diff options
Diffstat (limited to 'vendor/golang.org/x/crypto/curve25519/curve25519.go')
| -rw-r--r-- | vendor/golang.org/x/crypto/curve25519/curve25519.go | 834 |
1 files changed, 0 insertions, 834 deletions
diff --git a/vendor/golang.org/x/crypto/curve25519/curve25519.go b/vendor/golang.org/x/crypto/curve25519/curve25519.go deleted file mode 100644 index cb8fbc5..0000000 --- a/vendor/golang.org/x/crypto/curve25519/curve25519.go +++ /dev/null @@ -1,834 +0,0 @@ -// 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 an 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) -} |