build(deps): bump github.com/containers/image/v5 from 5.0.0 to 5.1.0

Bumps [github.com/containers/image/v5](https://github.com/containers/image) from 5.0.0 to 5.1.0. - [Release notes](https://github.com/containers/image/releases) - [Commits](https://github.com/containers/image/compare/v5.0.0...v5.1.0) Signed-off-by: dependabot-preview[bot] <support@dependabot.com> Signed-off-by: Daniel J Walsh <dwalsh@redhat.com>
author: Daniel J Walsh <dwalsh@redhat.com> 2019-12-19 13:29:25 -0500
committer: Daniel J Walsh <dwalsh@redhat.com> 2019-12-20 09:30:47 -0500
commit: 50ece79387dcf6c748e3ae1bd6a7067059c0dfe3 (patch)
tree: 6b30c4f66f7be315ff2257447be3818be98fb50f /vendor/golang.org
parent: a359ca0d1825859dd8b7c1384f11d703ec6625b4 (diff)
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8 files changed, 3595 insertions, 4 deletions
diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519.go b/vendor/golang.org/x/crypto/ed25519/ed25519.go
new file mode 100644
index 000000000..c7f8c7e64
--- /dev/null
+++ b/vendor/golang.org/x/crypto/ed25519/ed25519.go
@@ -0,0 +1,222 @@
+// 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.
+
+// In Go 1.13, the ed25519 package was promoted to the standard library as
+// crypto/ed25519, and this package became a wrapper for the standard library one.
+//
+// +build !go1.13
+
+// Package ed25519 implements the Ed25519 signature algorithm. See
+// https://ed25519.cr.yp.to/.
+//
+// These functions are also compatible with the “Ed25519” function defined in
+// RFC 8032. However, unlike RFC 8032's formulation, this package's private key
+// representation includes a public key suffix to make multiple signing
+// operations with the same key more efficient. This package refers to the RFC
+// 8032 private key as the “seed”.
+package ed25519
+
+// This code is a port of the public domain, “ref10” implementation of ed25519
+// from SUPERCOP.
+
+import (
+	"bytes"
+	"crypto"
+	cryptorand "crypto/rand"
+	"crypto/sha512"
+	"errors"
+	"io"
+	"strconv"
+
+	"golang.org/x/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
+	// SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032.
+	SeedSize = 32
+)
+
+// 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)
+}
+
+// Seed returns the private key seed corresponding to priv. It is provided for
+// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds
+// in this package.
+func (priv PrivateKey) Seed() []byte {
+	seed := make([]byte, SeedSize)
+	copy(seed, priv[:32])
+	return seed
+}
+
+// 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, PrivateKey, error) {
+	if rand == nil {
+		rand = cryptorand.Reader
+	}
+
+	seed := make([]byte, SeedSize)
+	if _, err := io.ReadFull(rand, seed); err != nil {
+		return nil, nil, err
+	}
+
+	privateKey := NewKeyFromSeed(seed)
+	publicKey := make([]byte, PublicKeySize)
+	copy(publicKey, privateKey[32:])
+
+	return publicKey, privateKey, nil
+}
+
+// NewKeyFromSeed calculates a private key from a seed. It will panic if
+// len(seed) is not SeedSize. This function is provided for interoperability
+// with RFC 8032. RFC 8032's private keys correspond to seeds in this
+// package.
+func NewKeyFromSeed(seed []byte) PrivateKey {
+	if l := len(seed); l != SeedSize {
+		panic("ed25519: bad seed length: " + strconv.Itoa(l))
+	}
+
+	digest := sha512.Sum512(seed)
+	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)
+
+	privateKey := make([]byte, PrivateKeySize)
+	copy(privateKey, seed)
+	copy(privateKey[32:], publicKeyBytes[:])
+
+	return privateKey
+}
+
+// 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 s [32]byte
+	copy(s[:], sig[32:])
+
+	// https://tools.ietf.org/html/rfc8032#section-5.1.7 requires that s be in
+	// the range [0, order) in order to prevent signature malleability.
+	if !edwards25519.ScMinimal(&s) {
+		return false
+	}
+
+	edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &s)
+
+	var checkR [32]byte
+	R.ToBytes(&checkR)
+	return bytes.Equal(sig[:32], checkR[:])
+}
diff --git a/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go b/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go
new file mode 100644
index 000000000..d1448d8d2
--- /dev/null
+++ b/vendor/golang.org/x/crypto/ed25519/ed25519_go113.go
@@ -0,0 +1,73 @@
+// Copyright 2019 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 go1.13
+
+// Package ed25519 implements the Ed25519 signature algorithm. See
+// https://ed25519.cr.yp.to/.
+//
+// These functions are also compatible with the “Ed25519” function defined in
+// RFC 8032. However, unlike RFC 8032's formulation, this package's private key
+// representation includes a public key suffix to make multiple signing
+// operations with the same key more efficient. This package refers to the RFC
+// 8032 private key as the “seed”.
+//
+// Beginning with Go 1.13, the functionality of this package was moved to the
+// standard library as crypto/ed25519. This package only acts as a compatibility
+// wrapper.
+package ed25519
+
+import (
+	"crypto/ed25519"
+	"io"
+)
+
+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
+	// SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032.
+	SeedSize = 32
+)
+
+// PublicKey is the type of Ed25519 public keys.
+//
+// This type is an alias for crypto/ed25519's PublicKey type.
+// See the crypto/ed25519 package for the methods on this type.
+type PublicKey = ed25519.PublicKey
+
+// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer.
+//
+// This type is an alias for crypto/ed25519's PrivateKey type.
+// See the crypto/ed25519 package for the methods on this type.
+type PrivateKey = ed25519.PrivateKey
+
+// 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, PrivateKey, error) {
+	return ed25519.GenerateKey(rand)
+}
+
+// NewKeyFromSeed calculates a private key from a seed. It will panic if
+// len(seed) is not SeedSize. This function is provided for interoperability
+// with RFC 8032. RFC 8032's private keys correspond to seeds in this
+// package.
+func NewKeyFromSeed(seed []byte) PrivateKey {
+	return ed25519.NewKeyFromSeed(seed)
+}
+
+// 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 {
+	return ed25519.Sign(privateKey, message)
+}
+
+// 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 {
+	return ed25519.Verify(publicKey, message, sig)
+}
diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go
new file mode 100644
index 000000000..e39f086c1
--- /dev/null
+++ b/vendor/golang.org/x/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},
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+	{
+		{
+			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/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go
new file mode 100644
index 000000000..fd03c252a
--- /dev/null
+++ b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go
@@ -0,0 +1,1793 @@
+// 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
+
+import "encoding/binary"
+
+// 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)
+}
+
+// order is the order of Curve25519 in little-endian form.
+var order = [4]uint64{0x5812631a5cf5d3ed, 0x14def9dea2f79cd6, 0, 0x1000000000000000}
+
+// ScMinimal returns true if the given scalar is less than the order of the
+// curve.
+func ScMinimal(scalar *[32]byte) bool {
+	for i := 3; ; i-- {
+		v := binary.LittleEndian.Uint64(scalar[i*8:])
+		if v > order[i] {
+			return false
+		} else if v < order[i] {
+			break
+		} else if i == 0 {
+			return false
+		}
+	}
+
+	return true
+}
diff --git a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go b/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go
index 73f4fe378..72a6a7394 100644
--- a/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go
+++ b/vendor/golang.org/x/crypto/openpgp/elgamal/elgamal.go
@@ -76,7 +76,9 @@ func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err
 // Bleichenbacher, Advances in Cryptology (Crypto '98),
 func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) {
 	s := new(big.Int).Exp(c1, priv.X, priv.P)
-	s.ModInverse(s, priv.P)
+	if s.ModInverse(s, priv.P) == nil {
+		return nil, errors.New("elgamal: invalid private key")
+	}
 	s.Mul(s, c2)
 	s.Mod(s, priv.P)
 	em := s.Bytes()
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go b/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go
index 02b372cf3..6d7639722 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go
+++ b/vendor/golang.org/x/crypto/openpgp/packet/encrypted_key.go
@@ -5,6 +5,7 @@
 package packet
 
 import (
+	"crypto"
 	"crypto/rsa"
 	"encoding/binary"
 	"io"
@@ -78,8 +79,9 @@ func (e *EncryptedKey) Decrypt(priv *PrivateKey, config *Config) error {
 	// padding oracle attacks.
 	switch priv.PubKeyAlgo {
 	case PubKeyAlgoRSA, PubKeyAlgoRSAEncryptOnly:
-		k := priv.PrivateKey.(*rsa.PrivateKey)
-		b, err = rsa.DecryptPKCS1v15(config.Random(), k, padToKeySize(&k.PublicKey, e.encryptedMPI1.bytes))
+		// Supports both *rsa.PrivateKey and crypto.Decrypter
+		k := priv.PrivateKey.(crypto.Decrypter)
+		b, err = k.Decrypt(config.Random(), padToKeySize(k.Public().(*rsa.PublicKey), e.encryptedMPI1.bytes), nil)
 	case PubKeyAlgoElGamal:
 		c1 := new(big.Int).SetBytes(e.encryptedMPI1.bytes)
 		c2 := new(big.Int).SetBytes(e.encryptedMPI2.bytes)
diff --git a/vendor/golang.org/x/crypto/openpgp/packet/private_key.go b/vendor/golang.org/x/crypto/openpgp/packet/private_key.go
index 6f8ec0938..81abb7cef 100644
--- a/vendor/golang.org/x/crypto/openpgp/packet/private_key.go
+++ b/vendor/golang.org/x/crypto/openpgp/packet/private_key.go
@@ -31,7 +31,7 @@ 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|dsa|ecdsa}.PrivateKey or crypto.Signer/crypto.Decrypter (Decryptor RSA only).
 	sha1Checksum  bool
 	iv            []byte
 }
diff --git a/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go b/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go
new file mode 100644
index 000000000..593f65300
--- /dev/null
+++ b/vendor/golang.org/x/crypto/pbkdf2/pbkdf2.go
@@ -0,0 +1,77 @@
+// 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 pbkdf2 implements the key derivation function PBKDF2 as defined in RFC
+2898 / PKCS #5 v2.0.
+
+A key derivation function is useful when encrypting data based on a password
+or any other not-fully-random data. It uses a pseudorandom function to derive
+a secure encryption key based on the password.
+
+While v2.0 of the standard defines only one pseudorandom function to use,
+HMAC-SHA1, the drafted v2.1 specification allows use of all five FIPS Approved
+Hash Functions SHA-1, SHA-224, SHA-256, SHA-384 and SHA-512 for HMAC. To
+choose, you can pass the `New` functions from the different SHA packages to
+pbkdf2.Key.
+*/
+package pbkdf2 // import "golang.org/x/crypto/pbkdf2"
+
+import (
+	"crypto/hmac"
+	"hash"
+)
+
+// Key derives a key from the password, salt and iteration count, returning a
+// []byte of length keylen that can be used as cryptographic key. The key is
+// derived based on the method described as PBKDF2 with the HMAC variant using
+// the supplied hash function.
+//
+// For example, to use a HMAC-SHA-1 based PBKDF2 key derivation function, you
+// can get a derived key for e.g. AES-256 (which needs a 32-byte key) by
+// doing:
+//
+// 	dk := pbkdf2.Key([]byte("some password"), salt, 4096, 32, sha1.New)
+//
+// Remember to get a good random salt. At least 8 bytes is recommended by the
+// RFC.
+//
+// Using a higher iteration count will increase the cost of an exhaustive
+// search but will also make derivation proportionally slower.
+func Key(password, salt []byte, iter, keyLen int, h func() hash.Hash) []byte {
+	prf := hmac.New(h, password)
+	hashLen := prf.Size()
+	numBlocks := (keyLen + hashLen - 1) / hashLen
+
+	var buf [4]byte
+	dk := make([]byte, 0, numBlocks*hashLen)
+	U := make([]byte, hashLen)
+	for block := 1; block <= numBlocks; block++ {
+		// N.B.: || means concatenation, ^ means XOR
+		// for each block T_i = U_1 ^ U_2 ^ ... ^ U_iter
+		// U_1 = PRF(password, salt || uint(i))
+		prf.Reset()
+		prf.Write(salt)
+		buf[0] = byte(block >> 24)
+		buf[1] = byte(block >> 16)
+		buf[2] = byte(block >> 8)
+		buf[3] = byte(block)
+		prf.Write(buf[:4])
+		dk = prf.Sum(dk)
+		T := dk[len(dk)-hashLen:]
+		copy(U, T)
+
+		// U_n = PRF(password, U_(n-1))
+		for n := 2; n <= iter; n++ {
+			prf.Reset()
+			prf.Write(U)
+			U = U[:0]
+			U = prf.Sum(U)
+			for x := range U {
+				T[x] ^= U[x]
+			}
+		}
+	}
+	return dk[:keyLen]
+}
author	Daniel J Walsh <dwalsh@redhat.com>	2019-12-19 13:29:25 -0500
committer	Daniel J Walsh <dwalsh@redhat.com>	2019-12-20 09:30:47 -0500
commit	50ece79387dcf6c748e3ae1bd6a7067059c0dfe3 (patch)
tree	6b30c4f66f7be315ff2257447be3818be98fb50f /vendor/golang.org
parent	a359ca0d1825859dd8b7c1384f11d703ec6625b4 (diff)
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