--- /dev/null
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
+ * All rights reserved.
+ *
+ * This package is an SSL implementation written
+ * by Eric Young (eay@cryptsoft.com).
+ * The implementation was written so as to conform with Netscapes SSL.
+ *
+ * This library is free for commercial and non-commercial use as long as
+ * the following conditions are aheared to. The following conditions
+ * apply to all code found in this distribution, be it the RC4, RSA,
+ * lhash, DES, etc., code; not just the SSL code. The SSL documentation
+ * included with this distribution is covered by the same copyright terms
+ * except that the holder is Tim Hudson (tjh@cryptsoft.com).
+ *
+ * Copyright remains Eric Young's, and as such any Copyright notices in
+ * the code are not to be removed.
+ * If this package is used in a product, Eric Young should be given attribution
+ * as the author of the parts of the library used.
+ * This can be in the form of a textual message at program startup or
+ * in documentation (online or textual) provided with the package.
+ *
+ * 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 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 acknowledgement:
+ * "This product includes cryptographic software written by
+ * Eric Young (eay@cryptsoft.com)"
+ * The word 'cryptographic' can be left out if the rouines from the library
+ * being used are not cryptographic related :-).
+ * 4. If you include any Windows specific code (or a derivative thereof) from
+ * the apps directory (application code) you must include an acknowledgement:
+ * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
+ * ANY EXPRESS 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 AUTHOR OR 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.
+ *
+ * The licence and distribution terms for any publically available version or
+ * derivative of this code cannot be changed. i.e. this code cannot simply be
+ * copied and put under another distribution licence
+ * [including the GNU Public Licence.]
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2006 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). */
+
+#include <openssl/bn.h>
+
+#include <assert.h>
+#include <string.h>
+
+#include <openssl/err.h>
+#include <openssl/mem.h>
+#include <openssl/thread.h>
+#include <openssl/type_check.h>
+
+#include "internal.h"
+#include "../../internal.h"
+
+
+#if !defined(OPENSSL_NO_ASM) && \
+ (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
+ defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
+#define OPENSSL_BN_ASM_MONT
+#endif
+
+
+BN_MONT_CTX *BN_MONT_CTX_new(void) {
+ BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
+
+ if (ret == NULL) {
+ return NULL;
+ }
+
+ OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX));
+ BN_init(&ret->RR);
+ BN_init(&ret->N);
+
+ return ret;
+}
+
+void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
+ if (mont == NULL) {
+ return;
+ }
+
+ BN_free(&mont->RR);
+ BN_free(&mont->N);
+ OPENSSL_free(mont);
+}
+
+BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
+ if (to == from) {
+ return to;
+ }
+
+ if (!BN_copy(&to->RR, &from->RR) ||
+ !BN_copy(&to->N, &from->N)) {
+ return NULL;
+ }
+ to->n0[0] = from->n0[0];
+ to->n0[1] = from->n0[1];
+ return to;
+}
+
+OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2,
+ BN_MONT_CTX_N0_LIMBS_VALUE_INVALID);
+OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS ==
+ sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch);
+
+int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
+ if (BN_is_zero(mod)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
+ return 0;
+ }
+ if (!BN_is_odd(mod)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return 0;
+ }
+ if (BN_is_negative(mod)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
+ return 0;
+ }
+
+ // Save the modulus.
+ if (!BN_copy(&mont->N, mod)) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
+ return 0;
+ }
+ // |mont->N| is always stored minimally. Computing RR efficiently leaks the
+ // size of the modulus. While the modulus may be private in RSA (one of the
+ // primes), their sizes are public, so this is fine.
+ bn_set_minimal_width(&mont->N);
+
+ // Find n0 such that n0 * N == -1 (mod r).
+ //
+ // Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the
+ // others, we could use a shorter R value and use faster |BN_ULONG|-based
+ // math instead of |uint64_t|-based math, which would be double-precision.
+ // However, currently only the assembler files know which is which.
+ uint64_t n0 = bn_mont_n0(&mont->N);
+ mont->n0[0] = (BN_ULONG)n0;
+#if BN_MONT_CTX_N0_LIMBS == 2
+ mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2);
+#else
+ mont->n0[1] = 0;
+#endif
+
+ BN_CTX *new_ctx = NULL;
+ if (ctx == NULL) {
+ new_ctx = BN_CTX_new();
+ if (new_ctx == NULL) {
+ return 0;
+ }
+ ctx = new_ctx;
+ }
+
+ // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R
+ // > mod. Even though the assembly on some 32-bit platforms works with 64-bit
+ // values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS *
+ // BN_BITS2|, is correct because R**2 will still be a multiple of the latter
+ // as |BN_MONT_CTX_N0_LIMBS| is either one or two.
+ unsigned lgBigR = mont->N.width * BN_BITS2;
+ int ok = bn_mod_exp_base_2_consttime(&mont->RR, lgBigR * 2, &mont->N, ctx);
+ BN_CTX_free(new_ctx);
+ return ok;
+}
+
+BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) {
+ BN_MONT_CTX *mont = BN_MONT_CTX_new();
+ if (mont == NULL ||
+ !BN_MONT_CTX_set(mont, mod, ctx)) {
+ BN_MONT_CTX_free(mont);
+ return NULL;
+ }
+ return mont;
+}
+
+int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
+ const BIGNUM *mod, BN_CTX *bn_ctx) {
+ CRYPTO_MUTEX_lock_read(lock);
+ BN_MONT_CTX *ctx = *pmont;
+ CRYPTO_MUTEX_unlock_read(lock);
+
+ if (ctx) {
+ return 1;
+ }
+
+ CRYPTO_MUTEX_lock_write(lock);
+ if (*pmont == NULL) {
+ *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx);
+ }
+ const int ok = *pmont != NULL;
+ CRYPTO_MUTEX_unlock_write(lock);
+ return ok;
+}
+
+int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
+ BN_CTX *ctx) {
+ return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
+}
+
+static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a,
+ size_t num_a, const BN_MONT_CTX *mont) {
+ const BN_ULONG *n = mont->N.d;
+ size_t num_n = mont->N.width;
+ if (num_r != num_n || num_a != 2 * num_n) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+
+ // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
+ // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
+ // includes |carry| which is stored separately.
+ BN_ULONG n0 = mont->n0[0];
+ BN_ULONG carry = 0;
+ for (size_t i = 0; i < num_n; i++) {
+ BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0);
+ v += carry + a[i + num_n];
+ carry |= (v != a[i + num_n]);
+ carry &= (v <= a[i + num_n]);
+ a[i + num_n] = v;
+ }
+
+ // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a|
+ // includes |carry| which is stored separately.
+ a += num_n;
+
+ // |a| thus requires at most one additional subtraction |n| to be reduced.
+ // Subtract |n| and select the answer in constant time.
+ OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
+ crypto_word_t_too_small);
+ BN_ULONG v = bn_sub_words(r, a, n, num_n) - carry;
+ // |v| is one if |a| - |n| underflowed or zero if it did not. Note |v| cannot
+ // be -1. That would imply the subtraction did not fit in |num_n| words, and
+ // we know at most one subtraction is needed.
+ v = 0u - v;
+ for (size_t i = 0; i < num_n; i++) {
+ r[i] = constant_time_select_w(v, a[i], r[i]);
+ a[i] = 0;
+ }
+ return 1;
+}
+
+static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
+ const BN_MONT_CTX *mont) {
+ if (r->neg) {
+ OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
+ return 0;
+ }
+
+ const BIGNUM *n = &mont->N;
+ if (n->width == 0) {
+ ret->width = 0;
+ return 1;
+ }
+
+ int max = 2 * n->width; // carry is stored separately
+ if (!bn_resize_words(r, max) ||
+ !bn_wexpand(ret, n->width)) {
+ return 0;
+ }
+
+ ret->width = n->width;
+ ret->neg = 0;
+ return bn_from_montgomery_in_place(ret->d, ret->width, r->d, r->width, mont);
+}
+
+int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont,
+ BN_CTX *ctx) {
+ int ret = 0;
+ BIGNUM *t;
+
+ BN_CTX_start(ctx);
+ t = BN_CTX_get(ctx);
+ if (t == NULL ||
+ !BN_copy(t, a)) {
+ goto err;
+ }
+
+ ret = BN_from_montgomery_word(r, t, mont);
+
+err:
+ BN_CTX_end(ctx);
+
+ return ret;
+}
+
+int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) {
+ // If the high bit of |n| is set, R = 2^(width*BN_BITS2) < 2 * |n|, so we
+ // compute R - |n| rather than perform Montgomery reduction.
+ const BIGNUM *n = &mont->N;
+ if (n->width > 0 && (n->d[n->width - 1] >> (BN_BITS2 - 1)) != 0) {
+ if (!bn_wexpand(r, n->width)) {
+ return 0;
+ }
+ r->d[0] = 0 - n->d[0];
+ for (int i = 1; i < n->width; i++) {
+ r->d[i] = ~n->d[i];
+ }
+ r->width = n->width;
+ r->neg = 0;
+ return 1;
+ }
+
+ return BN_from_montgomery(r, &mont->RR, mont, ctx);
+}
+
+static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
+ const BIGNUM *b,
+ const BN_MONT_CTX *mont,
+ BN_CTX *ctx) {
+ int ret = 0;
+
+ BN_CTX_start(ctx);
+ BIGNUM *tmp = BN_CTX_get(ctx);
+ if (tmp == NULL) {
+ goto err;
+ }
+
+ if (a == b) {
+ if (!bn_sqr_consttime(tmp, a, ctx)) {
+ goto err;
+ }
+ } else {
+ if (!bn_mul_consttime(tmp, a, b, ctx)) {
+ goto err;
+ }
+ }
+
+ // reduce from aRR to aR
+ if (!BN_from_montgomery_word(r, tmp, mont)) {
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ const BN_MONT_CTX *mont, BN_CTX *ctx) {
+ if (a->neg || b->neg) {
+ OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
+ return 0;
+ }
+
+#if defined(OPENSSL_BN_ASM_MONT)
+ // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
+ int num = mont->N.width;
+ if (num >= (128 / BN_BITS2) &&
+ a->width == num &&
+ b->width == num) {
+ if (!bn_wexpand(r, num)) {
+ return 0;
+ }
+ if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
+ // The check above ensures this won't happen.
+ assert(0);
+ OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
+ return 0;
+ }
+ r->neg = 0;
+ r->width = num;
+ return 1;
+ }
+#endif
+
+ return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
+}
+
+int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) {
+ return !BN_is_negative(bn) &&
+ bn_fits_in_words(bn, mont->N.width);
+}
+
+int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
+ size_t num_a, const BN_MONT_CTX *mont) {
+ return bn_mod_mul_montgomery_small(r, num_r, a, num_a, mont->RR.d,
+ mont->RR.width, mont);
+}
+
+int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
+ size_t num_a, const BN_MONT_CTX *mont) {
+ size_t num_n = mont->N.width;
+ if (num_a > 2 * num_n || num_r != num_n || num_n > BN_SMALL_MAX_WORDS) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+ BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2];
+ size_t num_tmp = 2 * num_n;
+ OPENSSL_memcpy(tmp, a, num_a * sizeof(BN_ULONG));
+ OPENSSL_memset(tmp + num_a, 0, (num_tmp - num_a) * sizeof(BN_ULONG));
+ int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont);
+ OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG));
+ return ret;
+}
+
+int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
+ const BN_MONT_CTX *mont) {
+ const BN_ULONG *n = mont->N.d;
+ size_t num_n = mont->N.width;
+ if (num_n == 0 || num_r != num_n) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+
+ // If the high bit of |n| is set, R = 2^(num_n*BN_BITS2) < 2 * |n|, so we
+ // compute R - |n| rather than perform Montgomery reduction.
+ if (num_n > 0 && (n[num_n - 1] >> (BN_BITS2 - 1)) != 0) {
+ r[0] = 0 - n[0];
+ for (size_t i = 1; i < num_n; i++) {
+ r[i] = ~n[i];
+ }
+ return 1;
+ }
+
+ return bn_from_montgomery_small(r, num_r, mont->RR.d, mont->RR.width, mont);
+}
+
+int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
+ size_t num_a, const BN_ULONG *b, size_t num_b,
+ const BN_MONT_CTX *mont) {
+ size_t num_n = mont->N.width;
+ if (num_r != num_n || num_a + num_b > 2 * num_n ||
+ num_n > BN_SMALL_MAX_WORDS) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+
+#if defined(OPENSSL_BN_ASM_MONT)
+ // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
+ if (num_n >= (128 / BN_BITS2) &&
+ num_a == num_n &&
+ num_b == num_n) {
+ if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num_n)) {
+ assert(0); // The check above ensures this won't happen.
+ OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
+ return 0;
+ }
+ return 1;
+ }
+#endif
+
+ // Compute the product.
+ BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
+ size_t num_tmp = 2 * num_n;
+ size_t num_ab = num_a + num_b;
+ if (a == b && num_a == num_b) {
+ if (!bn_sqr_small(tmp, num_ab, a, num_a)) {
+ return 0;
+ }
+ } else if (!bn_mul_small(tmp, num_ab, a, num_a, b, num_b)) {
+ return 0;
+ }
+
+ // Zero-extend to full width and reduce.
+ OPENSSL_memset(tmp + num_ab, 0, (num_tmp - num_ab) * sizeof(BN_ULONG));
+ int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont);
+ OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG));
+ return ret;
+}
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