ref: 2cdc6577ef8a251bf1740439cf5bfc47050dab41
dir: /third_party/boringssl/src/crypto/fipsmodule/ec/make_tables.go/
/* Copyright (c) 2020, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
package main
import (
"crypto/elliptic"
"fmt"
"io"
"math/big"
"os"
)
func main() {
if err := writeP256X86_64Table("p256-x86_64-table.h"); err != nil {
fmt.Fprintf(os.Stderr, "Error writing p256-x86_64-table.h: %s\n", err)
os.Exit(1)
}
if err := writeP256Table("p256_table.h"); err != nil {
fmt.Fprintf(os.Stderr, "Error writing p256_table.h: %s\n", err)
os.Exit(1)
}
}
func writeP256X86_64Table(path string) error {
curve := elliptic.P256()
tables := make([][][2]*big.Int, 0, 37)
for shift := 0; shift < 256; shift += 7 {
row := makeMultiples(curve, 64, shift)
tables = append(tables, row)
}
f, err := os.Create(path)
if err != nil {
return err
}
defer f.Close()
const fileHeader = `/*
* Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2015, Intel Inc.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
// This is the precomputed constant time access table for the code in
// p256-x86_64.c, for the default generator. The table consists of 37
// subtables, each subtable contains 64 affine points. The affine points are
// encoded as eight uint64's, four for the x coordinate and four for the y.
// Both values are in little-endian order. There are 37 tables because a
// signed, 6-bit wNAF form of the scalar is used and ceil(256/(6 + 1)) = 37.
// Within each table there are 64 values because the 6-bit wNAF value can take
// 64 values, ignoring the sign bit, which is implemented by performing a
// negation of the affine point when required. We would like to align it to 2MB
// in order to increase the chances of using a large page but that appears to
// lead to invalid ELF files being produced.
// This file is generated by make_tables.go.
static const alignas(4096) PRECOMP256_ROW ecp_nistz256_precomputed[37] = `
if _, err := f.WriteString(fileHeader); err != nil {
return err
}
if err := writeTables(f, curve, tables, true, 4, writeBNMont); err != nil {
return err
}
if _, err := f.WriteString(";\n"); err != nil {
return err
}
return nil
}
func writeP256Table(path string) error {
curve := elliptic.P256()
tables := [][][2]*big.Int{
makeComb(curve, 64, 4, 0),
makeComb(curve, 64, 4, 32),
}
f, err := os.Create(path)
if err != nil {
return err
}
defer f.Close()
const fileHeader = `/* Copyright (c) 2020, Google Inc.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
// This file is generated by make_tables.go.
// Base point pre computation
// --------------------------
//
// Two different sorts of precomputed tables are used in the following code.
// Each contain various points on the curve, where each point is three field
// elements (x, y, z).
//
// For the base point table, z is usually 1 (0 for the point at infinity).
// This table has 2 * 16 elements, starting with the following:
// index | bits | point
// ------+---------+------------------------------
// 0 | 0 0 0 0 | 0G
// 1 | 0 0 0 1 | 1G
// 2 | 0 0 1 0 | 2^64G
// 3 | 0 0 1 1 | (2^64 + 1)G
// 4 | 0 1 0 0 | 2^128G
// 5 | 0 1 0 1 | (2^128 + 1)G
// 6 | 0 1 1 0 | (2^128 + 2^64)G
// 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G
// 8 | 1 0 0 0 | 2^192G
// 9 | 1 0 0 1 | (2^192 + 1)G
// 10 | 1 0 1 0 | (2^192 + 2^64)G
// 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G
// 12 | 1 1 0 0 | (2^192 + 2^128)G
// 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G
// 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G
// 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G
// followed by a copy of this with each element multiplied by 2^32.
//
// The reason for this is so that we can clock bits into four different
// locations when doing simple scalar multiplies against the base point,
// and then another four locations using the second 16 elements.
//
// Tables for other points have table[i] = iG for i in 0 .. 16.
// fiat_p256_g_pre_comp is the table of precomputed base points
#if defined(BORINGSSL_NISTP256_64BIT)
static const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = `
if _, err := f.WriteString(fileHeader); err != nil {
return err
}
if err := writeTables(f, curve, tables, true, 4, writeU64Mont); err != nil {
return err
}
if _, err := f.WriteString(";\n#else\nstatic const fiat_p256_felem fiat_p256_g_pre_comp[2][15][2] = "); err != nil {
return err
}
if err := writeTables(f, curve, tables, true, 4, writeU32Mont); err != nil {
return err
}
if _, err := f.WriteString(";\n#endif\n"); err != nil {
return err
}
return nil
}
// makeMultiples returns a table of the first n multiples of 2^shift * G,
// starting from 1 * 2^shift * G.
func makeMultiples(curve elliptic.Curve, n, shift int) [][2]*big.Int {
ret := make([][2]*big.Int, n)
x, y := curve.Params().Gx, curve.Params().Gy
for j := 0; j < shift; j++ {
x, y = curve.Double(x, y)
}
ret[1-1] = [2]*big.Int{x, y}
for i := 2; i <= n; i++ {
if i&1 == 0 {
x, y := curve.Double(ret[i/2-1][0], ret[i/2-1][1])
ret[i-1] = [2]*big.Int{x, y}
} else {
x, y := curve.Add(ret[i-1-1][0], ret[i-1-1][1], ret[1-1][0], ret[1-1][1])
ret[i-1] = [2]*big.Int{x, y}
}
}
return ret
}
// makeComb returns a table of 2^size - 1 points. The i-1th entry is k*G.
// If i is represented in binary by b0*2^0 + b1*2^1 + ... bn*2^n, k is
// b0*2^(shift + 0*stride) + b1*2^(shift + 1*stride) + ... + bn*2^(shift + n*stride).
// The entry for i = 0 is omitted because it is always the point at infinity.
func makeComb(curve elliptic.Curve, stride, size, shift int) [][2]*big.Int {
ret := make([][2]*big.Int, 1<<size-1)
x, y := curve.Params().Gx, curve.Params().Gy
for j := 0; j < shift; j++ {
x, y = curve.Double(x, y)
}
ret[1<<0-1] = [2]*big.Int{x, y}
for i := 1; i < size; i++ {
// Entry 2^i is entry 2^(i-1) doubled stride times.
x, y = ret[1<<(i-1)-1][0], ret[1<<(i-1)-1][1]
for j := 0; j < stride; j++ {
x, y = curve.Double(x, y)
}
ret[1<<i-1] = [2]*big.Int{x, y}
// The remaining entries with MSB 2^i are computed by adding entry 2^i
// to the corresponding previous entry.
for j := 1; j < 1<<i; j++ {
x, y = curve.Add(ret[1<<i-1][0], ret[1<<i-1][1], ret[j-1][0], ret[j-1][1])
ret[1<<i+j-1] = [2]*big.Int{x, y}
}
}
return ret
}
// toMontgomery sets n to be n×R mod p, where R is the Montgomery factor.
func toMontgomery(curve elliptic.Curve, n *big.Int) *big.Int {
params := curve.Params()
// R is the bit width of p, rounded up to word size.
rounded64 := 64 * ((params.BitSize + 63) / 64)
rounded32 := 32 * ((params.BitSize + 31) / 32)
if rounded64 != rounded32 {
panic(fmt.Sprintf("Montgomery form for %s is inconsistent between 32-bit and 64-bit", params.Name))
}
R := new(big.Int).SetInt64(1)
R.Lsh(R, uint(rounded64))
ret := new(big.Int).Mul(n, R)
ret.Mod(ret, params.P)
return ret
}
func bigIntToU64s(curve elliptic.Curve, n *big.Int) []uint64 {
words := (curve.Params().BitSize + 63) / 64
ret := make([]uint64, words)
bytes := n.Bytes()
for i, b := range bytes {
i = len(bytes) - i - 1
ret[i/8] |= uint64(b) << (8 * (i % 8))
}
return ret
}
func bigIntToU32s(curve elliptic.Curve, n *big.Int) []uint64 {
words := (curve.Params().BitSize + 31) / 32
ret := make([]uint64, words)
bytes := n.Bytes()
for i, b := range bytes {
i = len(bytes) - i - 1
ret[i/4] |= uint64(b) << (8 * (i % 4))
}
return ret
}
func writeIndent(w io.Writer, indent int) error {
for i := 0; i < indent; i++ {
if _, err := io.WriteString(w, " "); err != nil {
return err
}
}
return nil
}
func writeWords(w io.Writer, words []uint64, wrap, indent int, format func(uint64) string) error {
if _, err := io.WriteString(w, "{"); err != nil {
return err
}
for i, word := range words {
if i > 0 {
if i%wrap == 0 {
if _, err := io.WriteString(w, ",\n"); err != nil {
return err
}
if err := writeIndent(w, indent+1); err != nil {
return err
}
} else {
if _, err := io.WriteString(w, ", "); err != nil {
return err
}
}
}
if _, err := io.WriteString(w, format(word)); err != nil {
return err
}
}
if _, err := io.WriteString(w, "}"); err != nil {
return err
}
return nil
}
func writeBNMont(w io.Writer, curve elliptic.Curve, n *big.Int, indent int) error {
n = toMontgomery(curve, n)
return writeWords(w, bigIntToU64s(curve, n), 2, indent, func(word uint64) string {
return fmt.Sprintf("TOBN(0x%08x, 0x%08x)", uint32(word>>32), uint32(word))
})
}
func writeU64Mont(w io.Writer, curve elliptic.Curve, n *big.Int, indent int) error {
n = toMontgomery(curve, n)
return writeWords(w, bigIntToU64s(curve, n), 3, indent, func(word uint64) string {
return fmt.Sprintf("0x%016x", word)
})
}
func writeU32Mont(w io.Writer, curve elliptic.Curve, n *big.Int, indent int) error {
n = toMontgomery(curve, n)
return writeWords(w, bigIntToU32s(curve, n), 6, indent, func(word uint64) string {
if word >= 1<<32 {
panic(fmt.Sprintf("word too large: 0x%x", word))
}
return fmt.Sprintf("0x%08x", word)
})
}
type writeBigIntFunc func(w io.Writer, curve elliptic.Curve, n *big.Int, indent int) error
func writeTable(w io.Writer, curve elliptic.Curve, table [][2]*big.Int, isRoot bool, indent int, writeBigInt writeBigIntFunc) error {
if _, err := io.WriteString(w, "{"); err != nil {
return err
}
if isRoot {
if _, err := io.WriteString(w, "\n"); err != nil {
return err
}
if err := writeIndent(w, indent); err != nil {
return err
}
} else {
indent++
}
for i, point := range table {
if i != 0 {
if _, err := io.WriteString(w, ",\n"); err != nil {
return err
}
if err := writeIndent(w, indent); err != nil {
return err
}
}
if _, err := io.WriteString(w, "{"); err != nil {
return err
}
if err := writeBigInt(w, curve, point[0], indent+1); err != nil {
return err
}
if _, err := io.WriteString(w, ",\n"); err != nil {
return err
}
if err := writeIndent(w, indent+1); err != nil {
return err
}
if err := writeBigInt(w, curve, point[1], indent+1); err != nil {
return err
}
if _, err := io.WriteString(w, "}"); err != nil {
return err
}
}
if _, err := io.WriteString(w, "}"); err != nil {
return err
}
return nil
}
func writeTables(w io.Writer, curve elliptic.Curve, tables [][][2]*big.Int, isRoot bool, indent int, writeBigInt writeBigIntFunc) error {
if _, err := io.WriteString(w, "{"); err != nil {
return err
}
if isRoot {
if _, err := io.WriteString(w, "\n"); err != nil {
return err
}
if err := writeIndent(w, indent); err != nil {
return err
}
} else {
indent++
}
for i, table := range tables {
if i != 0 {
if _, err := io.WriteString(w, ",\n"); err != nil {
return err
}
if err := writeIndent(w, indent); err != nil {
return err
}
}
if err := writeTable(w, curve, table, false, indent, writeBigInt); err != nil {
return err
}
}
if _, err := io.WriteString(w, "}"); err != nil {
return err
}
return nil
}