAuto:
+		saltLength = (priv.N.BitLen()+7)/8 - 2 - hash.Size()
+	case PSSSaltLengthEqualsHash:
+		saltLength = hash.Size()
+	}
+
+	if opts != nil && opts.Hash != 0 {
+		hash = opts.Hash
+	}
+
+	salt := make([]byte, saltLength)
+	if _, err = io.ReadFull(rand, salt); err != nil {
+		return
+	}
+	return signPSSWithSalt(rand, priv, hash, hashed, salt)
+}
+
+// VerifyPSS verifies a PSS signature.
+// hashed is the result of hashing the input message using the given hash
+// function and sig is the signature. A valid signature is indicated by
+// returning a nil error. The opts argument may be nil, in which case sensible
+// defaults are used.
+func VerifyPSS(pub *PublicKey, hash crypto.Hash, hashed []byte, sig []byte, opts *PSSOptions) error {
+	return verifyPSS(pub, hash, hashed, sig, opts.saltLength())
+}
+
+// verifyPSS verifies a PSS signature with the given salt length.
+func verifyPSS(pub *PublicKey, hash crypto.Hash, hashed []byte, sig []byte, saltLen int) error {
+	nBits := pub.N.BitLen()
+	if len(sig) != (nBits+7)/8 {
+		return ErrVerification
+	}
+	s := new(big.Int).SetBytes(sig)
+	m := encrypt(new(big.Int), pub, s)
+	emBits := nBits - 1
+	emLen := (emBits + 7) / 8
+	if emLen < len(m.Bytes()) {
+		return ErrVerification
+	}
+	em := make([]byte, emLen)
+	copyWithLeftPad(em, m.Bytes())
+	if saltLen == PSSSaltLengthEqualsHash {
+		saltLen = hash.Size()
+	}
+	return emsaPSSVerify(hashed, em, emBits, saltLen, hash.New())
+}
diff --git a/vendor/github.com/keybase/go-crypto/rsa/rsa.go b/vendor/github.com/keybase/go-crypto/rsa/rsa.go
new file mode 100644
index 000000000..ff6b11b3e
--- /dev/null
+++ b/vendor/github.com/keybase/go-crypto/rsa/rsa.go
@@ -0,0 +1,646 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package rsa implements RSA encryption as specified in PKCS#1.
+//
+// RSA is a single, fundamental operation that is used in this package to
+// implement either public-key encryption or public-key signatures.
+//
+// The original specification for encryption and signatures with RSA is PKCS#1
+// and the terms "RSA encryption" and "RSA signatures" by default refer to
+// PKCS#1 version 1.5. However, that specification has flaws and new designs
+// should use version two, usually called by just OAEP and PSS, where
+// possible.
+//
+// Two sets of interfaces are included in this package. When a more abstract
+// interface isn't neccessary, there are functions for encrypting/decrypting
+// with v1.5/OAEP and signing/verifying with v1.5/PSS. If one needs to abstract
+// over the public-key primitive, the PrivateKey struct implements the
+// Decrypter and Signer interfaces from the crypto package.
+package rsa
+
+import (
+	"crypto"
+	"crypto/rand"
+	"crypto/subtle"
+	"errors"
+	"hash"
+	"io"
+	"math/big"
+)
+
+var bigZero = big.NewInt(0)
+var bigOne = big.NewInt(1)
+
+// A PublicKey represents the public part of an RSA key.
+type PublicKey struct {
+	N *big.Int // modulus
+	E int64    // public exponent
+}
+
+// OAEPOptions is an interface for passing options to OAEP decryption using the
+// crypto.Decrypter interface.
+type OAEPOptions struct {
+	// Hash is the hash function that will be used when generating the mask.
+	Hash crypto.Hash
+	// Label is an arbitrary byte string that must be equal to the value
+	// used when encrypting.
+	Label []byte
+}
+
+var (
+	errPublicModulus       = errors.New("crypto/rsa: missing public modulus")
+	errPublicExponentSmall = errors.New("crypto/rsa: public exponent too small")
+	errPublicExponentLarge = errors.New("crypto/rsa: public exponent too large")
+)
+
+// checkPub sanity checks the public key before we use it.
+// We require pub.E to fit into a 32-bit integer so that we
+// do not have different behavior depending on whether
+// int is 32 or 64 bits. See also
+// http://www.imperialviolet.org/2012/03/16/rsae.html.
+func checkPub(pub *PublicKey) error {
+	if pub.N == nil {
+		return errPublicModulus
+	}
+	if pub.E < 2 {
+		return errPublicExponentSmall
+	}
+	if pub.E > 1<<63-1 {
+		return errPublicExponentLarge
+	}
+	return nil
+}
+
+// A PrivateKey represents an RSA key
+type PrivateKey struct {
+	PublicKey            // public part.
+	D         *big.Int   // private exponent
+	Primes    []*big.Int // prime factors of N, has >= 2 elements.
+
+	// Precomputed contains precomputed values that speed up private
+	// operations, if available.
+	Precomputed PrecomputedValues
+}
+
+// Public returns the public key corresponding to priv.
+func (priv *PrivateKey) Public() crypto.PublicKey {
+	return &priv.PublicKey
+}
+
+// Sign signs msg with priv, reading randomness from rand. If opts is a
+// *PSSOptions then the PSS algorithm will be used, otherwise PKCS#1 v1.5 will
+// be used. This method is intended to support keys where the private part is
+// kept in, for example, a hardware module. Common uses should use the Sign*
+// functions in this package.
+func (priv *PrivateKey) Sign(rand io.Reader, msg []byte, opts crypto.SignerOpts) ([]byte, error) {
+	if pssOpts, ok := opts.(*PSSOptions); ok {
+		return SignPSS(rand, priv, pssOpts.Hash, msg, pssOpts)
+	}
+
+	return SignPKCS1v15(rand, priv, opts.HashFunc(), msg)
+}
+
+// Decrypt decrypts ciphertext with priv. If opts is nil or of type
+// *PKCS1v15DecryptOptions then PKCS#1 v1.5 decryption is performed. Otherwise
+// opts must have type *OAEPOptions and OAEP decryption is done.
+func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) {
+	if opts == nil {
+		return DecryptPKCS1v15(rand, priv, ciphertext)
+	}
+
+	switch opts := opts.(type) {
+	case *OAEPOptions:
+		return DecryptOAEP(opts.Hash.New(), rand, priv, ciphertext, opts.Label)
+
+	case *PKCS1v15DecryptOptions:
+		if l := opts.SessionKeyLen; l > 0 {
+			plaintext = make([]byte, l)
+			if _, err := io.ReadFull(rand, plaintext); err != nil {
+				return nil, err
+			}
+			if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil {
+				return nil, err
+			}
+			return plaintext, nil
+		} else {
+			return DecryptPKCS1v15(rand, priv, ciphertext)
+		}
+
+	default:
+		return nil, errors.New("crypto/rsa: invalid options for Decrypt")
+	}
+}
+
+type PrecomputedValues struct {
+	Dp, Dq *big.Int // D mod (P-1) (or mod Q-1)
+	Qinv   *big.Int // Q^-1 mod P
+
+	// CRTValues is used for the 3rd and subsequent primes. Due to a
+	// historical accident, the CRT for the first two primes is handled
+	// differently in PKCS#1 and interoperability is sufficiently
+	// important that we mirror this.
+	CRTValues []CRTValue
+}
+
+// CRTValue contains the precomputed Chinese remainder theorem values.
+type CRTValue struct {
+	Exp   *big.Int // D mod (prime-1).
+	Coeff *big.Int // R·Coeff ≡ 1 mod Prime.
+	R     *big.Int // product of primes prior to this (inc p and q).
+}
+
+// Validate performs basic sanity checks on the key.
+// It returns nil if the key is valid, or else an error describing a problem.
+func (priv *PrivateKey) Validate() error {
+	if err := checkPub(&priv.PublicKey); err != nil {
+		return err
+	}
+
+	// Check that Πprimes == n.
+	modulus := new(big.Int).Set(bigOne)
+	for _, prime := range priv.Primes {
+		// Any primes ≤ 1 will cause divide-by-zero panics later.
+		if prime.Cmp(bigOne) <= 0 {
+			return errors.New("crypto/rsa: invalid prime value")
+		}
+		modulus.Mul(modulus, prime)
+	}
+	if modulus.Cmp(priv.N) != 0 {
+		return errors.New("crypto/rsa: invalid modulus")
+	}
+
+	// Check that de ≡ 1 mod p-1, for each prime.
+	// This implies that e is coprime to each p-1 as e has a multiplicative
+	// inverse. Therefore e is coprime to lcm(p-1,q-1,r-1,...) =
+	// exponent(ℤ/nℤ). It also implies that a^de ≡ a mod p as a^(p-1) ≡ 1
+	// mod p. Thus a^de ≡ a mod n for all a coprime to n, as required.
+	congruence := new(big.Int)
+	de := new(big.Int).SetInt64(int64(priv.E))
+	de.Mul(de, priv.D)
+	for _, prime := range priv.Primes {
+		pminus1 := new(big.Int).Sub(prime, bigOne)
+		congruence.Mod(de, pminus1)
+		if congruence.Cmp(bigOne) != 0 {
+			return errors.New("crypto/rsa: invalid exponents")
+		}
+	}
+	return nil
+}
+
+// GenerateKey generates an RSA keypair of the given bit size using the
+// random source random (for example, crypto/rand.Reader).
+func GenerateKey(random io.Reader, bits int) (priv *PrivateKey, err error) {
+	return GenerateMultiPrimeKey(random, 2, bits)
+}
+
+// GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
+// size and the given random source, as suggested in [1]. Although the public
+// keys are compatible (actually, indistinguishable) from the 2-prime case,
+// the private keys are not. Thus it may not be possible to export multi-prime
+// private keys in certain formats or to subsequently import them into other
+// code.
+//
+// Table 1 in [2] suggests maximum numbers of primes for a given size.
+//
+// [1] US patent 4405829 (1972, expired)
+// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
+func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (priv *PrivateKey, err error) {
+	priv = new(PrivateKey)
+	priv.E = 65537
+
+	if nprimes < 2 {
+		return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2")
+	}
+
+	primes := make([]*big.Int, nprimes)
+
+NextSetOfPrimes:
+	for {
+		todo := bits
+		// crypto/rand should set the top two bits in each prime.
+		// Thus each prime has the form
+		//   p_i = 2^bitlen(p_i) × 0.11... (in base 2).
+		// And the product is:
+		//   P = 2^todo × α
+		// where α is the product of nprimes numbers of the form 0.11...
+		//
+		// If α < 1/2 (which can happen for nprimes > 2), we need to
+		// shift todo to compensate for lost bits: the mean value of 0.11...
+		// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
+		// will give good results.
+		if nprimes >= 7 {
+			todo += (nprimes - 2) / 5
+		}
+		for i := 0; i < nprimes; i++ {
+			primes[i], err = rand.Prime(random, todo/(nprimes-i))
+			if err != nil {
+				return nil, err
+			}
+			todo -= primes[i].BitLen()
+		}
+
+		// Make sure that primes is pairwise unequal.
+		for i, prime := range primes {
+			for j := 0; j < i; j++ {
+				if prime.Cmp(primes[j]) == 0 {
+					continue NextSetOfPrimes
+				}
+			}
+		}
+
+		n := new(big.Int).Set(bigOne)
+		totient := new(big.Int).Set(bigOne)
+		pminus1 := new(big.Int)
+		for _, prime := range primes {
+			n.Mul(n, prime)
+			pminus1.Sub(prime, bigOne)
+			totient.Mul(totient, pminus1)
+		}
+		if n.BitLen() != bits {
+			// This should never happen for nprimes == 2 because
+			// crypto/rand should set the top two bits in each prime.
+			// For nprimes > 2 we hope it does not happen often.
+			continue NextSetOfPrimes
+		}
+
+		g := new(big.Int)
+		priv.D = new(big.Int)
+		y := new(big.Int)
+		e := big.NewInt(int64(priv.E))
+		g.GCD(priv.D, y, e, totient)
+
+		if g.Cmp(bigOne) == 0 {
+			if priv.D.Sign() < 0 {
+				priv.D.Add(priv.D, totient)
+			}
+			priv.Primes = primes
+			priv.N = n
+
+			break
+		}
+	}
+
+	priv.Precompute()
+	return
+}
+
+// incCounter increments a four byte, big-endian counter.
+func incCounter(c *[4]byte) {
+	if c[3]++; c[3] != 0 {
+		return
+	}
+	if c[2]++; c[2] != 0 {
+		return
+	}
+	if c[1]++; c[1] != 0 {
+		return
+	}
+	c[0]++
+}
+
+// mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
+// specified in PKCS#1 v2.1.
+func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
+	var counter [4]byte
+	var digest []byte
+
+	done := 0
+	for done < len(out) {
+		hash.Write(seed)
+		hash.Write(counter[0:4])
+		digest = hash.Sum(digest[:0])
+		hash.Reset()
+
+		for i := 0; i < len(digest) && done < len(out); i++ {
+			out[done] ^= digest[i]
+			done++
+		}
+		incCounter(&counter)
+	}
+}
+
+// ErrMessageTooLong is returned when attempting to encrypt a message which is
+// too large for the size of the public key.
+var ErrMessageTooLong = errors.New("crypto/rsa: message too long for RSA public key size")
+
+func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
+	e := big.NewInt(int64(pub.E))
+	c.Exp(m, e, pub.N)
+	return c
+}
+
+// EncryptOAEP encrypts the given message with RSA-OAEP.
+//
+// OAEP is parameterised by a hash function that is used as a random oracle.
+// Encryption and decryption of a given message must use the same hash function
+// and sha256.New() is a reasonable choice.
+//
+// The random parameter is used as a source of entropy to ensure that
+// encrypting the same message twice doesn't result in the same ciphertext.
+//
+// The label parameter may contain arbitrary data that will not be encrypted,
+// but which gives important context to the message. For example, if a given
+// public key is used to decrypt two types of messages then distinct label
+// values could be used to ensure that a ciphertext for one purpose cannot be
+// used for another by an attacker. If not required it can be empty.
+//
+// The message must be no longer than the length of the public modulus less
+// twice the hash length plus 2.
+func EncryptOAEP(hash hash.Hash, random io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err error) {
+	if err := checkPub(pub); err != nil {
+		return nil, err
+	}
+	hash.Reset()
+	k := (pub.N.BitLen() + 7) / 8
+	if len(msg) > k-2*hash.Size()-2 {
+		err = ErrMessageTooLong
+		return
+	}
+
+	hash.Write(label)
+	lHash := hash.Sum(nil)
+	hash.Reset()
+
+	em := make([]byte, k)
+	seed := em[1 : 1+hash.Size()]
+	db := em[1+hash.Size():]
+
+	copy(db[0:hash.Size()], lHash)
+	db[len(db)-len(msg)-1] = 1
+	copy(db[len(db)-len(msg):], msg)
+
+	_, err = io.ReadFull(random, seed)
+	if err != nil {
+		return
+	}
+
+	mgf1XOR(db, hash, seed)
+	mgf1XOR(seed, hash, db)
+
+	m := new(big.Int)
+	m.SetBytes(em)
+	c := encrypt(new(big.Int), pub, m)
+	out = c.Bytes()
+
+	if len(out) < k {
+		// If the output is too small, we need to left-pad with zeros.
+		t := make([]byte, k)
+		copy(t[k-len(out):], out)
+		out = t
+	}
+
+	return
+}
+
+// ErrDecryption represents a failure to decrypt a message.
+// It is deliberately vague to avoid adaptive attacks.
+var ErrDecryption = errors.New("crypto/rsa: decryption error")
+
+// ErrVerification represents a failure to verify a signature.
+// It is deliberately vague to avoid adaptive attacks.
+var ErrVerification = errors.New("crypto/rsa: verification error")
+
+// modInverse returns ia, the inverse of a in the multiplicative group of prime
+// order n. It requires that a be a member of the group (i.e. less than n).
+func modInverse(a, n *big.Int) (ia *big.Int, ok bool) {
+	g := new(big.Int)
+	x := new(big.Int)
+	y := new(big.Int)
+	g.GCD(x, y, a, n)
+	if g.Cmp(bigOne) != 0 {
+		// In this case, a and n aren't coprime and we cannot calculate
+		// the inverse. This happens because the values of n are nearly
+		// prime (being the product of two primes) rather than truly
+		// prime.
+		return
+	}
+
+	if x.Cmp(bigOne) < 0 {
+		// 0 is not the multiplicative inverse of any element so, if x
+		// < 1, then x is negative.
+		x.Add(x, n)
+	}
+
+	return x, true
+}
+
+// Precompute performs some calculations that speed up private key operations
+// in the future.
+func (priv *PrivateKey) Precompute() {
+	if priv.Precomputed.Dp != nil {
+		return
+	}
+
+	priv.Precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne)
+	priv.Precomputed.Dp.Mod(priv.D, priv.Precomputed.Dp)
+
+	priv.Precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne)
+	priv.Precomputed.Dq.Mod(priv.D, priv.Precomputed.Dq)
+
+	priv.Precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0])
+
+	r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1])
+	priv.Precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2)
+	for i := 2; i < len(priv.Primes); i++ {
+		prime := priv.Primes[i]
+		values := &priv.Precomputed.CRTValues[i-2]
+
+		values.Exp = new(big.Int).Sub(prime, bigOne)
+		values.Exp.Mod(priv.D, values.Exp)
+
+		values.R = new(big.Int).Set(r)
+		values.Coeff = new(big.Int).ModInverse(r, prime)
+
+		r.Mul(r, prime)
+	}
+}
+
+// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
+// random source is given, RSA blinding is used.
+func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
+	// TODO(agl): can we get away with reusing blinds?
+	if c.Cmp(priv.N) > 0 {
+		err = ErrDecryption
+		return
+	}
+
+	var ir *big.Int
+	if random != nil {
+		// Blinding enabled. Blinding involves multiplying c by r^e.
+		// Then the decryption operation performs (m^e * r^e)^d mod n
+		// which equals mr mod n. The factor of r can then be removed
+		// by multiplying by the multiplicative inverse of r.
+
+		var r *big.Int
+
+		for {
+			r, err = rand.Int(random, priv.N)
+			if err != nil {
+				return
+			}
+			if r.Cmp(bigZero) == 0 {
+				r = bigOne
+			}
+			var ok bool
+			ir, ok = modInverse(r, priv.N)
+			if ok {
+				break
+			}
+		}
+		bigE := big.NewInt(int64(priv.E))
+		rpowe := new(big.Int).Exp(r, bigE, priv.N)
+		cCopy := new(big.Int).Set(c)
+		cCopy.Mul(cCopy, rpowe)
+		cCopy.Mod(cCopy, priv.N)
+		c = cCopy
+	}
+
+	if priv.Precomputed.Dp == nil {
+		m = new(big.Int).Exp(c, priv.D, priv.N)
+	} else {
+		// We have the precalculated values needed for the CRT.
+		m = new(big.Int).Exp(c, priv.Precomputed.Dp, priv.Primes[0])
+		m2 := new(big.Int).Exp(c, priv.Precomputed.Dq, priv.Primes[1])
+		m.Sub(m, m2)
+		if m.Sign() < 0 {
+			m.Add(m, priv.Primes[0])
+		}
+		m.Mul(m, priv.Precomputed.Qinv)
+		m.Mod(m, priv.Primes[0])
+		m.Mul(m, priv.Primes[1])
+		m.Add(m, m2)
+
+		for i, values := range priv.Precomputed.CRTValues {
+			prime := priv.Primes[2+i]
+			m2.Exp(c, values.Exp, prime)
+			m2.Sub(m2, m)
+			m2.Mul(m2, values.Coeff)
+			m2.Mod(m2, prime)
+			if m2.Sign() < 0 {
+				m2.Add(m2, prime)
+			}
+			m2.Mul(m2, values.R)
+			m.Add(m, m2)
+		}
+	}
+
+	if ir != nil {
+		// Unblind.
+		m.Mul(m, ir)
+		m.Mod(m, priv.N)
+	}
+
+	return
+}
+
+func decryptAndCheck(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
+	m, err = decrypt(random, priv, c)
+	if err != nil {
+		return nil, err
+	}
+
+	// In order to defend against errors in the CRT computation, m^e is
+	// calculated, which should match the original ciphertext.
+	check := encrypt(new(big.Int), &priv.PublicKey, m)
+	if c.Cmp(check) != 0 {
+		return nil, errors.New("rsa: internal error")
+	}
+	return m, nil
+}
+
+// DecryptOAEP decrypts ciphertext using RSA-OAEP.
+
+// OAEP is parameterised by a hash function that is used as a random oracle.
+// Encryption and decryption of a given message must use the same hash function
+// and sha256.New() is a reasonable choice.
+//
+// The random parameter, if not nil, is used to blind the private-key operation
+// and avoid timing side-channel attacks. Blinding is purely internal to this
+// function – the random data need not match that used when encrypting.
+//
+// The label parameter must match the value given when encrypting. See
+// EncryptOAEP for details.
+func DecryptOAEP(hash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err error) {
+	if err := checkPub(&priv.PublicKey); err != nil {
+		return nil, err
+	}
+	k := (priv.N.BitLen() + 7) / 8
+	if len(ciphertext) > k ||
+		k < hash.Size()*2+2 {
+		err = ErrDecryption
+		return
+	}
+
+	c := new(big.Int).SetBytes(ciphertext)
+
+	m, err := decrypt(random, priv, c)
+	if err != nil {
+		return
+	}
+
+	hash.Write(label)
+	lHash := hash.Sum(nil)
+	hash.Reset()
+
+	// Converting the plaintext number to bytes will strip any
+	// leading zeros so we may have to left pad. We do this unconditionally
+	// to avoid leaking timing information. (Although we still probably
+	// leak the number of leading zeros. It's not clear that we can do
+	// anything about this.)
+	em := leftPad(m.Bytes(), k)
+
+	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
+
+	seed := em[1 : hash.Size()+1]
+	db := em[hash.Size()+1:]
+
+	mgf1XOR(seed, hash, db)
+	mgf1XOR(db, hash, seed)
+
+	lHash2 := db[0:hash.Size()]
+
+	// We have to validate the plaintext in constant time in order to avoid
+	// attacks like: J. Manger. A Chosen Ciphertext Attack on RSA Optimal
+	// Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1
+	// v2.0. In J. Kilian, editor, Advances in Cryptology.
+	lHash2Good := subtle.ConstantTimeCompare(lHash, lHash2)
+
+	// The remainder of the plaintext must be zero or more 0x00, followed
+	// by 0x01, followed by the message.
+	//   lookingForIndex: 1 iff we are still looking for the 0x01
+	//   index: the offset of the first 0x01 byte
+	//   invalid: 1 iff we saw a non-zero byte before the 0x01.
+	var lookingForIndex, index, invalid int
+	lookingForIndex = 1
+	rest := db[hash.Size():]
+
+	for i := 0; i < len(rest); i++ {
+		equals0 := subtle.ConstantTimeByteEq(rest[i], 0)
+		equals1 := subtle.ConstantTimeByteEq(rest[i], 1)
+		index = subtle.ConstantTimeSelect(lookingForIndex&equals1, i, index)
+		lookingForIndex = subtle.ConstantTimeSelect(equals1, 0, lookingForIndex)
+		invalid = subtle.ConstantTimeSelect(lookingForIndex&^equals0, 1, invalid)
+	}
+
+	if firstByteIsZero&lHash2Good&^invalid&^lookingForIndex != 1 {
+		err = ErrDecryption
+		return
+	}
+
+	msg = rest[index+1:]
+	return
+}
+
+// leftPad returns a new slice of length size. The contents of input are right
+// aligned in the new slice.
+func leftPad(input []byte, size int) (out []byte) {
+	n := len(input)
+	if n > size {
+		n = size
+	}
+	out = make([]byte, size)
+	copy(out[len(out)-n:], input)
+	return
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/keys.go b/vendor/golang.org/x/crypto/openpgp/keys.go
deleted file mode 100644
index 68b14c6ae..000000000
--- a/vendor/golang.org/x/crypto/openpgp/keys.go
+++ /dev/null
@@ -1,637 +0,0 @@
-// Copyright 2011 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package openpgp
-
-import (
-	"crypto/rsa"
-	"io"
-	"time"
-
-	"golang.org/x/crypto/openpgp/armor"
-	"golang.org/x/crypto/openpgp/errors"
-	"golang.org/x/crypto/openpgp/packet"
-)
-
-// PublicKeyType is the armor type for a PGP public key.
-var PublicKeyType = "PGP PUBLIC KEY BLOCK"
-
-// PrivateKeyType is the armor type for a PGP private key.
-var PrivateKeyType = "PGP PRIVATE KEY BLOCK"
-
-// An Entity represents the components of an OpenPGP key: a primary public key
-// (which must be a signing key), one or more identities claimed by that key,
-// and zero or more subkeys, which may be encryption keys.
-type Entity struct {
-	PrimaryKey  *packet.PublicKey
-	PrivateKey  *packet.PrivateKey
-	Identities  map[string]*Identity // indexed by Identity.Name
-	Revocations []*packet.Signature
-	Subkeys     []Subkey
-}
-
-// An Identity represents an identity claimed by an Entity and zero or more
-// assertions by other entities about that claim.
-type Identity struct {
-	Name          string // by convention, has the form "Full Name (comment) <email@example.com>"
-	UserId        *packet.UserId
-	SelfSignature *packet.Signature
-	Signatures    []*packet.Signature
-}
-
-// A Subkey is an additional public key in an Entity. Subkeys can be used for
-// encryption.
-type Subkey struct {
-	PublicKey  *packet.PublicKey
-	PrivateKey *packet.PrivateKey
-	Sig        *packet.Signature
-}
-
-// A Key identifies a specific public key in an Entity. This is either the
-// Entity's primary key or a subkey.
-type Key struct {
-	Entity        *Entity
-	PublicKey     *packet.PublicKey
-	PrivateKey    *packet.PrivateKey
-	SelfSignature *packet.Signature
-}
-
-// A KeyRing provides access to public and private keys.
-type KeyRing interface {
-	// KeysById returns the set of keys that have the given key id.
-	KeysById(id uint64) []Key
-	// KeysByIdAndUsage returns the set of keys with the given id
-	// that also meet the key usage given by requiredUsage.
-	// The requiredUsage is expressed as the bitwise-OR of
-	// packet.KeyFlag* values.
-	KeysByIdUsage(id uint64, requiredUsage byte) []Key
-	// DecryptionKeys returns all private keys that are valid for
-	// decryption.
-	DecryptionKeys() []Key
-}
-
-// primaryIdentity returns the Identity marked as primary or the first identity
-// if none are so marked.
-func (e *Entity) primaryIdentity() *Identity {
-	var firstIdentity *Identity
-	for _, ident := range e.Identities {
-		if firstIdentity == nil {
-			firstIdentity = ident
-		}
-		if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
-			return ident
-		}
-	}
-	return firstIdentity
-}
-
-// encryptionKey returns the best candidate Key for encrypting a message to the
-// given Entity.
-func (e *Entity) encryptionKey(now time.Time) (Key, bool) {
-	candidateSubkey := -1
-
-	// Iterate the keys to find the newest key
-	var maxTime time.Time
-	for i, subkey := range e.Subkeys {
-		if subkey.Sig.FlagsValid &&
-			subkey.Sig.FlagEncryptCommunications &&
-			subkey.PublicKey.PubKeyAlgo.CanEncrypt() &&
-			!subkey.Sig.KeyExpired(now) &&
-			(maxTime.IsZero() || subkey.Sig.CreationTime.After(maxTime)) {
-			candidateSubkey = i
-			maxTime = subkey.Sig.CreationTime
-		}
-	}
-
-	if candidateSubkey != -1 {
-		subkey := e.Subkeys[candidateSubkey]
-		return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig}, true
-	}
-
-	// If we don't have any candidate subkeys for encryption and
-	// the primary key doesn't have any usage metadata then we
-	// assume that the primary key is ok. Or, if the primary key is
-	// marked as ok to encrypt to, then we can obviously use it.
-	i := e.primaryIdentity()
-	if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagEncryptCommunications &&
-		e.PrimaryKey.PubKeyAlgo.CanEncrypt() &&
-		!i.SelfSignature.KeyExpired(now) {
-		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, true
-	}
-
-	// This Entity appears to be signing only.
-	return Key{}, false
-}
-
-// signingKey return the best candidate Key for signing a message with this
-// Entity.
-func (e *Entity) signingKey(now time.Time) (Key, bool) {
-	candidateSubkey := -1
-
-	for i, subkey := range e.Subkeys {
-		if subkey.Sig.FlagsValid &&
-			subkey.Sig.FlagSign &&
-			subkey.PublicKey.PubKeyAlgo.CanSign() &&
-			!subkey.Sig.KeyExpired(now) {
-			candidateSubkey = i
-			break
-		}
-	}
-
-	if candidateSubkey != -1 {
-		subkey := e.Subkeys[candidateSubkey]
-		return Key{e, subkey.PublicKey, subkey.PrivateKey, subkey.Sig}, true
-	}
-
-	// If we have no candidate subkey then we assume that it's ok to sign
-	// with the primary key.
-	i := e.primaryIdentity()
-	if !i.SelfSignature.FlagsValid || i.SelfSignature.FlagSign &&
-		!i.SelfSignature.KeyExpired(now) {
-		return Key{e, e.PrimaryKey, e.PrivateKey, i.SelfSignature}, true
-	}
-
-	return Key{}, false
-}
-
-// An EntityList contains one or more Entities.
-type EntityList []*Entity
-
-// KeysById returns the set of keys that have the given key id.
-func (el EntityList) KeysById(id uint64) (keys []Key) {
-	for _, e := range el {
-		if e.PrimaryKey.KeyId == id {
-			var selfSig *packet.Signature
-			for _, ident := range e.Identities {
-				if selfSig == nil {
-					selfSig = ident.SelfSignature
-				} else if ident.SelfSignature.IsPrimaryId != nil && *ident.SelfSignature.IsPrimaryId {
-					selfSig = ident.SelfSignature
-					break
-				}
-			}
-			keys = append(keys, Key{e, e.PrimaryKey, e.PrivateKey, selfSig})
-		}
-
-		for _, subKey := range e.Subkeys {
-			if subKey.PublicKey.KeyId == id {
-				keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig})
-			}
-		}
-	}
-	return
-}
-
-// KeysByIdAndUsage returns the set of keys with the given id that also meet
-// the key usage given by requiredUsage.  The requiredUsage is expressed as
-// the bitwise-OR of packet.KeyFlag* values.
-func (el EntityList) KeysByIdUsage(id uint64, requiredUsage byte) (keys []Key) {
-	for _, key := range el.KeysById(id) {
-		if len(key.Entity.Revocations) > 0 {
-			continue
-		}
-
-		if key.SelfSignature.RevocationReason != nil {
-			continue
-		}
-
-		if key.SelfSignature.FlagsValid && requiredUsage != 0 {
-			var usage byte
-			if key.SelfSignature.FlagCertify {
-				usage |= packet.KeyFlagCertify
-			}
-			if key.SelfSignature.FlagSign {
-				usage |= packet.KeyFlagSign
-			}
-			if key.SelfSignature.FlagEncryptCommunications {
-				usage |= packet.KeyFlagEncryptCommunications
-			}
-			if key.SelfSignature.FlagEncryptStorage {
-				usage |= packet.KeyFlagEncryptStorage
-			}
-			if usage&requiredUsage != requiredUsage {
-				continue
-			}
-		}
-
-		keys = append(keys, key)
-	}
-	return
-}
-
-// DecryptionKeys returns all private keys that are valid for decryption.
-func (el EntityList) DecryptionKeys() (keys []Key) {
-	for _, e := range el {
-		for _, subKey := range e.Subkeys {
-			if subKey.PrivateKey != nil && (!subKey.Sig.FlagsValid || subKey.Sig.FlagEncryptStorage || subKey.Sig.FlagEncryptCommunications) {
-				keys = append(keys, Key{e, subKey.PublicKey, subKey.PrivateKey, subKey.Sig})
-			}
-		}
-	}
-	return
-}
-
-// ReadArmoredKeyRing reads one or more public/private keys from an armor keyring file.
-func ReadArmoredKeyRing(r io.Reader) (EntityList, error) {
-	block, err := armor.Decode(r)
-	if err == io.EOF {
-		return nil, errors.InvalidArgumentError("no armored data found")
-	}
-	if err != nil {
-		return nil, err
-	}
-	if block.Type != PublicKeyType && block.Type != PrivateKeyType {
-		return nil, errors.InvalidArgumentError("expected public or private key block, got: " + block.Type)
-	}
-
-	return ReadKeyRing(block.Body)
-}
-
-// ReadKeyRing reads one or more public/private keys. Unsupported keys are
-// ignored as long as at least a single valid key is found.
-func ReadKeyRing(r io.Reader) (el EntityList, err error) {
-	packets := packet.NewReader(r)
-	var lastUnsupportedError error
-
-	for {
-		var e *Entity
-		e, err = ReadEntity(packets)
-		if err != nil {
-			// TODO: warn about skipped unsupported/unreadable keys
-			if _, ok := err.(errors.UnsupportedError); ok {
-				lastUnsupportedError = err
-				err = readToNextPublicKey(packets)
-			} else if _, ok := err.(errors.StructuralError); ok {
-				// Skip unreadable, badly-formatted keys
-				lastUnsupportedError = err
-				err = readToNextPublicKey(packets)
-			}
-			if err == io.EOF {
-				err = nil
-				break
-			}
-			if err != nil {
-				el = nil
-				break
-			}
-		} else {
-			el = append(el, e)
-		}
-	}
-
-	if len(el) == 0 && err == nil {
-		err = lastUnsupportedError
-	}
-	return
-}
-
-// readToNextPublicKey reads packets until the start of the entity and leaves
-// the first packet of the new entity in the Reader.
-func readToNextPublicKey(packets *packet.Reader) (err error) {
-	var p packet.Packet
-	for {
-		p, err = packets.Next()
-		if err == io.EOF {
-			return
-		} else if err != nil {
-			if _, ok := err.(errors.UnsupportedError); ok {
-				err = nil
-				continue
-			}
-			return
-		}
-
-		if pk, ok := p.(*packet.PublicKey); ok && !pk.IsSubkey {
-			packets.Unread(p)
-			return
-		}
-	}
-}
-
-// ReadEntity reads an entity (public key, identities, subkeys etc) from the
-// given Reader.
-func ReadEntity(packets *packet.Reader) (*Entity, error) {
-	e := new(Entity)
-	e.Identities = make(map[string]*Identity)
-
-	p, err := packets.Next()
-	if err != nil {
-		return nil, err
-	}
-
-	var ok bool
-	if e.PrimaryKey, ok = p.(*packet.PublicKey); !ok {
-		if e.PrivateKey, ok = p.(*packet.PrivateKey); !ok {
-			packets.Unread(p)
-			return nil, errors.StructuralError("first packet was not a public/private key")
-		} else {
-			e.PrimaryKey = &e.PrivateKey.PublicKey
-		}
-	}
-
-	if !e.PrimaryKey.PubKeyAlgo.CanSign() {
-		return nil, errors.StructuralError("primary key cannot be used for signatures")
-	}
-
-	var current *Identity
-	var revocations []*packet.Signature
-EachPacket:
-	for {
-		p, err := packets.Next()
-		if err == io.EOF {
-			break
-		} else if err != nil {
-			return nil, err
-		}
-
-		switch pkt := p.(type) {
-		case *packet.UserId:
-			current = new(Identity)
-			current.Name = pkt.Id
-			current.UserId = pkt
-			e.Identities[pkt.Id] = current
-
-			for {
-				p, err = packets.Next()
-				if err == io.EOF {
-					return nil, io.ErrUnexpectedEOF
-				} else if err != nil {
-					return nil, err
-				}
-
-				sig, ok := p.(*packet.Signature)
-				if !ok {
-					return nil, errors.StructuralError("user ID packet not followed by self-signature")
-				}
-
-				if (sig.SigType == packet.SigTypePositiveCert || sig.SigType == packet.SigTypeGenericCert) && sig.IssuerKeyId != nil && *sig.IssuerKeyId == e.PrimaryKey.KeyId {
-					if err = e.PrimaryKey.VerifyUserIdSignature(pkt.Id, e.PrimaryKey, sig); err != nil {
-						return nil, errors.StructuralError("user ID self-signature invalid: " + err.Error())
-					}
-					current.SelfSignature = sig
-					break
-				}
-				current.Signatures = append(current.Signatures, sig)
-			}
-		case *packet.Signature:
-			if pkt.SigType == packet.SigTypeKeyRevocation {
-				revocations = append(revocations, pkt)
-			} else if pkt.SigType == packet.SigTypeDirectSignature {
-				// TODO: RFC4880 5.2.1 permits signatures
-				// directly on keys (eg. to bind additional
-				// revocation keys).
-			} else if current == nil {
-				return nil, errors.StructuralError("signature packet found before user id packet")
-			} else {
-				current.Signatures = append(current.Signatures, pkt)
-			}
-		case *packet.PrivateKey:
-			if pkt.IsSubkey == false {
-				packets.Unread(p)
-				break EachPacket
-			}
-			err = addSubkey(e, packets, &pkt.PublicKey, pkt)
-			if err != nil {
-				return nil, err
-			}
-		case *packet.PublicKey:
-			if pkt.IsSubkey == false {
-				packets.Unread(p)
-				break EachPacket
-			}
-			err = addSubkey(e, packets, pkt, nil)
-			if err != nil {
-				return nil, err
-			}
-		default:
-			// we ignore unknown packets
-		}
-	}
-
-	if len(e.Identities) == 0 {
-		return nil, errors.StructuralError("entity without any identities")
-	}
-
-	for _, revocation := range revocations {
-		err = e.PrimaryKey.VerifyRevocationSignature(revocation)
-		if err == nil {
-			e.Revocations = append(e.Revocations, revocation)
-		} else {
-			// TODO: RFC 4880 5.2.3.15 defines revocation keys.
-			return nil, errors.StructuralError("revocation signature signed by alternate key")
-		}
-	}
-
-	return e, nil
-}
-
-func addSubkey(e *Entity, packets *packet.Reader, pub *packet.PublicKey, priv *packet.PrivateKey) error {
-	var subKey Subkey
-	subKey.PublicKey = pub
-	subKey.PrivateKey = priv
-	p, err := packets.Next()
-	if err == io.EOF {
-		return io.ErrUnexpectedEOF
-	}
-	if err != nil {
-		return errors.StructuralError("subkey signature invalid: " + err.Error())
-	}
-	var ok bool
-	subKey.Sig, ok = p.(*packet.Signature)
-	if !ok {
-		return errors.StructuralError("subkey packet not followed by signature")
-	}
-	if subKey.Sig.SigType != packet.SigTypeSubkeyBinding && subKey.Sig.SigType != packet.SigTypeSubkeyRevocation {
-		return errors.StructuralError("subkey signature with wrong type")
-	}
-	err = e.PrimaryKey.VerifyKeySignature(subKey.PublicKey, subKey.Sig)
-	if err != nil {
-		return errors.StructuralError("subkey signature invalid: " + err.Error())
-	}
-	e.Subkeys = append(e.Subkeys, subKey)
-	return nil
-}
-
-const defaultRSAKeyBits = 2048
-
-// NewEntity returns an Entity that contains a fresh RSA/RSA keypair with a
-// single identity composed of the given full name, comment and email, any of
-// which may be empty but must not contain any of "()<>\x00".
-// If config is nil, sensible defaults will be used.
-func NewEntity(name, comment, email string, config *packet.Config) (*Entity, error) {
-	currentTime := config.Now()
-
-	bits := defaultRSAKeyBits
-	if config != nil && config.RSABits != 0 {
-		bits = config.RSABits
-	}
-
-	uid := packet.NewUserId(name, comment, email)
-	if uid == nil {
-		return nil, errors.InvalidArgumentError("user id field contained invalid characters")
-	}
-	signingPriv, err := rsa.GenerateKey(config.Random(), bits)
-	if err != nil {
-		return nil, err
-	}
-	encryptingPriv, err := rsa.GenerateKey(config.Random(), bits)
-	if err != nil {
-		return nil, err
-	}
-
-	e := &Entity{
-		PrimaryKey: packet.NewRSAPublicKey(currentTime, &signingPriv.PublicKey),
-		PrivateKey: packet.NewRSAPrivateKey(currentTime, signingPriv),
-		Identities: make(map[string]*Identity),
-	}
-	isPrimaryId := true
-	e.Identities[uid.Id] = &Identity{
-		Name:   uid.Name,
-		UserId: uid,
-		SelfSignature: &packet.Signature{
-			CreationTime: currentTime,
-			SigType:      packet.SigTypePositiveCert,
-			PubKeyAlgo:   packet.PubKeyAlgoRSA,
-			Hash:         config.Hash(),
-			IsPrimaryId:  &isPrimaryId,
-			FlagsValid:   true,
-			FlagSign:     true,
-			FlagCertify:  true,
-			IssuerKeyId:  &e.PrimaryKey.KeyId,
-		},
-	}
-
-	// If the user passes in a DefaultHash via packet.Config,
-	// set the PreferredHash for the SelfSignature.
-	if config != nil && config.DefaultHash != 0 {
-		e.Identities[uid.Id].SelfSignature.PreferredHash = []uint8{hashToHashId(config.DefaultHash)}
-	}
-
-	e.Subkeys = make([]Subkey, 1)
-	e.Subkeys[0] = Subkey{
-		PublicKey:  packet.NewRSAPublicKey(currentTime, &encryptingPriv.PublicKey),
-		PrivateKey: packet.NewRSAPrivateKey(currentTime, encryptingPriv),
-		Sig: &packet.Signature{
-			CreationTime:              currentTime,
-			SigType:                   packet.SigTypeSubkeyBinding,
-			PubKeyAlgo:                packet.PubKeyAlgoRSA,
-			Hash:                      config.Hash(),
-			FlagsValid:                true,
-			FlagEncryptStorage:        true,
-			FlagEncryptCommunications: true,
-			IssuerKeyId:               &e.PrimaryKey.KeyId,
-		},
-	}
-	e.Subkeys[0].PublicKey.IsSubkey = true
-	e.Subkeys[0].PrivateKey.IsSubkey = true
-
-	return e, nil
-}
-
-// SerializePrivate serializes an Entity, including private key material, to
-// the given Writer. For now, it must only be used on an Entity returned from
-// NewEntity.
-// If config is nil, sensible defaults will be used.
-func (e *Entity) SerializePrivate(w io.Writer, config *packet.Config) (err error) {
-	err = e.PrivateKey.Serialize(w)
-	if err != nil {
-		return
-	}
-	for _, ident := range e.Identities {
-		err = ident.UserId.Serialize(w)
-		if err != nil {
-			return
-		}
-		err = ident.SelfSignature.SignUserId(ident.UserId.Id, e.PrimaryKey, e.PrivateKey, config)
-		if err != nil {
-			return
-		}
-		err = ident.SelfSignature.Serialize(w)
-		if err != nil {
-			return
-		}
-	}
-	for _, subkey := range e.Subkeys {
-		err = subkey.PrivateKey.Serialize(w)
-		if err != nil {
-			return
-		}
-		err = subkey.Sig.SignKey(subkey.PublicKey, e.PrivateKey, config)
-		if err != nil {
-			return
-		}
-		err = subkey.Sig.Serialize(w)
-		if err != nil {
-			return
-		}
-	}
-	return nil
-}
-
-// Serialize writes the public part of the given Entity to w. (No private
-// key material will be output).
-func (e *Entity) Serialize(w io.Writer) error {
-	err := e.PrimaryKey.Serialize(w)
-	if err != nil {
-		return err
-	}
-	for _, ident := range e.Identities {
-		err = ident.UserId.Serialize(w)
-		if err != nil {
-			return err
-		}
-		err = ident.SelfSignature.Serialize(w)
-		if err != nil {
-			return err
-		}
-		for _, sig := range ident.Signatures {
-			err = sig.Serialize(w)
-			if err != nil {
-				return err
-			}
-		}
-	}
-	for _, subkey := range e.Subkeys {
-		err = subkey.PublicKey.Serialize(w)
-		if err != nil {
-			return err
-		}
-		err = subkey.Sig.Serialize(w)
-		if err != nil {
-			return err
-		}
-	}
-	return nil
-}
-
-// SignIdentity adds a signature to e, from signer, attesting that identity is
-// associated with e. The provided identity must already be an element of
-// e.Identities and the private key of signer must have been decrypted if
-// necessary.
-// If config is nil, sensible defaults will be used.
-func (e *Entity) SignIdentity(identity string, signer *Entity, config *packet.Config) error {
-	if signer.PrivateKey == nil {
-		return errors.InvalidArgumentError("signing Entity must have a private key")
-	}
-	if signer.PrivateKey.Encrypted {
-		return errors.InvalidArgumentError("signing Entity's private key must be decrypted")
-	}
-	ident, ok := e.Identities[identity]
-	if !ok {
-		return errors.InvalidArgumentError("given identity string not found in Entity")
-	}
-
-	sig := &packet.Signature{
-		SigType:      packet.SigTypeGenericCert,
-		PubKeyAlgo:   signer.PrivateKey.PubKeyAlgo,
-		Hash:         config.Hash(),
-		CreationTime: config.Now(),
-		IssuerKeyId:  &signer.PrivateKey.KeyId,
-	}
-	if err := sig.SignUserId(identity, e.PrimaryKey, signer.PrivateKey, config); err != nil {
-		return err
-	}
-	ident.Signatures = append(ident.Signatures, sig)
-	return nil
-}
diff --git a/vendor/vendor.json b/vendor/vendor.json
index b00764c00..c0fb41870 100644
--- a/vendor/vendor.json
+++ b/vendor/vendor.json
@@ -515,6 +515,84 @@
 			"revision": "b2c7a7da5b2995941048f60146e67702a292e468",
 			"revisionTime": "2016-02-12T04:00:40Z"
 		},
+		{
+			"checksumSHA1": "VJk3rOWfxEV9Ilig5lgzH1qg8Ss=",
+			"path": "github.com/keybase/go-crypto/brainpool",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "rnRjEJs5luF+DIXp2J6LFcQk8Gg=",
+			"path": "github.com/keybase/go-crypto/cast5",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "F5++ZQS5Vt7hd6lxPCKTffvph1A=",
+			"path": "github.com/keybase/go-crypto/curve25519",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "IvrDXwIixB5yPPbo6tq1/1cSn78=",
+			"path": "github.com/keybase/go-crypto/ed25519",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "4+fslB6pCbplNq4viy6CrOkkY6Y=",
+			"path": "github.com/keybase/go-crypto/ed25519/internal/edwards25519",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "fgFlkfkaotUjBVhJik2979oCeJw=",
+			"path": "github.com/keybase/go-crypto/openpgp",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "+spfcEChljh3yeIg4K/xHOQ2pVM=",
+			"path": "github.com/keybase/go-crypto/openpgp/armor",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "nWhmwjBJqPSvkCWqaap2Z9EiS1k=",
+			"path": "github.com/keybase/go-crypto/openpgp/ecdh",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "uxXG9IC/XF8jwwvZUbW65+x8/+M=",
+			"path": "github.com/keybase/go-crypto/openpgp/elgamal",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "EyUf82Yknzc75m8RcA21CNQINw0=",
+			"path": "github.com/keybase/go-crypto/openpgp/errors",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "y16ATKgHL/k6rQZqdXP1sIAJxE0=",
+			"path": "github.com/keybase/go-crypto/openpgp/packet",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "BGDxg1Xtsz0DSPzdQGJLLQqfYc8=",
+			"path": "github.com/keybase/go-crypto/openpgp/s2k",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
+		{
+			"checksumSHA1": "rE3pp7b3gfcmBregzpIvN5IdFhY=",
+			"path": "github.com/keybase/go-crypto/rsa",
+			"revision": "00ac4db533f63ef97576cbc7b07939ff7daf7329",
+			"revisionTime": "2017-06-05T14:56:57Z"
+		},
 		{
 			"checksumSHA1": "fh+CcgeUUsnuwSORHYWg0ycbp+4=",
 			"path": "github.com/klauspost/compress/flate",
@@ -1182,12 +1260,6 @@
 			"revision": "2c050d2dae5345c417db301f11fda6fbf5ad0f0a",
 			"revisionTime": "2016-09-14T08:04:27Z"
 		},
-		{
-			"checksumSHA1": "TT1rac6kpQp2vz24m5yDGUNQ/QQ=",
-			"path": "golang.org/x/crypto/cast5",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
 		{
 			"checksumSHA1": "dwOedwBJ1EIK9+S3t108Bx054Y8=",
 			"path": "golang.org/x/crypto/curve25519",
@@ -1212,42 +1284,6 @@
 			"revision": "ede567c8e044a5913dad1d1af3696d9da953104c",
 			"revisionTime": "2016-11-04T19:41:44Z"
 		},
-		{
-			"checksumSHA1": "IIhFTrLlmlc6lEFSitqi4aw2lw0=",
-			"path": "golang.org/x/crypto/openpgp",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
-		{
-			"checksumSHA1": "olOKkhrdkYQHZ0lf1orrFQPQrv4=",
-			"path": "golang.org/x/crypto/openpgp/armor",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
-		{
-			"checksumSHA1": "eo/KtdjieJQXH7Qy+faXFcF70ME=",
-			"path": "golang.org/x/crypto/openpgp/elgamal",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
-		{
-			"checksumSHA1": "rlxVSaGgqdAgwblsErxTxIfuGfg=",
-			"path": "golang.org/x/crypto/openpgp/errors",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
-		{
-			"checksumSHA1": "LWdaR8Q9yn6eBCcnGl0HvJRDUBE=",
-			"path": "golang.org/x/crypto/openpgp/packet",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
-		{
-			"checksumSHA1": "s2qT4UwvzBSkzXuiuMkowif1Olw=",
-			"path": "golang.org/x/crypto/openpgp/s2k",
-			"revision": "b8a2a83acfe6e6770b75de42d5ff4c67596675c0",
-			"revisionTime": "2017-01-13T19:21:00Z"
-		},
 		{
 			"checksumSHA1": "1MGpGDQqnUoRpv7VEcQrXOBydXE=",
 			"path": "golang.org/x/crypto/pbkdf2",