| /* Copyright (c) 2016, 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. */ |
| |
| #include <openssl/curve25519.h> |
| |
| #include <assert.h> |
| #include <string.h> |
| |
| #include <openssl/bytestring.h> |
| #include <openssl/mem.h> |
| #include <openssl/rand.h> |
| #include <openssl/sha.h> |
| |
| #include "../internal.h" |
| #include "../../third_party/fiat/internal.h" |
| |
| |
| // The following precomputation tables are for the following |
| // points used in the SPAKE2 protocol. |
| // |
| // N: |
| // x: 49918732221787544735331783592030787422991506689877079631459872391322455579424 |
| // y: 54629554431565467720832445949441049581317094546788069926228343916274969994000 |
| // encoded: 10e3df0ae37d8e7a99b5fe74b44672103dbddcbd06af680d71329a11693bc778 |
| // |
| // M: |
| // x: 31406539342727633121250288103050113562375374900226415211311216773867585644232 |
| // y: 21177308356423958466833845032658859666296341766942662650232962324899758529114 |
| // encoded: 5ada7e4bf6ddd9adb6626d32131c6b5c51a1e347a3478f53cfcf441b88eed12e |
| // |
| // These points and their precomputation tables are generated with the |
| // following Python code. For a description of the precomputation table, |
| // see curve25519.c in this directory. |
| // |
| // Exact copies of the source code are kept in bug 27296743. |
| |
| /* |
| import hashlib |
| import ed25519 as E # http://ed25519.cr.yp.to/python/ed25519.py |
| |
| SEED_N = 'edwards25519 point generation seed (N)' |
| SEED_M = 'edwards25519 point generation seed (M)' |
| |
| def genpoint(seed): |
| v = hashlib.sha256(seed).digest() |
| it = 1 |
| while True: |
| try: |
| x,y = E.decodepoint(v) |
| except Exception, e: |
| print e |
| it += 1 |
| v = hashlib.sha256(v).digest() |
| continue |
| print "Found in %d iterations:" % it |
| print " x = %d" % x |
| print " y = %d" % y |
| print " Encoded (hex)" |
| print E.encodepoint((x,y)).encode('hex') |
| return (x,y) |
| |
| def gentable(P): |
| t = [] |
| for i in range(1,16): |
| k = ((i >> 3 & 1) * (1 << 192) + |
| (i >> 2 & 1) * (1 << 128) + |
| (i >> 1 & 1) * (1 << 64) + |
| (i & 1)) |
| t.append(E.scalarmult(P, k)) |
| return ''.join(E.encodeint(x) + E.encodeint(y) for (x,y) in t) |
| |
| def printtable(table, name): |
| print "static const uint8_t %s[15 * 2 * 32] = {" % name, |
| for i in range(15 * 2 * 32): |
| if i % 12 == 0: |
| print "\n ", |
| print " 0x%02x," % ord(table[i]), |
| print "\n};" |
| |
| if __name__ == "__main__": |
| print "Searching for N" |
| N = genpoint(SEED_N) |
| print "Generating precomputation table for N" |
| Ntable = gentable(N) |
| printtable(Ntable, "kSpakeNSmallPrecomp") |
| |
| print "Searching for M" |
| M = genpoint(SEED_M) |
| print "Generating precomputation table for M" |
| Mtable = gentable(M) |
| printtable(Mtable, "kSpakeMSmallPrecomp") |
| */ |
| |
| static const uint8_t kSpakeNSmallPrecomp[15 * 2 * 32] = { |
| 0x20, 0x1b, 0xc5, 0xb3, 0x43, 0x17, 0x71, 0x10, 0x44, 0x1e, 0x73, 0xb3, |
| 0xae, 0x3f, 0xbf, 0x9f, 0xf5, 0x44, 0xc8, 0x13, 0x8f, 0xd1, 0x01, 0xc2, |
| 0x8a, 0x1a, 0x6d, 0xea, 0x4d, 0x00, 0x5d, 0x6e, 0x10, 0xe3, 0xdf, 0x0a, |
| 0xe3, 0x7d, 0x8e, 0x7a, 0x99, 0xb5, 0xfe, 0x74, 0xb4, 0x46, 0x72, 0x10, |
| 0x3d, 0xbd, 0xdc, 0xbd, 0x06, 0xaf, 0x68, 0x0d, 0x71, 0x32, 0x9a, 0x11, |
| 0x69, 0x3b, 0xc7, 0x78, 0x93, 0xf1, 0x57, 0x97, 0x6e, 0xf0, 0x6e, 0x45, |
| 0x37, 0x4a, 0xf4, 0x0b, 0x18, 0x51, 0xf5, 0x4f, 0x67, 0x3c, 0xdc, 0xec, |
| 0x84, 0xed, 0xd0, 0xeb, 0xca, 0xfb, 0xdb, 0xff, 0x7f, 0xeb, 0xa8, 0x23, |
| 0x68, 0x87, 0x13, 0x64, 0x6a, 0x10, 0xf7, 0x45, 0xe0, 0x0f, 0x32, 0x21, |
| 0x59, 0x7c, 0x0e, 0x50, 0xad, 0x56, 0xd7, 0x12, 0x69, 0x7b, 0x58, 0xf8, |
| 0xb9, 0x3b, 0xa5, 0xbb, 0x4d, 0x1b, 0x87, 0x1c, 0x46, 0xa7, 0x17, 0x9d, |
| 0x6d, 0x84, 0x45, 0xbe, 0x7f, 0x95, 0xd2, 0x34, 0xcd, 0x89, 0x95, 0xc0, |
| 0xf0, 0xd3, 0xdf, 0x6e, 0x10, 0x4a, 0xe3, 0x7b, 0xce, 0x7f, 0x40, 0x27, |
| 0xc7, 0x2b, 0xab, 0x66, 0x03, 0x59, 0xb4, 0x7b, 0xc7, 0xc7, 0xf0, 0x39, |
| 0x9a, 0x33, 0x35, 0xbf, 0xcc, 0x2f, 0xf3, 0x2e, 0x68, 0x9d, 0x53, 0x5c, |
| 0x88, 0x52, 0xe3, 0x77, 0x90, 0xa1, 0x27, 0x85, 0xc5, 0x74, 0x7f, 0x23, |
| 0x0e, 0x93, 0x01, 0x3e, 0xe7, 0x2e, 0x2e, 0x95, 0xf3, 0x0d, 0xc2, 0x25, |
| 0x25, 0x39, 0x39, 0x3d, 0x6e, 0x8e, 0x89, 0xbd, 0xe8, 0xbb, 0x67, 0x5e, |
| 0x8c, 0x66, 0x8b, 0x63, 0x28, 0x1e, 0x4e, 0x74, 0x85, 0xa8, 0xaf, 0x0f, |
| 0x12, 0x5d, 0xb6, 0x8a, 0x83, 0x1a, 0x77, 0x76, 0x5e, 0x62, 0x8a, 0xa7, |
| 0x3c, 0xb8, 0x05, 0x57, 0x2b, 0xaf, 0x36, 0x2e, 0x10, 0x90, 0xb2, 0x39, |
| 0xb4, 0x3e, 0x75, 0x6d, 0x3a, 0xa8, 0x31, 0x35, 0xc2, 0x1e, 0x8f, 0xc2, |
| 0x79, 0x89, 0x35, 0x16, 0x26, 0xd1, 0xc7, 0x0b, 0x04, 0x1f, 0x1d, 0xf9, |
| 0x9c, 0x05, 0xa6, 0x6b, 0xb5, 0x19, 0x5a, 0x24, 0x6d, 0x91, 0xc5, 0x31, |
| 0xfd, 0xc5, 0xfa, 0xe7, 0xa6, 0xcb, 0x0e, 0x4b, 0x18, 0x0d, 0x94, 0xc7, |
| 0xee, 0x1d, 0x46, 0x1f, 0x92, 0xb1, 0xb2, 0x4a, 0x2b, 0x43, 0x37, 0xfe, |
| 0xc2, 0x15, 0x11, 0x89, 0xef, 0x59, 0x73, 0x3c, 0x06, 0x76, 0x78, 0xcb, |
| 0xa6, 0x0d, 0x79, 0x5f, 0x28, 0x0b, 0x5b, 0x8c, 0x9e, 0xe4, 0xaa, 0x51, |
| 0x9a, 0x42, 0x6f, 0x11, 0x50, 0x3d, 0x01, 0xd6, 0x21, 0xc0, 0x99, 0x5e, |
| 0x1a, 0xe8, 0x81, 0x25, 0x80, 0xeb, 0xed, 0x5d, 0x37, 0x47, 0x30, 0x70, |
| 0xa0, 0x4e, 0x0b, 0x43, 0x17, 0xbe, 0xb6, 0x47, 0xe7, 0x2a, 0x62, 0x9d, |
| 0x5d, 0xa6, 0xc5, 0x33, 0x62, 0x9d, 0x56, 0x24, 0x9d, 0x1d, 0xb2, 0x13, |
| 0xbc, 0x17, 0x66, 0x43, 0xd1, 0x68, 0xd5, 0x3b, 0x17, 0x69, 0x17, 0xa6, |
| 0x06, 0x9e, 0x12, 0xb8, 0x7c, 0xd5, 0xaf, 0x3e, 0x21, 0x1b, 0x31, 0xeb, |
| 0x0b, 0xa4, 0x98, 0x1c, 0xf2, 0x6a, 0x5e, 0x7c, 0x9b, 0x45, 0x8f, 0xb2, |
| 0x12, 0x06, 0xd5, 0x8c, 0x1d, 0xb2, 0xa7, 0x57, 0x5f, 0x2f, 0x4f, 0xdb, |
| 0x52, 0x99, 0x7c, 0x58, 0x01, 0x5f, 0xf2, 0xa5, 0xf6, 0x51, 0x86, 0x21, |
| 0x2f, 0x5b, 0x8d, 0x6a, 0xae, 0x83, 0x34, 0x6d, 0x58, 0x4b, 0xef, 0xfe, |
| 0xbf, 0x73, 0x5d, 0xdb, 0xc4, 0x97, 0x2a, 0x85, 0xf3, 0x6c, 0x46, 0x42, |
| 0xb3, 0x90, 0xc1, 0x57, 0x97, 0x50, 0x35, 0xb1, 0x9d, 0xb7, 0xc7, 0x3c, |
| 0x85, 0x6d, 0x6c, 0xfd, 0xce, 0xb0, 0xc9, 0xa2, 0x77, 0xee, 0xc3, 0x6b, |
| 0x0c, 0x37, 0xfa, 0x30, 0x91, 0xd1, 0x2c, 0xb8, 0x5e, 0x7f, 0x81, 0x5f, |
| 0x87, 0xfd, 0x18, 0x02, 0x5a, 0x30, 0x4e, 0x62, 0xbc, 0x65, 0xc6, 0xce, |
| 0x1a, 0xcf, 0x2b, 0xaa, 0x56, 0x3e, 0x4d, 0xcf, 0xba, 0x62, 0x5f, 0x9a, |
| 0xd0, 0x72, 0xff, 0xef, 0x28, 0xbd, 0xbe, 0xd8, 0x57, 0x3d, 0xf5, 0x57, |
| 0x7d, 0xe9, 0x71, 0x31, 0xec, 0x98, 0x90, 0x94, 0xd9, 0x54, 0xbf, 0x84, |
| 0x0b, 0xe3, 0x06, 0x47, 0x19, 0x9a, 0x13, 0x1d, 0xef, 0x9d, 0x13, 0xf3, |
| 0xdb, 0xc3, 0x5c, 0x72, 0x9e, 0xed, 0x24, 0xaa, 0x64, 0xed, 0xe7, 0x0d, |
| 0xa0, 0x7c, 0x73, 0xba, 0x9b, 0x86, 0xa7, 0x3b, 0x55, 0xab, 0x58, 0x30, |
| 0xf1, 0x15, 0x81, 0x83, 0x2f, 0xf9, 0x62, 0x84, 0x98, 0x66, 0xf6, 0x55, |
| 0x21, 0xd8, 0xf2, 0x25, 0x64, 0x71, 0x4b, 0x12, 0x76, 0x59, 0xc5, 0xaa, |
| 0x93, 0x67, 0xc3, 0x86, 0x25, 0xab, 0x4e, 0x4b, 0xf6, 0xd8, 0x3f, 0x44, |
| 0x2e, 0x11, 0xe0, 0xbd, 0x6a, 0xf2, 0x5d, 0xf5, 0xf9, 0x53, 0xea, 0xa4, |
| 0xc8, 0xd9, 0x50, 0x33, 0x81, 0xd9, 0xa8, 0x2d, 0x91, 0x7d, 0x13, 0x2a, |
| 0x11, 0xcf, 0xde, 0x3f, 0x0a, 0xd2, 0xbc, 0x33, 0xb2, 0x62, 0x53, 0xea, |
| 0x77, 0x88, 0x43, 0x66, 0x27, 0x43, 0x85, 0xe9, 0x5f, 0x55, 0xf5, 0x2a, |
| 0x8a, 0xac, 0xdf, 0xff, 0x9b, 0x4c, 0x96, 0x9c, 0xa5, 0x7a, 0xce, 0xd5, |
| 0x79, 0x18, 0xf1, 0x0b, 0x58, 0x95, 0x7a, 0xe7, 0xd3, 0x74, 0x65, 0x0b, |
| 0xa4, 0x64, 0x30, 0xe8, 0x5c, 0xfc, 0x55, 0x56, 0xee, 0x14, 0x14, 0xd3, |
| 0x45, 0x3b, 0xf8, 0xde, 0x05, 0x3e, 0xb9, 0x3c, 0xd7, 0x6a, 0x52, 0x72, |
| 0x5b, 0x39, 0x09, 0xbe, 0x82, 0x23, 0x10, 0x4a, 0xb7, 0xc3, 0xdc, 0x4c, |
| 0x5d, 0xc9, 0xf1, 0x14, 0x83, 0xf9, 0x0b, 0x9b, 0xe9, 0x23, 0x84, 0x6a, |
| 0xc4, 0x08, 0x3d, 0xda, 0x3d, 0x12, 0x95, 0x87, 0x18, 0xa4, 0x7d, 0x3f, |
| 0x23, 0xde, 0xd4, 0x1e, 0xa8, 0x47, 0xc3, 0x71, 0xdb, 0xf5, 0x03, 0x6c, |
| 0x57, 0xe7, 0xa4, 0x43, 0x82, 0x33, 0x7b, 0x62, 0x46, 0x7d, 0xf7, 0x10, |
| 0x69, 0x18, 0x38, 0x27, 0x9a, 0x6f, 0x38, 0xac, 0xfa, 0x92, 0xc5, 0xae, |
| 0x66, 0xa6, 0x73, 0x95, 0x15, 0x0e, 0x4c, 0x04, 0xb6, 0xfc, 0xf5, 0xc7, |
| 0x21, 0x3a, 0x99, 0xdb, 0x0e, 0x36, 0xf0, 0x56, 0xbc, 0x75, 0xf9, 0x87, |
| 0x9b, 0x11, 0x18, 0x92, 0x64, 0x1a, 0xe7, 0xc7, 0xab, 0x5a, 0xc7, 0x26, |
| 0x7f, 0x13, 0x98, 0x42, 0x52, 0x43, 0xdb, 0xc8, 0x6d, 0x0b, 0xb7, 0x31, |
| 0x93, 0x24, 0xd6, 0xe8, 0x24, 0x1f, 0x6f, 0x21, 0xa7, 0x8c, 0xeb, 0xdb, |
| 0x83, 0xb8, 0x89, 0xe3, 0xc1, 0xd7, 0x69, 0x3b, 0x02, 0x6b, 0x54, 0x0f, |
| 0x84, 0x2f, 0xb5, 0x5c, 0x17, 0x77, 0xbe, 0xe5, 0x61, 0x0d, 0xc5, 0xdf, |
| 0x3b, 0xcf, 0x3e, 0x93, 0x4f, 0xf5, 0x89, 0xb9, 0x5a, 0xc5, 0x29, 0x31, |
| 0xc0, 0xc2, 0xff, 0xe5, 0x3f, 0xa6, 0xac, 0x03, 0xca, 0xf5, 0xff, 0xe0, |
| 0x36, 0xce, 0xf3, 0xe2, 0xb7, 0x9c, 0x02, 0xe9, 0x9e, 0xd2, 0xbc, 0x87, |
| 0x2f, 0x3d, 0x9a, 0x1d, 0x8f, 0xc5, 0x72, 0xb8, 0xa2, 0x01, 0xd4, 0x68, |
| 0xb1, 0x84, 0x16, 0x10, 0xf6, 0xf3, 0x52, 0x25, 0xd9, 0xdc, 0x4c, 0xdd, |
| 0x0f, 0xd6, 0x4a, 0xcf, 0x60, 0x96, 0x7e, 0xcc, 0x42, 0x0f, 0x64, 0x9d, |
| 0x72, 0x46, 0x04, 0x07, 0xf2, 0x5b, 0xf4, 0x07, 0xd1, 0xf4, 0x59, 0x71, |
| }; |
| |
| static const uint8_t kSpakeMSmallPrecomp[15 * 2 * 32] = { |
| 0xc8, 0xa6, 0x63, 0xc5, 0x97, 0xf1, 0xee, 0x40, 0xab, 0x62, 0x42, 0xee, |
| 0x25, 0x6f, 0x32, 0x6c, 0x75, 0x2c, 0xa7, 0xd3, 0xbd, 0x32, 0x3b, 0x1e, |
| 0x11, 0x9c, 0xbd, 0x04, 0xa9, 0x78, 0x6f, 0x45, 0x5a, 0xda, 0x7e, 0x4b, |
| 0xf6, 0xdd, 0xd9, 0xad, 0xb6, 0x62, 0x6d, 0x32, 0x13, 0x1c, 0x6b, 0x5c, |
| 0x51, 0xa1, 0xe3, 0x47, 0xa3, 0x47, 0x8f, 0x53, 0xcf, 0xcf, 0x44, 0x1b, |
| 0x88, 0xee, 0xd1, 0x2e, 0x03, 0x89, 0xaf, 0xc0, 0x61, 0x2d, 0x9e, 0x35, |
| 0xeb, 0x0e, 0x03, 0xe0, 0xb7, 0xfb, 0xa5, 0xbc, 0x44, 0xbe, 0x0c, 0x89, |
| 0x0a, 0x0f, 0xd6, 0x59, 0x47, 0x9e, 0xe6, 0x3d, 0x36, 0x9d, 0xff, 0x44, |
| 0x5e, 0xac, 0xab, 0xe5, 0x3a, 0xd5, 0xb0, 0x35, 0x9f, 0x6d, 0x7f, 0xba, |
| 0xc0, 0x85, 0x0e, 0xf4, 0x70, 0x3f, 0x13, 0x90, 0x4c, 0x50, 0x1a, 0xee, |
| 0xc5, 0xeb, 0x69, 0xfe, 0x98, 0x42, 0x87, 0x1d, 0xce, 0x6c, 0x29, 0xaa, |
| 0x2b, 0x31, 0xc2, 0x38, 0x7b, 0x6b, 0xee, 0x88, 0x0b, 0xba, 0xce, 0xa8, |
| 0xca, 0x19, 0x60, 0x1b, 0x16, 0xf1, 0x25, 0x1e, 0xcf, 0x63, 0x66, 0x1e, |
| 0xbb, 0x63, 0xeb, 0x7d, 0xca, 0xd2, 0xb4, 0x23, 0x5a, 0x01, 0x6f, 0x05, |
| 0xd1, 0xdc, 0x41, 0x73, 0x75, 0xc0, 0xfd, 0x30, 0x91, 0x52, 0x68, 0x96, |
| 0x45, 0xb3, 0x66, 0x01, 0x3b, 0x53, 0x89, 0x3c, 0x69, 0xbc, 0x6c, 0x69, |
| 0xe3, 0x51, 0x8f, 0xe3, 0xd2, 0x84, 0xd5, 0x28, 0x66, 0xb5, 0xe6, 0x06, |
| 0x09, 0xfe, 0x6d, 0xb0, 0x72, 0x16, 0xe0, 0x8a, 0xce, 0x61, 0x65, 0xa9, |
| 0x21, 0x32, 0x48, 0xdc, 0x7a, 0x1d, 0xe1, 0x38, 0x7f, 0x8c, 0x75, 0x88, |
| 0x3d, 0x08, 0xa9, 0x4a, 0x6f, 0x3d, 0x9f, 0x7f, 0x3f, 0xbd, 0x57, 0x6b, |
| 0x19, 0xce, 0x3f, 0x4a, 0xc9, 0xd3, 0xf9, 0x6e, 0x72, 0x7b, 0x5b, 0x74, |
| 0xea, 0xbe, 0x9c, 0x7a, 0x6d, 0x9c, 0x40, 0x49, 0xe6, 0xfb, 0x2a, 0x1a, |
| 0x75, 0x70, 0xe5, 0x4e, 0xed, 0x74, 0xe0, 0x75, 0xac, 0xc0, 0xb1, 0x11, |
| 0x3e, 0xf2, 0xaf, 0x88, 0x4d, 0x66, 0xb6, 0xf6, 0x15, 0x4f, 0x3c, 0x6c, |
| 0x77, 0xae, 0x47, 0x51, 0x63, 0x9a, 0xfe, 0xe1, 0xb4, 0x1a, 0x12, 0xdf, |
| 0xe9, 0x54, 0x8d, 0x3b, 0x30, 0x2a, 0x75, 0xe3, 0xe5, 0x29, 0xb1, 0x4c, |
| 0xb0, 0x7c, 0x6d, 0xb5, 0xae, 0x85, 0xdb, 0x1e, 0x38, 0x55, 0x96, 0xa5, |
| 0x5b, 0x9f, 0x15, 0x23, 0x28, 0x36, 0xb8, 0xa2, 0x41, 0xb4, 0xd7, 0x19, |
| 0x91, 0x8d, 0x26, 0x3e, 0xca, 0x9c, 0x05, 0x7a, 0x2b, 0x60, 0x45, 0x86, |
| 0x8b, 0xee, 0x64, 0x6f, 0x5c, 0x09, 0x4d, 0x4b, 0x5a, 0x7f, 0xb0, 0xc3, |
| 0x26, 0x9d, 0x8b, 0xb8, 0x83, 0x69, 0xcf, 0x16, 0x72, 0x62, 0x3e, 0x5e, |
| 0x53, 0x4f, 0x9c, 0x73, 0x76, 0xfc, 0x19, 0xef, 0xa0, 0x74, 0x3a, 0x11, |
| 0x1e, 0xd0, 0x4d, 0xb7, 0x87, 0xa1, 0xd6, 0x87, 0x6c, 0x0e, 0x6c, 0x8c, |
| 0xe9, 0xa0, 0x44, 0xc4, 0x72, 0x3e, 0x73, 0x17, 0x13, 0xd1, 0x4e, 0x3d, |
| 0x8e, 0x1d, 0x5a, 0x8b, 0x75, 0xcb, 0x59, 0x2c, 0x47, 0x87, 0x15, 0x41, |
| 0xfe, 0x08, 0xe9, 0xa6, 0x97, 0x17, 0x08, 0x26, 0x6a, 0xb5, 0xbb, 0x73, |
| 0xaa, 0xb8, 0x5b, 0x65, 0x65, 0x5b, 0x30, 0x9e, 0x62, 0x59, 0x02, 0xf8, |
| 0xb8, 0x0f, 0x32, 0x10, 0xc1, 0x36, 0x08, 0x52, 0x98, 0x4a, 0x1e, 0xf0, |
| 0xab, 0x21, 0x5e, 0xde, 0x16, 0x0c, 0xda, 0x09, 0x99, 0x6b, 0x9e, 0xc0, |
| 0x90, 0xa5, 0x5a, 0xcc, 0xb0, 0xb7, 0xbb, 0xd2, 0x8b, 0x5f, 0xd3, 0x3b, |
| 0x3e, 0x8c, 0xa5, 0x71, 0x66, 0x06, 0xe3, 0x28, 0xd4, 0xf8, 0x3f, 0xe5, |
| 0x27, 0xdf, 0xfe, 0x0f, 0x09, 0xb2, 0x8a, 0x09, 0x5a, 0x23, 0x61, 0x0d, |
| 0x2d, 0xf5, 0x44, 0xf1, 0x5c, 0xf8, 0x82, 0x4e, 0xdc, 0x78, 0x7a, 0xab, |
| 0xc3, 0x57, 0x91, 0xaf, 0x65, 0x6e, 0x71, 0xf1, 0x44, 0xbf, 0xed, 0x43, |
| 0x50, 0xb4, 0x67, 0x48, 0xef, 0x5a, 0x10, 0x46, 0x81, 0xb4, 0x0c, 0xc8, |
| 0x48, 0xed, 0x99, 0x7a, 0x45, 0xa5, 0x92, 0xc3, 0x69, 0xd6, 0xd7, 0x8a, |
| 0x20, 0x1b, 0xeb, 0x8f, 0xb2, 0xff, 0xec, 0x6d, 0x76, 0x04, 0xf8, 0xc2, |
| 0x58, 0x9b, 0xf2, 0x20, 0x53, 0xc4, 0x74, 0x91, 0x19, 0xdd, 0x2d, 0x12, |
| 0x53, 0xc7, 0x6e, 0xd0, 0x02, 0x51, 0x3c, 0xa6, 0x7d, 0x80, 0x75, 0x6b, |
| 0x1d, 0xdf, 0xf8, 0x6a, 0x52, 0xbb, 0x81, 0xf8, 0x30, 0x45, 0xef, 0x51, |
| 0x85, 0x36, 0xbe, 0x8e, 0xcf, 0x0b, 0x9a, 0x46, 0xe8, 0x3f, 0x99, 0xfd, |
| 0xf7, 0xd9, 0x3e, 0x84, 0xe5, 0xe3, 0x37, 0xcf, 0x98, 0x7f, 0xeb, 0x5e, |
| 0x5a, 0x53, 0x77, 0x1c, 0x20, 0xdc, 0xf1, 0x20, 0x99, 0xec, 0x60, 0x40, |
| 0x93, 0xef, 0x5c, 0x1c, 0x81, 0xe2, 0xa5, 0xad, 0x2a, 0xc2, 0xdb, 0x6b, |
| 0xc1, 0x7e, 0x8f, 0xa9, 0x23, 0x5b, 0xd9, 0x0d, 0xfe, 0xa0, 0xac, 0x11, |
| 0x28, 0xba, 0x8e, 0x92, 0x07, 0x2d, 0x07, 0x40, 0x83, 0x14, 0x4c, 0x35, |
| 0x8d, 0xd0, 0x11, 0xff, 0x98, 0xdb, 0x00, 0x30, 0x6f, 0x65, 0xb6, 0xa0, |
| 0x7f, 0x9c, 0x08, 0xb8, 0xce, 0xb3, 0xa8, 0x42, 0xd3, 0x84, 0x45, 0xe1, |
| 0xe3, 0x8f, 0xa6, 0x89, 0x21, 0xd7, 0x74, 0x02, 0x4d, 0x64, 0xdf, 0x54, |
| 0x15, 0x9e, 0xba, 0x12, 0x49, 0x09, 0x41, 0xf6, 0x10, 0x24, 0xa1, 0x84, |
| 0x15, 0xfd, 0x68, 0x6a, 0x57, 0x66, 0xb3, 0x6d, 0x4c, 0xea, 0xbf, 0xbc, |
| 0x60, 0x3f, 0x52, 0x1c, 0x44, 0x1b, 0xc0, 0x4a, 0x25, 0xe3, 0xd9, 0x4c, |
| 0x9a, 0x74, 0xad, 0xfc, 0x9e, 0x8d, 0x0b, 0x18, 0x66, 0x24, 0xd1, 0x06, |
| 0xac, 0x68, 0xc1, 0xae, 0x14, 0xce, 0xb1, 0xf3, 0x86, 0x9f, 0x87, 0x11, |
| 0xd7, 0x9f, 0x30, 0x92, 0xdb, 0xec, 0x0b, 0x4a, 0xe8, 0xf6, 0x53, 0x36, |
| 0x68, 0x12, 0x11, 0x5e, 0xe0, 0x34, 0xa4, 0xff, 0x00, 0x0a, 0x26, 0xb8, |
| 0x62, 0x79, 0x9c, 0x0c, 0xd5, 0xe5, 0xf5, 0x1c, 0x1a, 0x16, 0x84, 0x4d, |
| 0x8e, 0x5d, 0x31, 0x7e, 0xf7, 0xe2, 0xd3, 0xa1, 0x41, 0x90, 0x61, 0x5d, |
| 0x04, 0xb2, 0x9a, 0x18, 0x9e, 0x54, 0xfb, 0xd1, 0x61, 0x95, 0x1b, 0x08, |
| 0xca, 0x7c, 0x49, 0x44, 0x74, 0x1d, 0x2f, 0xca, 0xc4, 0x7a, 0xe1, 0x8b, |
| 0x2f, 0xbb, 0x96, 0xee, 0x19, 0x8a, 0x5d, 0xfb, 0x3e, 0x82, 0xe7, 0x15, |
| 0xdb, 0x29, 0x14, 0xee, 0xc9, 0x4d, 0x9a, 0xfb, 0x9f, 0x8a, 0xbb, 0x17, |
| 0x37, 0x1b, 0x6e, 0x28, 0x6c, 0xf9, 0xff, 0xb5, 0xb5, 0x8b, 0x9d, 0x88, |
| 0x20, 0x08, 0x10, 0xd7, 0xca, 0x58, 0xf6, 0xe1, 0x32, 0x91, 0x6f, 0x36, |
| 0xc0, 0xad, 0xc1, 0x57, 0x5d, 0x76, 0x31, 0x43, 0xf3, 0xdd, 0xec, 0xf1, |
| 0xa9, 0x79, 0xe9, 0xe9, 0x85, 0xd7, 0x91, 0xc7, 0x31, 0x62, 0x3c, 0xd2, |
| 0x90, 0x2c, 0x9c, 0xa4, 0x56, 0x37, 0x7b, 0xbe, 0x40, 0x58, 0xc0, 0x81, |
| 0x83, 0x22, 0xe8, 0x13, 0x79, 0x18, 0xdb, 0x3a, 0x1b, 0x31, 0x0d, 0x00, |
| 0x6c, 0x22, 0x62, 0x75, 0x70, 0xd8, 0x96, 0x59, 0x99, 0x44, 0x79, 0x71, |
| 0xa6, 0x76, 0x81, 0x28, 0xb2, 0x65, 0xe8, 0x47, 0x14, 0xc6, 0x39, 0x06, |
| }; |
| |
| SPAKE2_CTX *SPAKE2_CTX_new(enum spake2_role_t my_role, |
| const uint8_t *my_name, size_t my_name_len, |
| const uint8_t *their_name, size_t their_name_len) { |
| SPAKE2_CTX *ctx = OPENSSL_malloc(sizeof(SPAKE2_CTX)); |
| if (ctx == NULL) { |
| return NULL; |
| } |
| |
| OPENSSL_memset(ctx, 0, sizeof(SPAKE2_CTX)); |
| ctx->my_role = my_role; |
| |
| CBS my_name_cbs, their_name_cbs; |
| CBS_init(&my_name_cbs, my_name, my_name_len); |
| CBS_init(&their_name_cbs, their_name, their_name_len); |
| if (!CBS_stow(&my_name_cbs, &ctx->my_name, &ctx->my_name_len) || |
| !CBS_stow(&their_name_cbs, &ctx->their_name, &ctx->their_name_len)) { |
| SPAKE2_CTX_free(ctx); |
| return NULL; |
| } |
| |
| return ctx; |
| } |
| |
| void SPAKE2_CTX_free(SPAKE2_CTX *ctx) { |
| if (ctx == NULL) { |
| return; |
| } |
| |
| OPENSSL_free(ctx->my_name); |
| OPENSSL_free(ctx->their_name); |
| OPENSSL_free(ctx); |
| } |
| |
| // left_shift_3 sets |n| to |n|*8, where |n| is represented in little-endian |
| // order. |
| static void left_shift_3(uint8_t n[32]) { |
| uint8_t carry = 0; |
| unsigned i; |
| |
| for (i = 0; i < 32; i++) { |
| const uint8_t next_carry = n[i] >> 5; |
| n[i] = (n[i] << 3) | carry; |
| carry = next_carry; |
| } |
| } |
| |
| typedef union { |
| uint8_t bytes[32]; |
| uint32_t words[8]; |
| } scalar; |
| |
| // kOrder is the order of the prime-order subgroup of curve25519 in |
| // little-endian order. |
| static const scalar kOrder = {{0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, |
| 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, |
| 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, |
| 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10}}; |
| |
| // scalar_cmov copies |src| to |dest| if |mask| is all ones. |
| static void scalar_cmov(scalar *dest, const scalar *src, crypto_word_t mask) { |
| for (size_t i = 0; i < 8; i++) { |
| dest->words[i] = |
| constant_time_select_w(mask, src->words[i], dest->words[i]); |
| } |
| } |
| |
| // scalar_double sets |s| to |2×s|. |
| static void scalar_double(scalar *s) { |
| uint32_t carry = 0; |
| |
| for (size_t i = 0; i < 8; i++) { |
| const uint32_t carry_out = s->words[i] >> 31; |
| s->words[i] = (s->words[i] << 1) | carry; |
| carry = carry_out; |
| } |
| } |
| |
| // scalar_add sets |dest| to |dest| plus |src|. |
| static void scalar_add(scalar *dest, const scalar *src) { |
| uint32_t carry = 0; |
| |
| for (size_t i = 0; i < 8; i++) { |
| uint64_t tmp = ((uint64_t)dest->words[i] + src->words[i]) + carry; |
| dest->words[i] = (uint32_t)tmp; |
| carry = (uint32_t)(tmp >> 32); |
| } |
| } |
| |
| int SPAKE2_generate_msg(SPAKE2_CTX *ctx, uint8_t *out, size_t *out_len, |
| size_t max_out_len, const uint8_t *password, |
| size_t password_len) { |
| if (ctx->state != spake2_state_init) { |
| return 0; |
| } |
| |
| if (max_out_len < sizeof(ctx->my_msg)) { |
| return 0; |
| } |
| |
| uint8_t private_tmp[64]; |
| RAND_bytes(private_tmp, sizeof(private_tmp)); |
| x25519_sc_reduce(private_tmp); |
| // Multiply by the cofactor (eight) so that we'll clear it when operating on |
| // the peer's point later in the protocol. |
| left_shift_3(private_tmp); |
| OPENSSL_memcpy(ctx->private_key, private_tmp, sizeof(ctx->private_key)); |
| |
| ge_p3 P; |
| x25519_ge_scalarmult_base(&P, ctx->private_key); |
| |
| // mask = h(password) * <N or M>. |
| uint8_t password_tmp[SHA512_DIGEST_LENGTH]; |
| SHA512(password, password_len, password_tmp); |
| OPENSSL_memcpy(ctx->password_hash, password_tmp, sizeof(ctx->password_hash)); |
| x25519_sc_reduce(password_tmp); |
| |
| // Due to a copy-paste error, the call to |left_shift_3| was omitted after |
| // the |x25519_sc_reduce|, just above. This meant that |ctx->password_scalar| |
| // was not a multiple of eight to clear the cofactor and thus three bits of |
| // the password hash would leak. In order to fix this in a unilateral way, |
| // points of small order are added to the mask point such that it is in the |
| // prime-order subgroup. Since the ephemeral scalar is a multiple of eight, |
| // these points will cancel out when calculating the shared secret. |
| // |
| // Adding points of small order is the same as adding multiples of the prime |
| // order to the password scalar. Since that's faster, that is what is done |
| // below. The prime order (kOrder) is a large prime, thus odd, thus the LSB |
| // is one. So adding it will flip the LSB. Adding twice it will flip the next |
| // bit and so one for all the bottom three bits. |
| |
| scalar password_scalar; |
| OPENSSL_memcpy(&password_scalar, password_tmp, sizeof(password_scalar)); |
| |
| // |password_scalar| is the result of |x25519_sc_reduce| and thus is, at |
| // most, $l-1$ (where $l$ is |kOrder|, the order of the prime-order subgroup |
| // of Ed25519). In the following, we may add $l + 2×l + 4×l$ for a max value |
| // of $8×l-1$. That is < 2**256, as required. |
| |
| if (!ctx->disable_password_scalar_hack) { |
| scalar order = kOrder; |
| scalar tmp; |
| |
| OPENSSL_memset(&tmp, 0, sizeof(tmp)); |
| scalar_cmov(&tmp, &order, |
| constant_time_eq_w(password_scalar.bytes[0] & 1, 1)); |
| scalar_add(&password_scalar, &tmp); |
| |
| scalar_double(&order); |
| OPENSSL_memset(&tmp, 0, sizeof(tmp)); |
| scalar_cmov(&tmp, &order, |
| constant_time_eq_w(password_scalar.bytes[0] & 2, 2)); |
| scalar_add(&password_scalar, &tmp); |
| |
| scalar_double(&order); |
| OPENSSL_memset(&tmp, 0, sizeof(tmp)); |
| scalar_cmov(&tmp, &order, |
| constant_time_eq_w(password_scalar.bytes[0] & 4, 4)); |
| scalar_add(&password_scalar, &tmp); |
| |
| assert((password_scalar.bytes[0] & 7) == 0); |
| } |
| |
| OPENSSL_memcpy(ctx->password_scalar, password_scalar.bytes, |
| sizeof(ctx->password_scalar)); |
| |
| ge_p3 mask; |
| x25519_ge_scalarmult_small_precomp(&mask, ctx->password_scalar, |
| ctx->my_role == spake2_role_alice |
| ? kSpakeMSmallPrecomp |
| : kSpakeNSmallPrecomp); |
| |
| // P* = P + mask. |
| ge_cached mask_cached; |
| x25519_ge_p3_to_cached(&mask_cached, &mask); |
| ge_p1p1 Pstar; |
| x25519_ge_add(&Pstar, &P, &mask_cached); |
| |
| // Encode P* |
| ge_p2 Pstar_proj; |
| x25519_ge_p1p1_to_p2(&Pstar_proj, &Pstar); |
| x25519_ge_tobytes(ctx->my_msg, &Pstar_proj); |
| |
| OPENSSL_memcpy(out, ctx->my_msg, sizeof(ctx->my_msg)); |
| *out_len = sizeof(ctx->my_msg); |
| ctx->state = spake2_state_msg_generated; |
| |
| return 1; |
| } |
| |
| static void update_with_length_prefix(SHA512_CTX *sha, const uint8_t *data, |
| const size_t len) { |
| uint8_t len_le[8]; |
| size_t l = len; |
| unsigned i; |
| |
| for (i = 0; i < 8; i++) { |
| len_le[i] = l & 0xff; |
| l >>= 8; |
| } |
| |
| SHA512_Update(sha, len_le, sizeof(len_le)); |
| SHA512_Update(sha, data, len); |
| } |
| |
| int SPAKE2_process_msg(SPAKE2_CTX *ctx, uint8_t *out_key, size_t *out_key_len, |
| size_t max_out_key_len, const uint8_t *their_msg, |
| size_t their_msg_len) { |
| if (ctx->state != spake2_state_msg_generated || |
| their_msg_len != 32) { |
| return 0; |
| } |
| |
| ge_p3 Qstar; |
| if (!x25519_ge_frombytes_vartime(&Qstar, their_msg)) { |
| // Point received from peer was not on the curve. |
| return 0; |
| } |
| |
| // Unmask peer's value. |
| ge_p3 peers_mask; |
| x25519_ge_scalarmult_small_precomp(&peers_mask, ctx->password_scalar, |
| ctx->my_role == spake2_role_alice |
| ? kSpakeNSmallPrecomp |
| : kSpakeMSmallPrecomp); |
| |
| ge_cached peers_mask_cached; |
| x25519_ge_p3_to_cached(&peers_mask_cached, &peers_mask); |
| |
| ge_p1p1 Q_compl; |
| ge_p3 Q_ext; |
| x25519_ge_sub(&Q_compl, &Qstar, &peers_mask_cached); |
| x25519_ge_p1p1_to_p3(&Q_ext, &Q_compl); |
| |
| ge_p2 dh_shared; |
| x25519_ge_scalarmult(&dh_shared, ctx->private_key, &Q_ext); |
| |
| uint8_t dh_shared_encoded[32]; |
| x25519_ge_tobytes(dh_shared_encoded, &dh_shared); |
| |
| SHA512_CTX sha; |
| SHA512_Init(&sha); |
| if (ctx->my_role == spake2_role_alice) { |
| update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len); |
| update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len); |
| update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg)); |
| update_with_length_prefix(&sha, their_msg, 32); |
| } else { |
| update_with_length_prefix(&sha, ctx->their_name, ctx->their_name_len); |
| update_with_length_prefix(&sha, ctx->my_name, ctx->my_name_len); |
| update_with_length_prefix(&sha, their_msg, 32); |
| update_with_length_prefix(&sha, ctx->my_msg, sizeof(ctx->my_msg)); |
| } |
| update_with_length_prefix(&sha, dh_shared_encoded, sizeof(dh_shared_encoded)); |
| update_with_length_prefix(&sha, ctx->password_hash, |
| sizeof(ctx->password_hash)); |
| |
| uint8_t key[SHA512_DIGEST_LENGTH]; |
| SHA512_Final(key, &sha); |
| |
| size_t to_copy = max_out_key_len; |
| if (to_copy > sizeof(key)) { |
| to_copy = sizeof(key); |
| } |
| OPENSSL_memcpy(out_key, key, to_copy); |
| *out_key_len = to_copy; |
| ctx->state = spake2_state_key_generated; |
| |
| return 1; |
| } |
