--- /dev/null
+/* 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 <openssl/type_check.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
+
+int ec_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.width, 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);
+
+ OPENSSL_COMPILE_ASSERT(
+ OPENSSL_ARRAY_SIZE(g_wNAF) == OPENSSL_ARRAY_SIZE(p_wNAF),
+ g_wNAF_and_p_wNAF_are_different_sizes);
+
+ if (wNAF_len > OPENSSL_ARRAY_SIZE(g_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 (!ec_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 (!ec_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;
+}
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