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don't use libsodium for new sigs

This commit is contained in:
Jeff Becker 2017-08-25 08:52:41 -04:00
parent ed2f88c0fc
commit aa3cf130b3
No known key found for this signature in database
GPG Key ID: F357B3B42F6F9B05
17 changed files with 6553 additions and 1 deletions

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@ -12,6 +12,8 @@ import (
"encoding/hex" "encoding/hex"
"fmt" "fmt"
"github.com/majestrate/nacl" "github.com/majestrate/nacl"
"golang.org/x/crypto/curve25519"
"golang.org/x/crypto/ed25519"
"io" "io"
"log" "log"
"net" "net"
@ -400,9 +402,22 @@ func cryptoSign(h, sk []byte) string {
return hexify(sig) return hexify(sig)
} }
// convert seed to secret key
func seedToSecretNew(seed []byte) (full ed25519.PrivateKey) {
var out [32]byte
var in [32]byte
copy(in[:], seed[0:32])
curve25519.ScalarBaseMult(&out, &in)
copy(full[:], in[:])
copy(full[:32], out[:])
return
}
func cryptoSignNew(h, sk []byte) string { func cryptoSignNew(h, sk []byte) string {
// convert key
key := seedToSecretNew(sk)
// sign // sign
sig := nacl.CryptoSignDetached(h, sk) sig := ed25519.Sign(key, h)
if sig == nil { if sig == nil {
return "[failed to sign]" return "[failed to sign]"
} }

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@ -0,0 +1,8 @@
// 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: https://bench.cr.yp.to/supercop.html
#define REDMASK51 0x0007FFFFFFFFFFFF

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@ -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: https://bench.cr.yp.to/supercop.html
// +build amd64,!gccgo,!appengine
// These constants cannot be encoded in non-MOVQ immediates.
// We access them directly from memory instead.
DATA ·_121666_213(SB)/8, $996687872
GLOBL ·_121666_213(SB), 8, $8
DATA ·_2P0(SB)/8, $0xFFFFFFFFFFFDA
GLOBL ·_2P0(SB), 8, $8
DATA ·_2P1234(SB)/8, $0xFFFFFFFFFFFFE
GLOBL ·_2P1234(SB), 8, $8

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@ -0,0 +1,65 @@
// Copyright 2012 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build amd64,!gccgo,!appengine
// func cswap(inout *[4][5]uint64, v uint64)
TEXT ·cswap(SB),7,$0
MOVQ inout+0(FP),DI
MOVQ v+8(FP),SI
SUBQ $1, SI
NOTQ SI
MOVQ SI, X15
PSHUFD $0x44, X15, X15
MOVOU 0(DI), X0
MOVOU 16(DI), X2
MOVOU 32(DI), X4
MOVOU 48(DI), X6
MOVOU 64(DI), X8
MOVOU 80(DI), X1
MOVOU 96(DI), X3
MOVOU 112(DI), X5
MOVOU 128(DI), X7
MOVOU 144(DI), X9
MOVO X1, X10
MOVO X3, X11
MOVO X5, X12
MOVO X7, X13
MOVO X9, X14
PXOR X0, X10
PXOR X2, X11
PXOR X4, X12
PXOR X6, X13
PXOR X8, X14
PAND X15, X10
PAND X15, X11
PAND X15, X12
PAND X15, X13
PAND X15, X14
PXOR X10, X0
PXOR X10, X1
PXOR X11, X2
PXOR X11, X3
PXOR X12, X4
PXOR X12, X5
PXOR X13, X6
PXOR X13, X7
PXOR X14, X8
PXOR X14, X9
MOVOU X0, 0(DI)
MOVOU X2, 16(DI)
MOVOU X4, 32(DI)
MOVOU X6, 48(DI)
MOVOU X8, 64(DI)
MOVOU X1, 80(DI)
MOVOU X3, 96(DI)
MOVOU X5, 112(DI)
MOVOU X7, 128(DI)
MOVOU X9, 144(DI)
RET

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@ -0,0 +1,834 @@
// 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
import (
"encoding/binary"
)
// 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) {
b = -b
for i := range f {
t := b & (f[i] ^ g[i])
f[i] ^= t
g[i] ^= t
}
}
// 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 {
return int64(binary.LittleEndian.Uint32(in))
}
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)
}

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// Copyright 2012 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package curve25519
import (
"fmt"
"testing"
)
const expectedHex = "89161fde887b2b53de549af483940106ecc114d6982daa98256de23bdf77661a"
func TestBaseScalarMult(t *testing.T) {
var a, b [32]byte
in := &a
out := &b
a[0] = 1
for i := 0; i < 200; i++ {
ScalarBaseMult(out, in)
in, out = out, in
}
result := fmt.Sprintf("%x", in[:])
if result != expectedHex {
t.Errorf("incorrect result: got %s, want %s", result, expectedHex)
}
}
func BenchmarkScalarBaseMult(b *testing.B) {
var in, out [32]byte
in[0] = 1
b.SetBytes(32)
for i := 0; i < b.N; i++ {
ScalarBaseMult(&out, &in)
}
}

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// Copyright 2012 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package curve25519 provides an implementation of scalar multiplication on
// the elliptic curve known as curve25519. See https://cr.yp.to/ecdh.html
package curve25519 // import "golang.org/x/crypto/curve25519"
// basePoint is the x coordinate of the generator of the curve.
var basePoint = [32]byte{9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
// ScalarMult sets dst to the product in*base where dst and base are the x
// coordinates of group points and all values are in little-endian form.
func ScalarMult(dst, in, base *[32]byte) {
scalarMult(dst, in, base)
}
// ScalarBaseMult sets dst to the product in*base where dst and base are the x
// coordinates of group points, base is the standard generator and all values
// are in little-endian form.
func ScalarBaseMult(dst, in *[32]byte) {
ScalarMult(dst, in, &basePoint)
}

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// 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: https://bench.cr.yp.to/supercop.html
// +build amd64,!gccgo,!appengine
#include "const_amd64.h"
// func freeze(inout *[5]uint64)
TEXT ·freeze(SB),7,$0-8
MOVQ inout+0(FP), DI
MOVQ 0(DI),SI
MOVQ 8(DI),DX
MOVQ 16(DI),CX
MOVQ 24(DI),R8
MOVQ 32(DI),R9
MOVQ $REDMASK51,AX
MOVQ AX,R10
SUBQ $18,R10
MOVQ $3,R11
REDUCELOOP:
MOVQ SI,R12
SHRQ $51,R12
ANDQ AX,SI
ADDQ R12,DX
MOVQ DX,R12
SHRQ $51,R12
ANDQ AX,DX
ADDQ R12,CX
MOVQ CX,R12
SHRQ $51,R12
ANDQ AX,CX
ADDQ R12,R8
MOVQ R8,R12
SHRQ $51,R12
ANDQ AX,R8
ADDQ R12,R9
MOVQ R9,R12
SHRQ $51,R12
ANDQ AX,R9
IMUL3Q $19,R12,R12
ADDQ R12,SI
SUBQ $1,R11
JA REDUCELOOP
MOVQ $1,R12
CMPQ R10,SI
CMOVQLT R11,R12
CMPQ AX,DX
CMOVQNE R11,R12
CMPQ AX,CX
CMOVQNE R11,R12
CMPQ AX,R8
CMOVQNE R11,R12
CMPQ AX,R9
CMOVQNE R11,R12
NEGQ R12
ANDQ R12,AX
ANDQ R12,R10
SUBQ R10,SI
SUBQ AX,DX
SUBQ AX,CX
SUBQ AX,R8
SUBQ AX,R9
MOVQ SI,0(DI)
MOVQ DX,8(DI)
MOVQ CX,16(DI)
MOVQ R8,24(DI)
MOVQ R9,32(DI)
RET

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// Copyright 2012 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build amd64,!gccgo,!appengine
package curve25519
// These functions are implemented in the .s files. The names of the functions
// in the rest of the file are also taken from the SUPERCOP sources to help
// people following along.
//go:noescape
func cswap(inout *[5]uint64, v uint64)
//go:noescape
func ladderstep(inout *[5][5]uint64)
//go:noescape
func freeze(inout *[5]uint64)
//go:noescape
func mul(dest, a, b *[5]uint64)
//go:noescape
func square(out, in *[5]uint64)
// mladder uses a Montgomery ladder to calculate (xr/zr) *= s.
func mladder(xr, zr *[5]uint64, s *[32]byte) {
var work [5][5]uint64
work[0] = *xr
setint(&work[1], 1)
setint(&work[2], 0)
work[3] = *xr
setint(&work[4], 1)
j := uint(6)
var prevbit byte
for i := 31; i >= 0; i-- {
for j < 8 {
bit := ((*s)[i] >> j) & 1
swap := bit ^ prevbit
prevbit = bit
cswap(&work[1], uint64(swap))
ladderstep(&work)
j--
}
j = 7
}
*xr = work[1]
*zr = work[2]
}
func scalarMult(out, in, base *[32]byte) {
var e [32]byte
copy(e[:], (*in)[:])
e[0] &= 248
e[31] &= 127
e[31] |= 64
var t, z [5]uint64
unpack(&t, base)
mladder(&t, &z, &e)
invert(&z, &z)
mul(&t, &t, &z)
pack(out, &t)
}
func setint(r *[5]uint64, v uint64) {
r[0] = v
r[1] = 0
r[2] = 0
r[3] = 0
r[4] = 0
}
// unpack sets r = x where r consists of 5, 51-bit limbs in little-endian
// order.
func unpack(r *[5]uint64, x *[32]byte) {
r[0] = uint64(x[0]) |
uint64(x[1])<<8 |
uint64(x[2])<<16 |
uint64(x[3])<<24 |
uint64(x[4])<<32 |
uint64(x[5])<<40 |
uint64(x[6]&7)<<48
r[1] = uint64(x[6])>>3 |
uint64(x[7])<<5 |
uint64(x[8])<<13 |
uint64(x[9])<<21 |
uint64(x[10])<<29 |
uint64(x[11])<<37 |
uint64(x[12]&63)<<45
r[2] = uint64(x[12])>>6 |
uint64(x[13])<<2 |
uint64(x[14])<<10 |
uint64(x[15])<<18 |
uint64(x[16])<<26 |
uint64(x[17])<<34 |
uint64(x[18])<<42 |
uint64(x[19]&1)<<50
r[3] = uint64(x[19])>>1 |
uint64(x[20])<<7 |
uint64(x[21])<<15 |
uint64(x[22])<<23 |
uint64(x[23])<<31 |
uint64(x[24])<<39 |
uint64(x[25]&15)<<47
r[4] = uint64(x[25])>>4 |
uint64(x[26])<<4 |
uint64(x[27])<<12 |
uint64(x[28])<<20 |
uint64(x[29])<<28 |
uint64(x[30])<<36 |
uint64(x[31]&127)<<44
}
// pack sets out = x where out is the usual, little-endian form of the 5,
// 51-bit limbs in x.
func pack(out *[32]byte, x *[5]uint64) {
t := *x
freeze(&t)
out[0] = byte(t[0])
out[1] = byte(t[0] >> 8)
out[2] = byte(t[0] >> 16)
out[3] = byte(t[0] >> 24)
out[4] = byte(t[0] >> 32)
out[5] = byte(t[0] >> 40)
out[6] = byte(t[0] >> 48)
out[6] ^= byte(t[1]<<3) & 0xf8
out[7] = byte(t[1] >> 5)
out[8] = byte(t[1] >> 13)
out[9] = byte(t[1] >> 21)
out[10] = byte(t[1] >> 29)
out[11] = byte(t[1] >> 37)
out[12] = byte(t[1] >> 45)
out[12] ^= byte(t[2]<<6) & 0xc0
out[13] = byte(t[2] >> 2)
out[14] = byte(t[2] >> 10)
out[15] = byte(t[2] >> 18)
out[16] = byte(t[2] >> 26)
out[17] = byte(t[2] >> 34)
out[18] = byte(t[2] >> 42)
out[19] = byte(t[2] >> 50)
out[19] ^= byte(t[3]<<1) & 0xfe
out[20] = byte(t[3] >> 7)
out[21] = byte(t[3] >> 15)
out[22] = byte(t[3] >> 23)
out[23] = byte(t[3] >> 31)
out[24] = byte(t[3] >> 39)
out[25] = byte(t[3] >> 47)
out[25] ^= byte(t[4]<<4) & 0xf0
out[26] = byte(t[4] >> 4)
out[27] = byte(t[4] >> 12)
out[28] = byte(t[4] >> 20)
out[29] = byte(t[4] >> 28)
out[30] = byte(t[4] >> 36)
out[31] = byte(t[4] >> 44)
}
// invert calculates r = x^-1 mod p using Fermat's little theorem.
func invert(r *[5]uint64, x *[5]uint64) {
var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t [5]uint64
square(&z2, x) /* 2 */
square(&t, &z2) /* 4 */
square(&t, &t) /* 8 */
mul(&z9, &t, x) /* 9 */
mul(&z11, &z9, &z2) /* 11 */
square(&t, &z11) /* 22 */
mul(&z2_5_0, &t, &z9) /* 2^5 - 2^0 = 31 */
square(&t, &z2_5_0) /* 2^6 - 2^1 */
for i := 1; i < 5; i++ { /* 2^20 - 2^10 */
square(&t, &t)
}
mul(&z2_10_0, &t, &z2_5_0) /* 2^10 - 2^0 */
square(&t, &z2_10_0) /* 2^11 - 2^1 */
for i := 1; i < 10; i++ { /* 2^20 - 2^10 */
square(&t, &t)
}
mul(&z2_20_0, &t, &z2_10_0) /* 2^20 - 2^0 */
square(&t, &z2_20_0) /* 2^21 - 2^1 */
for i := 1; i < 20; i++ { /* 2^40 - 2^20 */
square(&t, &t)
}
mul(&t, &t, &z2_20_0) /* 2^40 - 2^0 */
square(&t, &t) /* 2^41 - 2^1 */
for i := 1; i < 10; i++ { /* 2^50 - 2^10 */
square(&t, &t)
}
mul(&z2_50_0, &t, &z2_10_0) /* 2^50 - 2^0 */
square(&t, &z2_50_0) /* 2^51 - 2^1 */
for i := 1; i < 50; i++ { /* 2^100 - 2^50 */
square(&t, &t)
}
mul(&z2_100_0, &t, &z2_50_0) /* 2^100 - 2^0 */
square(&t, &z2_100_0) /* 2^101 - 2^1 */
for i := 1; i < 100; i++ { /* 2^200 - 2^100 */
square(&t, &t)
}
mul(&t, &t, &z2_100_0) /* 2^200 - 2^0 */
square(&t, &t) /* 2^201 - 2^1 */
for i := 1; i < 50; i++ { /* 2^250 - 2^50 */
square(&t, &t)
}
mul(&t, &t, &z2_50_0) /* 2^250 - 2^0 */
square(&t, &t) /* 2^251 - 2^1 */
square(&t, &t) /* 2^252 - 2^2 */
square(&t, &t) /* 2^253 - 2^3 */
square(&t, &t) /* 2^254 - 2^4 */
square(&t, &t) /* 2^255 - 2^5 */
mul(r, &t, &z11) /* 2^255 - 21 */
}

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// 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: https://bench.cr.yp.to/supercop.html
// +build amd64,!gccgo,!appengine
#include "const_amd64.h"
// func mul(dest, a, b *[5]uint64)
TEXT ·mul(SB),0,$16-24
MOVQ dest+0(FP), DI
MOVQ a+8(FP), SI
MOVQ b+16(FP), DX
MOVQ DX,CX
MOVQ 24(SI),DX
IMUL3Q $19,DX,AX
MOVQ AX,0(SP)
MULQ 16(CX)
MOVQ AX,R8
MOVQ DX,R9
MOVQ 32(SI),DX
IMUL3Q $19,DX,AX
MOVQ AX,8(SP)
MULQ 8(CX)
ADDQ AX,R8
ADCQ DX,R9
MOVQ 0(SI),AX
MULQ 0(CX)
ADDQ AX,R8
ADCQ DX,R9
MOVQ 0(SI),AX
MULQ 8(CX)
MOVQ AX,R10
MOVQ DX,R11
MOVQ 0(SI),AX
MULQ 16(CX)
MOVQ AX,R12
MOVQ DX,R13
MOVQ 0(SI),AX
MULQ 24(CX)
MOVQ AX,R14
MOVQ DX,R15
MOVQ 0(SI),AX
MULQ 32(CX)
MOVQ AX,BX
MOVQ DX,BP
MOVQ 8(SI),AX
MULQ 0(CX)
ADDQ AX,R10
ADCQ DX,R11
MOVQ 8(SI),AX
MULQ 8(CX)
ADDQ AX,R12
ADCQ DX,R13
MOVQ 8(SI),AX
MULQ 16(CX)
ADDQ AX,R14
ADCQ DX,R15
MOVQ 8(SI),AX
MULQ 24(CX)
ADDQ AX,BX
ADCQ DX,BP
MOVQ 8(SI),DX
IMUL3Q $19,DX,AX
MULQ 32(CX)
ADDQ AX,R8
ADCQ DX,R9
MOVQ 16(SI),AX
MULQ 0(CX)
ADDQ AX,R12
ADCQ DX,R13
MOVQ 16(SI),AX
MULQ 8(CX)
ADDQ AX,R14
ADCQ DX,R15
MOVQ 16(SI),AX
MULQ 16(CX)
ADDQ AX,BX
ADCQ DX,BP
MOVQ 16(SI),DX
IMUL3Q $19,DX,AX
MULQ 24(CX)
ADDQ AX,R8
ADCQ DX,R9
MOVQ 16(SI),DX
IMUL3Q $19,DX,AX
MULQ 32(CX)
ADDQ AX,R10
ADCQ DX,R11
MOVQ 24(SI),AX
MULQ 0(CX)
ADDQ AX,R14
ADCQ DX,R15
MOVQ 24(SI),AX
MULQ 8(CX)
ADDQ AX,BX
ADCQ DX,BP
MOVQ 0(SP),AX
MULQ 24(CX)
ADDQ AX,R10
ADCQ DX,R11
MOVQ 0(SP),AX
MULQ 32(CX)
ADDQ AX,R12
ADCQ DX,R13
MOVQ 32(SI),AX
MULQ 0(CX)
ADDQ AX,BX
ADCQ DX,BP
MOVQ 8(SP),AX
MULQ 16(CX)
ADDQ AX,R10
ADCQ DX,R11
MOVQ 8(SP),AX
MULQ 24(CX)
ADDQ AX,R12
ADCQ DX,R13
MOVQ 8(SP),AX
MULQ 32(CX)
ADDQ AX,R14
ADCQ DX,R15
MOVQ $REDMASK51,SI
SHLQ $13,R9:R8
ANDQ SI,R8
SHLQ $13,R11:R10
ANDQ SI,R10
ADDQ R9,R10
SHLQ $13,R13:R12
ANDQ SI,R12
ADDQ R11,R12
SHLQ $13,R15:R14
ANDQ SI,R14
ADDQ R13,R14
SHLQ $13,BP:BX
ANDQ SI,BX
ADDQ R15,BX
IMUL3Q $19,BP,DX
ADDQ DX,R8
MOVQ R8,DX
SHRQ $51,DX
ADDQ R10,DX
MOVQ DX,CX
SHRQ $51,DX
ANDQ SI,R8
ADDQ R12,DX
MOVQ DX,R9
SHRQ $51,DX
ANDQ SI,CX
ADDQ R14,DX
MOVQ DX,AX
SHRQ $51,DX
ANDQ SI,R9
ADDQ BX,DX
MOVQ DX,R10
SHRQ $51,DX
ANDQ SI,AX
IMUL3Q $19,DX,DX
ADDQ DX,R8
ANDQ SI,R10
MOVQ R8,0(DI)
MOVQ CX,8(DI)
MOVQ R9,16(DI)
MOVQ AX,24(DI)
MOVQ R10,32(DI)
RET

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// 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: https://bench.cr.yp.to/supercop.html
// +build amd64,!gccgo,!appengine
#include "const_amd64.h"
// func square(out, in *[5]uint64)
TEXT ·square(SB),7,$0-16
MOVQ out+0(FP), DI
MOVQ in+8(FP), SI
MOVQ 0(SI),AX
MULQ 0(SI)
MOVQ AX,CX
MOVQ DX,R8
MOVQ 0(SI),AX
SHLQ $1,AX
MULQ 8(SI)
MOVQ AX,R9
MOVQ DX,R10
MOVQ 0(SI),AX
SHLQ $1,AX
MULQ 16(SI)
MOVQ AX,R11
MOVQ DX,R12
MOVQ 0(SI),AX
SHLQ $1,AX
MULQ 24(SI)
MOVQ AX,R13
MOVQ DX,R14
MOVQ 0(SI),AX
SHLQ $1,AX
MULQ 32(SI)
MOVQ AX,R15
MOVQ DX,BX
MOVQ 8(SI),AX
MULQ 8(SI)
ADDQ AX,R11
ADCQ DX,R12
MOVQ 8(SI),AX
SHLQ $1,AX
MULQ 16(SI)
ADDQ AX,R13
ADCQ DX,R14
MOVQ 8(SI),AX
SHLQ $1,AX
MULQ 24(SI)
ADDQ AX,R15
ADCQ DX,BX
MOVQ 8(SI),DX
IMUL3Q $38,DX,AX
MULQ 32(SI)
ADDQ AX,CX
ADCQ DX,R8
MOVQ 16(SI),AX
MULQ 16(SI)
ADDQ AX,R15
ADCQ DX,BX
MOVQ 16(SI),DX
IMUL3Q $38,DX,AX
MULQ 24(SI)
ADDQ AX,CX
ADCQ DX,R8
MOVQ 16(SI),DX
IMUL3Q $38,DX,AX
MULQ 32(SI)
ADDQ AX,R9
ADCQ DX,R10
MOVQ 24(SI),DX
IMUL3Q $19,DX,AX
MULQ 24(SI)
ADDQ AX,R9
ADCQ DX,R10
MOVQ 24(SI),DX
IMUL3Q $38,DX,AX
MULQ 32(SI)
ADDQ AX,R11
ADCQ DX,R12
MOVQ 32(SI),DX
IMUL3Q $19,DX,AX
MULQ 32(SI)
ADDQ AX,R13
ADCQ DX,R14
MOVQ $REDMASK51,SI
SHLQ $13,R8:CX
ANDQ SI,CX
SHLQ $13,R10:R9
ANDQ SI,R9
ADDQ R8,R9
SHLQ $13,R12:R11
ANDQ SI,R11
ADDQ R10,R11
SHLQ $13,R14:R13
ANDQ SI,R13
ADDQ R12,R13
SHLQ $13,BX:R15
ANDQ SI,R15
ADDQ R14,R15
IMUL3Q $19,BX,DX
ADDQ DX,CX
MOVQ CX,DX
SHRQ $51,DX
ADDQ R9,DX
ANDQ SI,CX
MOVQ DX,R8
SHRQ $51,DX
ADDQ R11,DX
ANDQ SI,R8
MOVQ DX,R9
SHRQ $51,DX
ADDQ R13,DX
ANDQ SI,R9
MOVQ DX,AX
SHRQ $51,DX
ADDQ R15,DX
ANDQ SI,AX
MOVQ DX,R10
SHRQ $51,DX
IMUL3Q $19,DX,DX
ADDQ DX,CX
ANDQ SI,R10
MOVQ CX,0(DI)
MOVQ R8,8(DI)
MOVQ R9,16(DI)
MOVQ AX,24(DI)
MOVQ R10,32(DI)
RET

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// Copyright 2016 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package ed25519 implements the Ed25519 signature algorithm. See
// https://ed25519.cr.yp.to/.
//
// These functions are also compatible with the “Ed25519” function defined in
// https://tools.ietf.org/html/draft-irtf-cfrg-eddsa-05.
package ed25519
// This code is a port of the public domain, “ref10” implementation of ed25519
// from SUPERCOP.
import (
"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
)
// PublicKey is the type of Ed25519 public keys.
type PublicKey []byte
// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer.
type PrivateKey []byte
// Public returns the PublicKey corresponding to priv.
func (priv PrivateKey) Public() crypto.PublicKey {
publicKey := make([]byte, PublicKeySize)
copy(publicKey, priv[32:])
return PublicKey(publicKey)
}
// Sign signs the given message with priv.
// Ed25519 performs two passes over messages to be signed and therefore cannot
// handle pre-hashed messages. Thus opts.HashFunc() must return zero to
// indicate the message hasn't been hashed. This can be achieved by passing
// crypto.Hash(0) as the value for opts.
func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) {
if opts.HashFunc() != crypto.Hash(0) {
return nil, errors.New("ed25519: cannot sign hashed message")
}
return Sign(priv, message), nil
}
// GenerateKey generates a public/private key pair using entropy from rand.
// If rand is nil, crypto/rand.Reader will be used.
func GenerateKey(rand io.Reader) (publicKey PublicKey, privateKey PrivateKey, err error) {
if rand == nil {
rand = cryptorand.Reader
}
privateKey = make([]byte, PrivateKeySize)
publicKey = make([]byte, PublicKeySize)
_, err = io.ReadFull(rand, privateKey[:32])
if err != nil {
return nil, nil, err
}
digest := sha512.Sum512(privateKey[:32])
digest[0] &= 248
digest[31] &= 127
digest[31] |= 64
var A edwards25519.ExtendedGroupElement
var hBytes [32]byte
copy(hBytes[:], digest[:])
edwards25519.GeScalarMultBase(&A, &hBytes)
var publicKeyBytes [32]byte
A.ToBytes(&publicKeyBytes)
copy(privateKey[32:], publicKeyBytes[:])
copy(publicKey, publicKeyBytes[:])
return publicKey, privateKey, nil
}
// Sign signs the message with privateKey and returns a signature. It will
// panic if len(privateKey) is not PrivateKeySize.
func Sign(privateKey PrivateKey, message []byte) []byte {
if l := len(privateKey); l != PrivateKeySize {
panic("ed25519: bad private key length: " + strconv.Itoa(l))
}
h := sha512.New()
h.Write(privateKey[:32])
var digest1, messageDigest, hramDigest [64]byte
var expandedSecretKey [32]byte
h.Sum(digest1[:0])
copy(expandedSecretKey[:], digest1[:])
expandedSecretKey[0] &= 248
expandedSecretKey[31] &= 63
expandedSecretKey[31] |= 64
h.Reset()
h.Write(digest1[32:])
h.Write(message)
h.Sum(messageDigest[:0])
var messageDigestReduced [32]byte
edwards25519.ScReduce(&messageDigestReduced, &messageDigest)
var R edwards25519.ExtendedGroupElement
edwards25519.GeScalarMultBase(&R, &messageDigestReduced)
var encodedR [32]byte
R.ToBytes(&encodedR)
h.Reset()
h.Write(encodedR[:])
h.Write(privateKey[32:])
h.Write(message)
h.Sum(hramDigest[:0])
var hramDigestReduced [32]byte
edwards25519.ScReduce(&hramDigestReduced, &hramDigest)
var s [32]byte
edwards25519.ScMulAdd(&s, &hramDigestReduced, &expandedSecretKey, &messageDigestReduced)
signature := make([]byte, SignatureSize)
copy(signature[:], encodedR[:])
copy(signature[32:], s[:])
return signature
}
// Verify reports whether sig is a valid signature of message by publicKey. It
// will panic if len(publicKey) is not PublicKeySize.
func Verify(publicKey PublicKey, message, sig []byte) bool {
if l := len(publicKey); l != PublicKeySize {
panic("ed25519: bad public key length: " + strconv.Itoa(l))
}
if len(sig) != SignatureSize || sig[63]&224 != 0 {
return false
}
var A edwards25519.ExtendedGroupElement
var publicKeyBytes [32]byte
copy(publicKeyBytes[:], publicKey)
if !A.FromBytes(&publicKeyBytes) {
return false
}
edwards25519.FeNeg(&A.X, &A.X)
edwards25519.FeNeg(&A.T, &A.T)
h := sha512.New()
h.Write(sig[:32])
h.Write(publicKey[:])
h.Write(message)
var digest [64]byte
h.Sum(digest[:0])
var hReduced [32]byte
edwards25519.ScReduce(&hReduced, &digest)
var R edwards25519.ProjectiveGroupElement
var b [32]byte
copy(b[:], sig[32:])
edwards25519.GeDoubleScalarMultVartime(&R, &hReduced, &A, &b)
var checkR [32]byte
R.ToBytes(&checkR)
return bytes.Equal(sig[:32], checkR[:])
}

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// Copyright 2016 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package ed25519
import (
"bufio"
"bytes"
"compress/gzip"
"crypto"
"crypto/rand"
"encoding/hex"
"os"
"strings"
"testing"
"golang.org/x/crypto/ed25519/internal/edwards25519"
)
type zeroReader struct{}
func (zeroReader) Read(buf []byte) (int, error) {
for i := range buf {
buf[i] = 0
}
return len(buf), nil
}
func TestUnmarshalMarshal(t *testing.T) {
pub, _, _ := GenerateKey(rand.Reader)
var A edwards25519.ExtendedGroupElement
var pubBytes [32]byte
copy(pubBytes[:], pub)
if !A.FromBytes(&pubBytes) {
t.Fatalf("ExtendedGroupElement.FromBytes failed")
}
var pub2 [32]byte
A.ToBytes(&pub2)
if pubBytes != pub2 {
t.Errorf("FromBytes(%v)->ToBytes does not round-trip, got %x\n", pubBytes, pub2)
}
}
func TestSignVerify(t *testing.T) {
var zero zeroReader
public, private, _ := GenerateKey(zero)
message := []byte("test message")
sig := Sign(private, message)
if !Verify(public, message, sig) {
t.Errorf("valid signature rejected")
}
wrongMessage := []byte("wrong message")
if Verify(public, wrongMessage, sig) {
t.Errorf("signature of different message accepted")
}
}
func TestCryptoSigner(t *testing.T) {
var zero zeroReader
public, private, _ := GenerateKey(zero)
signer := crypto.Signer(private)
publicInterface := signer.Public()
public2, ok := publicInterface.(PublicKey)
if !ok {
t.Fatalf("expected PublicKey from Public() but got %T", publicInterface)
}
if !bytes.Equal(public, public2) {
t.Errorf("public keys do not match: original:%x vs Public():%x", public, public2)
}
message := []byte("message")
var noHash crypto.Hash
signature, err := signer.Sign(zero, message, noHash)
if err != nil {
t.Fatalf("error from Sign(): %s", err)
}
if !Verify(public, message, signature) {
t.Errorf("Verify failed on signature from Sign()")
}
}
func TestGolden(t *testing.T) {
// sign.input.gz is a selection of test cases from
// https://ed25519.cr.yp.to/python/sign.input
testDataZ, err := os.Open("testdata/sign.input.gz")
if err != nil {
t.Fatal(err)
}
defer testDataZ.Close()
testData, err := gzip.NewReader(testDataZ)
if err != nil {
t.Fatal(err)
}
defer testData.Close()
scanner := bufio.NewScanner(testData)
lineNo := 0
for scanner.Scan() {
lineNo++
line := scanner.Text()
parts := strings.Split(line, ":")
if len(parts) != 5 {
t.Fatalf("bad number of parts on line %d", lineNo)
}
privBytes, _ := hex.DecodeString(parts[0])
pubKey, _ := hex.DecodeString(parts[1])
msg, _ := hex.DecodeString(parts[2])
sig, _ := hex.DecodeString(parts[3])
// The signatures in the test vectors also include the message
// at the end, but we just want R and S.
sig = sig[:SignatureSize]
if l := len(pubKey); l != PublicKeySize {
t.Fatalf("bad public key length on line %d: got %d bytes", lineNo, l)
}
var priv [PrivateKeySize]byte
copy(priv[:], privBytes)
copy(priv[32:], pubKey)
sig2 := Sign(priv[:], msg)
if !bytes.Equal(sig, sig2[:]) {
t.Errorf("different signature result on line %d: %x vs %x", lineNo, sig, sig2)
}
if !Verify(pubKey, msg, sig2) {
t.Errorf("signature failed to verify on line %d", lineNo)
}
}
if err := scanner.Err(); err != nil {
t.Fatalf("error reading test data: %s", err)
}
}
func BenchmarkKeyGeneration(b *testing.B) {
var zero zeroReader
for i := 0; i < b.N; i++ {
if _, _, err := GenerateKey(zero); err != nil {
b.Fatal(err)
}
}
}
func BenchmarkSigning(b *testing.B) {
var zero zeroReader
_, priv, err := GenerateKey(zero)
if err != nil {
b.Fatal(err)
}
message := []byte("Hello, world!")
b.ResetTimer()
for i := 0; i < b.N; i++ {
Sign(priv, message)
}
}
func BenchmarkVerification(b *testing.B) {
var zero zeroReader
pub, priv, err := GenerateKey(zero)
if err != nil {
b.Fatal(err)
}
message := []byte("Hello, world!")
signature := Sign(priv, message)
b.ResetTimer()
for i := 0; i < b.N; i++ {
Verify(pub, message, signature)
}
}

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