834 lines
21 KiB
Go
834 lines
21 KiB
Go
// Copyright 2013 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// We have a implementation in amd64 assembly so this code is only run on
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// non-amd64 platforms. The amd64 assembly does not support gccgo.
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// +build !amd64 gccgo appengine
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package curve25519
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import (
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"encoding/binary"
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)
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// This code is a port of the public domain, "ref10" implementation of
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// curve25519 from SUPERCOP 20130419 by D. J. Bernstein.
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// fieldElement represents an element of the field GF(2^255 - 19). An element
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// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
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// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
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// context.
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type fieldElement [10]int32
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func feZero(fe *fieldElement) {
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for i := range fe {
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fe[i] = 0
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}
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}
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func feOne(fe *fieldElement) {
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feZero(fe)
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fe[0] = 1
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}
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func feAdd(dst, a, b *fieldElement) {
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for i := range dst {
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dst[i] = a[i] + b[i]
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}
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}
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func feSub(dst, a, b *fieldElement) {
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for i := range dst {
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dst[i] = a[i] - b[i]
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}
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}
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func feCopy(dst, src *fieldElement) {
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for i := range dst {
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dst[i] = src[i]
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}
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}
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// feCSwap replaces (f,g) with (g,f) if b == 1; replaces (f,g) with (f,g) if b == 0.
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//
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// Preconditions: b in {0,1}.
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func feCSwap(f, g *fieldElement, b int32) {
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b = -b
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for i := range f {
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t := b & (f[i] ^ g[i])
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f[i] ^= t
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g[i] ^= t
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}
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}
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// load3 reads a 24-bit, little-endian value from in.
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func load3(in []byte) int64 {
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var r int64
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r = int64(in[0])
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r |= int64(in[1]) << 8
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r |= int64(in[2]) << 16
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return r
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}
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// load4 reads a 32-bit, little-endian value from in.
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func load4(in []byte) int64 {
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return int64(binary.LittleEndian.Uint32(in))
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}
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func feFromBytes(dst *fieldElement, src *[32]byte) {
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h0 := load4(src[:])
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h1 := load3(src[4:]) << 6
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h2 := load3(src[7:]) << 5
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h3 := load3(src[10:]) << 3
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h4 := load3(src[13:]) << 2
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h5 := load4(src[16:])
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h6 := load3(src[20:]) << 7
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h7 := load3(src[23:]) << 5
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h8 := load3(src[26:]) << 4
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h9 := load3(src[29:]) << 2
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var carry [10]int64
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carry[9] = (h9 + 1<<24) >> 25
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h0 += carry[9] * 19
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h9 -= carry[9] << 25
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carry[1] = (h1 + 1<<24) >> 25
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h2 += carry[1]
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h1 -= carry[1] << 25
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carry[3] = (h3 + 1<<24) >> 25
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h4 += carry[3]
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h3 -= carry[3] << 25
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carry[5] = (h5 + 1<<24) >> 25
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h6 += carry[5]
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h5 -= carry[5] << 25
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carry[7] = (h7 + 1<<24) >> 25
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h8 += carry[7]
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h7 -= carry[7] << 25
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carry[0] = (h0 + 1<<25) >> 26
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h1 += carry[0]
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h0 -= carry[0] << 26
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carry[2] = (h2 + 1<<25) >> 26
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h3 += carry[2]
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h2 -= carry[2] << 26
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carry[4] = (h4 + 1<<25) >> 26
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h5 += carry[4]
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h4 -= carry[4] << 26
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carry[6] = (h6 + 1<<25) >> 26
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h7 += carry[6]
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h6 -= carry[6] << 26
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carry[8] = (h8 + 1<<25) >> 26
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h9 += carry[8]
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h8 -= carry[8] << 26
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dst[0] = int32(h0)
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dst[1] = int32(h1)
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dst[2] = int32(h2)
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dst[3] = int32(h3)
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dst[4] = int32(h4)
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dst[5] = int32(h5)
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dst[6] = int32(h6)
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dst[7] = int32(h7)
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dst[8] = int32(h8)
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dst[9] = int32(h9)
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}
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// feToBytes marshals h to s.
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// Preconditions:
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// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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//
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// Write p=2^255-19; q=floor(h/p).
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// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
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//
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// Proof:
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// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
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// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
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//
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// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
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// Then 0<y<1.
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//
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// Write r=h-pq.
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// Have 0<=r<=p-1=2^255-20.
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// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
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//
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// Write x=r+19(2^-255)r+y.
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// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
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//
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// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
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// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
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func feToBytes(s *[32]byte, h *fieldElement) {
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var carry [10]int32
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q := (19*h[9] + (1 << 24)) >> 25
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q = (h[0] + q) >> 26
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q = (h[1] + q) >> 25
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q = (h[2] + q) >> 26
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q = (h[3] + q) >> 25
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q = (h[4] + q) >> 26
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q = (h[5] + q) >> 25
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q = (h[6] + q) >> 26
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q = (h[7] + q) >> 25
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q = (h[8] + q) >> 26
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q = (h[9] + q) >> 25
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// Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
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h[0] += 19 * q
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// Goal: Output h-2^255 q, which is between 0 and 2^255-20.
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carry[0] = h[0] >> 26
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h[1] += carry[0]
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h[0] -= carry[0] << 26
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carry[1] = h[1] >> 25
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h[2] += carry[1]
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h[1] -= carry[1] << 25
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carry[2] = h[2] >> 26
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h[3] += carry[2]
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h[2] -= carry[2] << 26
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carry[3] = h[3] >> 25
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h[4] += carry[3]
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h[3] -= carry[3] << 25
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carry[4] = h[4] >> 26
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h[5] += carry[4]
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h[4] -= carry[4] << 26
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carry[5] = h[5] >> 25
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h[6] += carry[5]
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h[5] -= carry[5] << 25
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carry[6] = h[6] >> 26
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h[7] += carry[6]
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h[6] -= carry[6] << 26
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carry[7] = h[7] >> 25
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h[8] += carry[7]
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h[7] -= carry[7] << 25
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carry[8] = h[8] >> 26
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h[9] += carry[8]
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h[8] -= carry[8] << 26
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carry[9] = h[9] >> 25
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h[9] -= carry[9] << 25
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// h10 = carry9
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// Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
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// Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
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// evidently 2^255 h10-2^255 q = 0.
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// Goal: Output h[0]+...+2^230 h[9].
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s[0] = byte(h[0] >> 0)
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s[1] = byte(h[0] >> 8)
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s[2] = byte(h[0] >> 16)
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s[3] = byte((h[0] >> 24) | (h[1] << 2))
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s[4] = byte(h[1] >> 6)
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s[5] = byte(h[1] >> 14)
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s[6] = byte((h[1] >> 22) | (h[2] << 3))
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s[7] = byte(h[2] >> 5)
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s[8] = byte(h[2] >> 13)
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s[9] = byte((h[2] >> 21) | (h[3] << 5))
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s[10] = byte(h[3] >> 3)
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s[11] = byte(h[3] >> 11)
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s[12] = byte((h[3] >> 19) | (h[4] << 6))
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s[13] = byte(h[4] >> 2)
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s[14] = byte(h[4] >> 10)
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s[15] = byte(h[4] >> 18)
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s[16] = byte(h[5] >> 0)
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s[17] = byte(h[5] >> 8)
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s[18] = byte(h[5] >> 16)
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s[19] = byte((h[5] >> 24) | (h[6] << 1))
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s[20] = byte(h[6] >> 7)
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s[21] = byte(h[6] >> 15)
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s[22] = byte((h[6] >> 23) | (h[7] << 3))
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s[23] = byte(h[7] >> 5)
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s[24] = byte(h[7] >> 13)
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s[25] = byte((h[7] >> 21) | (h[8] << 4))
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s[26] = byte(h[8] >> 4)
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s[27] = byte(h[8] >> 12)
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s[28] = byte((h[8] >> 20) | (h[9] << 6))
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s[29] = byte(h[9] >> 2)
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s[30] = byte(h[9] >> 10)
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s[31] = byte(h[9] >> 18)
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}
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// feMul calculates h = f * g
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// Can overlap h with f or g.
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//
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// Preconditions:
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// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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//
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// Postconditions:
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// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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//
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// Notes on implementation strategy:
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//
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// Using schoolbook multiplication.
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// Karatsuba would save a little in some cost models.
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//
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// Most multiplications by 2 and 19 are 32-bit precomputations;
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// cheaper than 64-bit postcomputations.
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//
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// There is one remaining multiplication by 19 in the carry chain;
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// one *19 precomputation can be merged into this,
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// but the resulting data flow is considerably less clean.
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//
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// There are 12 carries below.
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// 10 of them are 2-way parallelizable and vectorizable.
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// Can get away with 11 carries, but then data flow is much deeper.
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//
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// With tighter constraints on inputs can squeeze carries into int32.
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func feMul(h, f, g *fieldElement) {
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f0 := f[0]
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f1 := f[1]
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f2 := f[2]
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f3 := f[3]
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f4 := f[4]
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f5 := f[5]
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f6 := f[6]
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f7 := f[7]
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f8 := f[8]
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f9 := f[9]
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g0 := g[0]
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g1 := g[1]
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g2 := g[2]
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g3 := g[3]
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g4 := g[4]
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g5 := g[5]
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g6 := g[6]
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g7 := g[7]
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g8 := g[8]
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g9 := g[9]
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g1_19 := 19 * g1 // 1.4*2^29
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g2_19 := 19 * g2 // 1.4*2^30; still ok
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g3_19 := 19 * g3
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g4_19 := 19 * g4
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g5_19 := 19 * g5
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g6_19 := 19 * g6
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g7_19 := 19 * g7
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g8_19 := 19 * g8
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g9_19 := 19 * g9
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f1_2 := 2 * f1
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f3_2 := 2 * f3
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f5_2 := 2 * f5
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f7_2 := 2 * f7
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f9_2 := 2 * f9
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f0g0 := int64(f0) * int64(g0)
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f0g1 := int64(f0) * int64(g1)
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f0g2 := int64(f0) * int64(g2)
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f0g3 := int64(f0) * int64(g3)
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f0g4 := int64(f0) * int64(g4)
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f0g5 := int64(f0) * int64(g5)
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f0g6 := int64(f0) * int64(g6)
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f0g7 := int64(f0) * int64(g7)
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f0g8 := int64(f0) * int64(g8)
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f0g9 := int64(f0) * int64(g9)
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f1g0 := int64(f1) * int64(g0)
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f1g1_2 := int64(f1_2) * int64(g1)
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f1g2 := int64(f1) * int64(g2)
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f1g3_2 := int64(f1_2) * int64(g3)
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f1g4 := int64(f1) * int64(g4)
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f1g5_2 := int64(f1_2) * int64(g5)
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f1g6 := int64(f1) * int64(g6)
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f1g7_2 := int64(f1_2) * int64(g7)
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f1g8 := int64(f1) * int64(g8)
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f1g9_38 := int64(f1_2) * int64(g9_19)
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f2g0 := int64(f2) * int64(g0)
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f2g1 := int64(f2) * int64(g1)
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f2g2 := int64(f2) * int64(g2)
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f2g3 := int64(f2) * int64(g3)
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f2g4 := int64(f2) * int64(g4)
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f2g5 := int64(f2) * int64(g5)
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f2g6 := int64(f2) * int64(g6)
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f2g7 := int64(f2) * int64(g7)
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f2g8_19 := int64(f2) * int64(g8_19)
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f2g9_19 := int64(f2) * int64(g9_19)
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f3g0 := int64(f3) * int64(g0)
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f3g1_2 := int64(f3_2) * int64(g1)
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f3g2 := int64(f3) * int64(g2)
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f3g3_2 := int64(f3_2) * int64(g3)
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f3g4 := int64(f3) * int64(g4)
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f3g5_2 := int64(f3_2) * int64(g5)
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f3g6 := int64(f3) * int64(g6)
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f3g7_38 := int64(f3_2) * int64(g7_19)
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f3g8_19 := int64(f3) * int64(g8_19)
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f3g9_38 := int64(f3_2) * int64(g9_19)
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f4g0 := int64(f4) * int64(g0)
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f4g1 := int64(f4) * int64(g1)
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f4g2 := int64(f4) * int64(g2)
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f4g3 := int64(f4) * int64(g3)
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f4g4 := int64(f4) * int64(g4)
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f4g5 := int64(f4) * int64(g5)
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f4g6_19 := int64(f4) * int64(g6_19)
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f4g7_19 := int64(f4) * int64(g7_19)
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f4g8_19 := int64(f4) * int64(g8_19)
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f4g9_19 := int64(f4) * int64(g9_19)
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f5g0 := int64(f5) * int64(g0)
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f5g1_2 := int64(f5_2) * int64(g1)
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f5g2 := int64(f5) * int64(g2)
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f5g3_2 := int64(f5_2) * int64(g3)
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f5g4 := int64(f5) * int64(g4)
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f5g5_38 := int64(f5_2) * int64(g5_19)
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f5g6_19 := int64(f5) * int64(g6_19)
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f5g7_38 := int64(f5_2) * int64(g7_19)
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f5g8_19 := int64(f5) * int64(g8_19)
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f5g9_38 := int64(f5_2) * int64(g9_19)
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f6g0 := int64(f6) * int64(g0)
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f6g1 := int64(f6) * int64(g1)
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f6g2 := int64(f6) * int64(g2)
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f6g3 := int64(f6) * int64(g3)
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f6g4_19 := int64(f6) * int64(g4_19)
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f6g5_19 := int64(f6) * int64(g5_19)
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f6g6_19 := int64(f6) * int64(g6_19)
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f6g7_19 := int64(f6) * int64(g7_19)
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f6g8_19 := int64(f6) * int64(g8_19)
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f6g9_19 := int64(f6) * int64(g9_19)
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f7g0 := int64(f7) * int64(g0)
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f7g1_2 := int64(f7_2) * int64(g1)
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f7g2 := int64(f7) * int64(g2)
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f7g3_38 := int64(f7_2) * int64(g3_19)
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f7g4_19 := int64(f7) * int64(g4_19)
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f7g5_38 := int64(f7_2) * int64(g5_19)
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f7g6_19 := int64(f7) * int64(g6_19)
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f7g7_38 := int64(f7_2) * int64(g7_19)
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f7g8_19 := int64(f7) * int64(g8_19)
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f7g9_38 := int64(f7_2) * int64(g9_19)
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f8g0 := int64(f8) * int64(g0)
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f8g1 := int64(f8) * int64(g1)
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f8g2_19 := int64(f8) * int64(g2_19)
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f8g3_19 := int64(f8) * int64(g3_19)
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f8g4_19 := int64(f8) * int64(g4_19)
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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)
|
|
}
|