| /* Originally written by Bodo Moeller for the OpenSSL project. |
| * ==================================================================== |
| * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * |
| * 3. All advertising materials mentioning features or use of this |
| * software must display the following acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| * |
| * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| * endorse or promote products derived from this software without |
| * prior written permission. For written permission, please contact |
| * openssl-core@openssl.org. |
| * |
| * 5. Products derived from this software may not be called "OpenSSL" |
| * nor may "OpenSSL" appear in their names without prior written |
| * permission of the OpenSSL Project. |
| * |
| * 6. Redistributions of any form whatsoever must retain the following |
| * acknowledgment: |
| * "This product includes software developed by the OpenSSL Project |
| * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| * OF THE POSSIBILITY OF SUCH DAMAGE. |
| * ==================================================================== |
| * |
| * This product includes cryptographic software written by Eric Young |
| * (eay@cryptsoft.com). This product includes software written by Tim |
| * Hudson (tjh@cryptsoft.com). |
| * |
| */ |
| /* ==================================================================== |
| * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| * |
| * Portions of the attached software ("Contribution") are developed by |
| * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. |
| * |
| * The Contribution is licensed pursuant to the OpenSSL open source |
| * license provided above. |
| * |
| * The elliptic curve binary polynomial software is originally written by |
| * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems |
| * Laboratories. */ |
| |
| #include <openssl/ec.h> |
| |
| #include <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| #include <openssl/thread.h> |
| |
| #include "internal.h" |
| #include "../bn/internal.h" |
| #include "../../internal.h" |
| |
| |
| // This file implements the wNAF-based interleaving multi-exponentiation method |
| // at: |
| // http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 |
| // http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf |
| |
| // compute_wNAF writes the modified width-(w+1) Non-Adjacent Form (wNAF) of |
| // |scalar| to |out| and returns one on success or zero on internal error. |out| |
| // must have room for |bits| + 1 elements, each of which will be either zero or |
| // odd with an absolute value less than 2^w satisfying |
| // scalar = \sum_j out[j]*2^j |
| // where at most one of any w+1 consecutive digits is non-zero |
| // with the exception that the most significant digit may be only |
| // w-1 zeros away from that next non-zero digit. |
| static int compute_wNAF(const EC_GROUP *group, int8_t *out, |
| const EC_SCALAR *scalar, size_t bits, int w) { |
| // 'int8_t' can represent integers with absolute values less than 2^7. |
| if (w <= 0 || w > 7 || bits == 0) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| return 0; |
| } |
| int bit = 1 << w; // at most 128 |
| int next_bit = bit << 1; // at most 256 |
| int mask = next_bit - 1; // at most 255 |
| |
| int window_val = scalar->words[0] & mask; |
| size_t j = 0; |
| // If j+w+1 >= bits, window_val will not increase. |
| while (window_val != 0 || j + w + 1 < bits) { |
| int digit = 0; |
| |
| // 0 <= window_val <= 2^(w+1) |
| |
| if (window_val & 1) { |
| // 0 < window_val < 2^(w+1) |
| |
| if (window_val & bit) { |
| digit = window_val - next_bit; // -2^w < digit < 0 |
| |
| #if 1 // modified wNAF |
| if (j + w + 1 >= bits) { |
| // special case for generating modified wNAFs: |
| // no new bits will be added into window_val, |
| // so using a positive digit here will decrease |
| // the total length of the representation |
| |
| digit = window_val & (mask >> 1); // 0 < digit < 2^w |
| } |
| #endif |
| } else { |
| digit = window_val; // 0 < digit < 2^w |
| } |
| |
| if (digit <= -bit || digit >= bit || !(digit & 1)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| return 0; |
| } |
| |
| window_val -= digit; |
| |
| // Now window_val is 0 or 2^(w+1) in standard wNAF generation; |
| // for modified window NAFs, it may also be 2^w. |
| if (window_val != 0 && window_val != next_bit && window_val != bit) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| return 0; |
| } |
| } |
| |
| out[j++] = digit; |
| |
| window_val >>= 1; |
| window_val += |
| bit * bn_is_bit_set_words(scalar->words, group->order.top, j + w); |
| |
| if (window_val > next_bit) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| return 0; |
| } |
| } |
| |
| // Fill the rest of the wNAF with zeros. |
| if (j > bits + 1) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| return 0; |
| } |
| for (size_t i = j; i < bits + 1; i++) { |
| out[i] = 0; |
| } |
| |
| return 1; |
| } |
| |
| // TODO: table should be optimised for the wNAF-based implementation, |
| // sometimes smaller windows will give better performance |
| // (thus the boundaries should be increased) |
| static size_t window_bits_for_scalar_size(size_t b) { |
| if (b >= 300) { |
| return 4; |
| } |
| |
| if (b >= 70) { |
| return 3; |
| } |
| |
| if (b >= 20) { |
| return 2; |
| } |
| |
| return 1; |
| } |
| |
| // EC_WNAF_MAX_WINDOW_BITS is the largest value returned by |
| // |window_bits_for_scalar_size|. |
| #define EC_WNAF_MAX_WINDOW_BITS 4 |
| |
| // compute_precomp sets |out[i]| to a newly-allocated |EC_POINT| containing |
| // (2*i+1)*p, for i from 0 to |len|. It returns one on success and |
| // zero on error. |
| static int compute_precomp(const EC_GROUP *group, EC_POINT **out, |
| const EC_POINT *p, size_t len, BN_CTX *ctx) { |
| out[0] = EC_POINT_new(group); |
| if (out[0] == NULL || |
| !EC_POINT_copy(out[0], p)) { |
| return 0; |
| } |
| |
| int ret = 0; |
| EC_POINT *two_p = EC_POINT_new(group); |
| if (two_p == NULL || |
| !EC_POINT_dbl(group, two_p, p, ctx)) { |
| goto err; |
| } |
| |
| for (size_t i = 1; i < len; i++) { |
| out[i] = EC_POINT_new(group); |
| if (out[i] == NULL || |
| !EC_POINT_add(group, out[i], out[i - 1], two_p, ctx)) { |
| goto err; |
| } |
| } |
| |
| ret = 1; |
| |
| err: |
| EC_POINT_free(two_p); |
| return ret; |
| } |
| |
| static int lookup_precomp(const EC_GROUP *group, EC_POINT *out, |
| EC_POINT *const *precomp, int digit, BN_CTX *ctx) { |
| if (digit < 0) { |
| digit = -digit; |
| return EC_POINT_copy(out, precomp[digit >> 1]) && |
| EC_POINT_invert(group, out, ctx); |
| } |
| |
| return EC_POINT_copy(out, precomp[digit >> 1]); |
| } |
| |
| int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const EC_SCALAR *g_scalar, |
| const EC_POINT *p, const EC_SCALAR *p_scalar, BN_CTX *ctx) { |
| BN_CTX *new_ctx = NULL; |
| EC_POINT *precomp_storage[2 * (1 << (EC_WNAF_MAX_WINDOW_BITS - 1))] = {NULL}; |
| EC_POINT **g_precomp = NULL, **p_precomp = NULL; |
| int8_t g_wNAF[EC_MAX_SCALAR_BYTES * 8 + 1]; |
| int8_t p_wNAF[EC_MAX_SCALAR_BYTES * 8 + 1]; |
| EC_POINT *tmp = NULL; |
| int ret = 0; |
| |
| if (ctx == NULL) { |
| ctx = new_ctx = BN_CTX_new(); |
| if (ctx == NULL) { |
| goto err; |
| } |
| } |
| |
| size_t bits = BN_num_bits(&group->order); |
| size_t wsize = window_bits_for_scalar_size(bits); |
| size_t wNAF_len = bits + 1; |
| size_t precomp_len = (size_t)1 << (wsize - 1); |
| if (wNAF_len > OPENSSL_ARRAY_SIZE(g_wNAF) || |
| wNAF_len > OPENSSL_ARRAY_SIZE(p_wNAF) || |
| 2 * precomp_len > OPENSSL_ARRAY_SIZE(precomp_storage)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR); |
| goto err; |
| } |
| |
| // TODO(davidben): |mul_public| is for ECDSA verification which can assume |
| // non-NULL inputs, but this code is also used for |mul| which cannot. It's |
| // not constant-time, so replace the generic |mul| and remove the NULL checks. |
| size_t total_precomp = 0; |
| if (g_scalar != NULL) { |
| const EC_POINT *g = EC_GROUP_get0_generator(group); |
| if (g == NULL) { |
| OPENSSL_PUT_ERROR(EC, EC_R_UNDEFINED_GENERATOR); |
| goto err; |
| } |
| g_precomp = precomp_storage + total_precomp; |
| total_precomp += precomp_len; |
| if (!compute_wNAF(group, g_wNAF, g_scalar, bits, wsize) || |
| !compute_precomp(group, g_precomp, g, precomp_len, ctx)) { |
| goto err; |
| } |
| } |
| |
| if (p_scalar != NULL) { |
| p_precomp = precomp_storage + total_precomp; |
| total_precomp += precomp_len; |
| if (!compute_wNAF(group, p_wNAF, p_scalar, bits, wsize) || |
| !compute_precomp(group, p_precomp, p, precomp_len, ctx)) { |
| goto err; |
| } |
| } |
| |
| tmp = EC_POINT_new(group); |
| if (tmp == NULL || |
| // |window_bits_for_scalar_size| assumes we do this step. |
| !EC_POINTs_make_affine(group, total_precomp, precomp_storage, ctx)) { |
| goto err; |
| } |
| |
| int r_is_at_infinity = 1; |
| for (size_t k = wNAF_len - 1; k < wNAF_len; k--) { |
| if (!r_is_at_infinity && !EC_POINT_dbl(group, r, r, ctx)) { |
| goto err; |
| } |
| |
| if (g_scalar != NULL) { |
| if (g_wNAF[k] != 0) { |
| if (!lookup_precomp(group, tmp, g_precomp, g_wNAF[k], ctx)) { |
| goto err; |
| } |
| if (r_is_at_infinity) { |
| if (!EC_POINT_copy(r, tmp)) { |
| goto err; |
| } |
| r_is_at_infinity = 0; |
| } else if (!EC_POINT_add(group, r, r, tmp, ctx)) { |
| goto err; |
| } |
| } |
| } |
| |
| if (p_scalar != NULL) { |
| if (p_wNAF[k] != 0) { |
| if (!lookup_precomp(group, tmp, p_precomp, p_wNAF[k], ctx)) { |
| goto err; |
| } |
| if (r_is_at_infinity) { |
| if (!EC_POINT_copy(r, tmp)) { |
| goto err; |
| } |
| r_is_at_infinity = 0; |
| } else if (!EC_POINT_add(group, r, r, tmp, ctx)) { |
| goto err; |
| } |
| } |
| } |
| } |
| |
| if (r_is_at_infinity && |
| !EC_POINT_set_to_infinity(group, r)) { |
| goto err; |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_free(new_ctx); |
| EC_POINT_free(tmp); |
| OPENSSL_cleanse(&g_wNAF, sizeof(g_wNAF)); |
| OPENSSL_cleanse(&p_wNAF, sizeof(p_wNAF)); |
| for (size_t i = 0; i < OPENSSL_ARRAY_SIZE(precomp_storage); i++) { |
| EC_POINT_free(precomp_storage[i]); |
| } |
| return ret; |
| } |