Switch to keybase go-crypto (for some elliptic curve key) + test (#1925)
* Switch to keybase go-crypto (for some elliptic curve key) + test
* Use assert.NoError
and add a little more context to failing test description
* Use assert.(No)Error everywhere ๐
and assert.Error in place of .Nil/.NotNil
release/v1.2
Antoine GIRARD
6 years ago
committed by
Lunny Xiao
parent
5e92b82ac6
commit
274149dd14
@ -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.
|
||||
@ -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.
|
||||
@ -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
|
||||
}
|
||||
@ -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))
|
||||
}
|
||||
@ -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 ยทREDMASK51(SB)/8, $0x0007FFFFFFFFFFFF
|
||||
GLOBL ยทREDMASK51(SB), 8, $8
|
||||
|
||||
DATA ยท_121666_213(SB)/8, $996687872
|
||||
GLOBL ยท_121666_213(SB), 8, $8
|
||||
|
||||
DATA ยท_2P0(SB)/8, $0xFFFFFFFFFFFDA
|
||||
GLOBL ยท_2P0(SB), 8, $8
|
||||
|
||||
DATA ยท_2P1234(SB)/8, $0xFFFFFFFFFFFFE
|
||||
GLOBL ยท_2P1234(SB), 8, $8
|
||||
@ -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 ยทcswap(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
|
||||
@ -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)
|
||||
}
|
||||
@ -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])
|
||||