/* Copyright (c) 2018, 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" "math/big" "os" ) const fileHeader = `/* Copyright (c) 2015, Intel 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 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_p256-x86_64-table.go. static const alignas(4096) PRECOMP256_ROW ecp_nistz256_precomputed[37] = { ` func main() { os.Stdout.WriteString(fileHeader) scalar, tmp := new(big.Int), new(big.Int) p256 := elliptic.P256() p := p256.Params().P // The wNAF windows are 7 bits wide, so advance across the 256-bit scalar // space in 7-bit increments. for shift := uint(0); shift < 256; shift += 7 { // For each window, encode 64 multiples of the base point. for multiple := 1; multiple <= 64; multiple++ { scalar.SetInt64(int64(multiple)) scalar.Lsh(scalar, shift) x, y := p256.ScalarBaseMult(scalar.Bytes()) toMontgomery(x, p) toMontgomery(y, p) if multiple == 1 { os.Stdout.WriteString(" {{") } else { os.Stdout.WriteString(" {") } printNum(x, tmp) os.Stdout.WriteString(",\n ") printNum(y, tmp) if multiple == 64 { os.Stdout.WriteString("}}") } else { os.Stdout.WriteString("},\n") } } if shift+7 < 256 { os.Stdout.WriteString(",\n") } else { os.Stdout.WriteString("};\n") } } } var mask, R *big.Int func init() { mask = new(big.Int).SetUint64(0xffffffffffffffff) R = new(big.Int).SetInt64(1) R.Lsh(R, 256) } func printNum(n, tmp *big.Int) { fmt.Printf("{") for i := 0; i < 4; i++ { tmp.And(n, mask) limb := tmp.Uint64() fmt.Printf("TOBN(0x%08x, 0x%08x)", uint32(limb>>32), uint32(limb)) n.Rsh(n, 64) switch i { case 0, 2: os.Stdout.WriteString(", ") case 1: os.Stdout.WriteString(",\n ") } } fmt.Printf("}") } // toMontgomery sets n to be n×R mod p func toMontgomery(n, p *big.Int) { n.Mul(n, R) n.Mod(n, p) }