/* 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 #include #include #include #include #include #include #include "internal.h" #include "../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, 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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) * . 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 (0 != 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; }