diff options
author | kali kaneko (leap communications) <kali@leap.se> | 2021-04-14 16:54:42 +0200 |
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committer | kali kaneko (leap communications) <kali@leap.se> | 2021-04-14 16:54:42 +0200 |
commit | 67a0eb7111d3f89e4a0cb21e43aefe6d87d37e04 (patch) | |
tree | c9b18e0da6e06ac165a485ee957b7850adb12e86 /vendor/golang.org/x/crypto/curve25519/curve25519.go | |
parent | 2e8f2a2e8e83fd89f956cdde886d5d9d808132da (diff) |
[pkg] go mod vendor to build debian/ubuntu packages
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, 834 insertions, 0 deletions
diff --git a/vendor/golang.org/x/crypto/curve25519/curve25519.go b/vendor/golang.org/x/crypto/curve25519/curve25519.go new file mode 100644 index 0000000..75f24ba --- /dev/null +++ b/vendor/golang.org/x/crypto/curve25519/curve25519.go @@ -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 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:]) & 0x7fffff) << 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) +} |