--- /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) 1998-2005 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). */
+
+#include <openssl/bn.h>
+
+#include <assert.h>
+#include <string.h>
+
+#include <openssl/cpu.h>
+#include <openssl/err.h>
+#include <openssl/mem.h>
+
+#include "internal.h"
+
+
+#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64)
+#define OPENSSL_BN_ASM_MONT5
+#define RSAZ_ENABLED
+
+#include "rsaz_exp.h"
+
+void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap, const void *table,
+ const BN_ULONG *np, const BN_ULONG *n0, int num,
+ int power);
+void bn_scatter5(const BN_ULONG *inp, size_t num, void *table, size_t power);
+void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
+void bn_power5(BN_ULONG *rp, const BN_ULONG *ap, const void *table,
+ const BN_ULONG *np, const BN_ULONG *n0, int num, int power);
+int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
+ const BN_ULONG *not_used, const BN_ULONG *np,
+ const BN_ULONG *n0, int num);
+#endif
+
+int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) {
+ int i, bits, ret = 0;
+ BIGNUM *v, *rr;
+
+ BN_CTX_start(ctx);
+ if (r == a || r == p) {
+ rr = BN_CTX_get(ctx);
+ } else {
+ rr = r;
+ }
+
+ v = BN_CTX_get(ctx);
+ if (rr == NULL || v == NULL) {
+ goto err;
+ }
+
+ if (BN_copy(v, a) == NULL) {
+ goto err;
+ }
+ bits = BN_num_bits(p);
+
+ if (BN_is_odd(p)) {
+ if (BN_copy(rr, a) == NULL) {
+ goto err;
+ }
+ } else {
+ if (!BN_one(rr)) {
+ goto err;
+ }
+ }
+
+ for (i = 1; i < bits; i++) {
+ if (!BN_sqr(v, v, ctx)) {
+ goto err;
+ }
+ if (BN_is_bit_set(p, i)) {
+ if (!BN_mul(rr, rr, v, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ if (r != rr && !BN_copy(r, rr)) {
+ goto err;
+ }
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+typedef struct bn_recp_ctx_st {
+ BIGNUM N; // the divisor
+ BIGNUM Nr; // the reciprocal
+ int num_bits;
+ int shift;
+ int flags;
+} BN_RECP_CTX;
+
+static void BN_RECP_CTX_init(BN_RECP_CTX *recp) {
+ BN_init(&recp->N);
+ BN_init(&recp->Nr);
+ recp->num_bits = 0;
+ recp->shift = 0;
+ recp->flags = 0;
+}
+
+static void BN_RECP_CTX_free(BN_RECP_CTX *recp) {
+ if (recp == NULL) {
+ return;
+ }
+
+ BN_free(&recp->N);
+ BN_free(&recp->Nr);
+}
+
+static int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) {
+ if (!BN_copy(&(recp->N), d)) {
+ return 0;
+ }
+ BN_zero(&recp->Nr);
+ recp->num_bits = BN_num_bits(d);
+ recp->shift = 0;
+
+ return 1;
+}
+
+// len is the expected size of the result We actually calculate with an extra
+// word of precision, so we can do faster division if the remainder is not
+// required.
+// r := 2^len / m
+static int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) {
+ int ret = -1;
+ BIGNUM *t;
+
+ BN_CTX_start(ctx);
+ t = BN_CTX_get(ctx);
+ if (t == NULL) {
+ goto err;
+ }
+
+ if (!BN_set_bit(t, len)) {
+ goto err;
+ }
+
+ if (!BN_div(r, NULL, t, m, ctx)) {
+ goto err;
+ }
+
+ ret = len;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+static int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
+ BN_RECP_CTX *recp, BN_CTX *ctx) {
+ int i, j, ret = 0;
+ BIGNUM *a, *b, *d, *r;
+
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ b = BN_CTX_get(ctx);
+ if (dv != NULL) {
+ d = dv;
+ } else {
+ d = BN_CTX_get(ctx);
+ }
+
+ if (rem != NULL) {
+ r = rem;
+ } else {
+ r = BN_CTX_get(ctx);
+ }
+
+ if (a == NULL || b == NULL || d == NULL || r == NULL) {
+ goto err;
+ }
+
+ if (BN_ucmp(m, &recp->N) < 0) {
+ BN_zero(d);
+ if (!BN_copy(r, m)) {
+ goto err;
+ }
+ BN_CTX_end(ctx);
+ return 1;
+ }
+
+ // We want the remainder
+ // Given input of ABCDEF / ab
+ // we need multiply ABCDEF by 3 digests of the reciprocal of ab
+
+ // i := max(BN_num_bits(m), 2*BN_num_bits(N))
+ i = BN_num_bits(m);
+ j = recp->num_bits << 1;
+ if (j > i) {
+ i = j;
+ }
+
+ // Nr := round(2^i / N)
+ if (i != recp->shift) {
+ recp->shift =
+ BN_reciprocal(&(recp->Nr), &(recp->N), i,
+ ctx); // BN_reciprocal returns i, or -1 for an error
+ }
+
+ if (recp->shift == -1) {
+ goto err;
+ }
+
+ // d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i -
+ // BN_num_bits(N)))|
+ // = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i -
+ // BN_num_bits(N)))|
+ // <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
+ // = |m/N|
+ if (!BN_rshift(a, m, recp->num_bits)) {
+ goto err;
+ }
+ if (!BN_mul(b, a, &(recp->Nr), ctx)) {
+ goto err;
+ }
+ if (!BN_rshift(d, b, i - recp->num_bits)) {
+ goto err;
+ }
+ d->neg = 0;
+
+ if (!BN_mul(b, &(recp->N), d, ctx)) {
+ goto err;
+ }
+ if (!BN_usub(r, m, b)) {
+ goto err;
+ }
+ r->neg = 0;
+
+ j = 0;
+ while (BN_ucmp(r, &(recp->N)) >= 0) {
+ if (j++ > 2) {
+ OPENSSL_PUT_ERROR(BN, BN_R_BAD_RECIPROCAL);
+ goto err;
+ }
+ if (!BN_usub(r, r, &(recp->N))) {
+ goto err;
+ }
+ if (!BN_add_word(d, 1)) {
+ goto err;
+ }
+ }
+
+ r->neg = BN_is_zero(r) ? 0 : m->neg;
+ d->neg = m->neg ^ recp->N.neg;
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+static int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
+ BN_RECP_CTX *recp, BN_CTX *ctx) {
+ int ret = 0;
+ BIGNUM *a;
+ const BIGNUM *ca;
+
+ BN_CTX_start(ctx);
+ a = BN_CTX_get(ctx);
+ if (a == NULL) {
+ goto err;
+ }
+
+ if (y != NULL) {
+ if (x == y) {
+ if (!BN_sqr(a, x, ctx)) {
+ goto err;
+ }
+ } else {
+ if (!BN_mul(a, x, y, ctx)) {
+ goto err;
+ }
+ }
+ ca = a;
+ } else {
+ ca = x; // Just do the mod
+ }
+
+ ret = BN_div_recp(NULL, r, ca, recp, ctx);
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+// BN_window_bits_for_exponent_size returns sliding window size for mod_exp with
+// a |b| bit exponent.
+//
+// For window size 'w' (w >= 2) and a random 'b' bits exponent, the number of
+// multiplications is a constant plus on average
+//
+// 2^(w-1) + (b-w)/(w+1);
+//
+// here 2^(w-1) is for precomputing the table (we actually need entries only
+// for windows that have the lowest bit set), and (b-w)/(w+1) is an
+// approximation for the expected number of w-bit windows, not counting the
+// first one.
+//
+// Thus we should use
+//
+// w >= 6 if b > 671
+// w = 5 if 671 > b > 239
+// w = 4 if 239 > b > 79
+// w = 3 if 79 > b > 23
+// w <= 2 if 23 > b
+//
+// (with draws in between). Very small exponents are often selected
+// with low Hamming weight, so we use w = 1 for b <= 23.
+static int BN_window_bits_for_exponent_size(int b) {
+ if (b > 671) {
+ return 6;
+ }
+ if (b > 239) {
+ return 5;
+ }
+ if (b > 79) {
+ return 4;
+ }
+ if (b > 23) {
+ return 3;
+ }
+ return 1;
+}
+
+// TABLE_SIZE is the maximum precomputation table size for *variable* sliding
+// windows. This must be 2^(max_window - 1), where max_window is the largest
+// value returned from |BN_window_bits_for_exponent_size|.
+#define TABLE_SIZE 32
+
+// TABLE_BITS_SMALL is the smallest value returned from
+// |BN_window_bits_for_exponent_size| when |b| is at most |BN_BITS2| *
+// |BN_SMALL_MAX_WORDS| words.
+#define TABLE_BITS_SMALL 5
+
+// TABLE_SIZE_SMALL is the same as |TABLE_SIZE|, but when |b| is at most
+// |BN_BITS2| * |BN_SMALL_MAX_WORDS|.
+#define TABLE_SIZE_SMALL (1 << (TABLE_BITS_SMALL - 1))
+
+static int mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx) {
+ int i, j, bits, ret = 0, wstart, window;
+ int start = 1;
+ BIGNUM *aa;
+ // Table of variables obtained from 'ctx'
+ BIGNUM *val[TABLE_SIZE];
+ BN_RECP_CTX recp;
+
+ bits = BN_num_bits(p);
+
+ if (bits == 0) {
+ // x**0 mod 1 is still zero.
+ if (BN_is_one(m)) {
+ BN_zero(r);
+ return 1;
+ }
+ return BN_one(r);
+ }
+
+ BN_CTX_start(ctx);
+ aa = BN_CTX_get(ctx);
+ val[0] = BN_CTX_get(ctx);
+ if (!aa || !val[0]) {
+ goto err;
+ }
+
+ BN_RECP_CTX_init(&recp);
+ if (m->neg) {
+ // ignore sign of 'm'
+ if (!BN_copy(aa, m)) {
+ goto err;
+ }
+ aa->neg = 0;
+ if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0) {
+ goto err;
+ }
+ } else {
+ if (BN_RECP_CTX_set(&recp, m, ctx) <= 0) {
+ goto err;
+ }
+ }
+
+ if (!BN_nnmod(val[0], a, m, ctx)) {
+ goto err; // 1
+ }
+ if (BN_is_zero(val[0])) {
+ BN_zero(r);
+ ret = 1;
+ goto err;
+ }
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1) {
+ if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx)) {
+ goto err; // 2
+ }
+ j = 1 << (window - 1);
+ for (i = 1; i < j; i++) {
+ if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
+ !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ start = 1; // This is used to avoid multiplication etc
+ // when there is only the value '1' in the
+ // buffer.
+ wstart = bits - 1; // The top bit of the window
+
+ if (!BN_one(r)) {
+ goto err;
+ }
+
+ for (;;) {
+ int wvalue; // The 'value' of the window
+ int wend; // The bottom bit of the window
+
+ if (!BN_is_bit_set(p, wstart)) {
+ if (!start) {
+ if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) {
+ goto err;
+ }
+ }
+ if (wstart == 0) {
+ break;
+ }
+ wstart--;
+ continue;
+ }
+
+ // We now have wstart on a 'set' bit, we now need to work out
+ // how bit a window to do. To do this we need to scan
+ // forward until the last set bit before the end of the
+ // window
+ wvalue = 1;
+ wend = 0;
+ for (i = 1; i < window; i++) {
+ if (wstart - i < 0) {
+ break;
+ }
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wend);
+ wvalue |= 1;
+ wend = i;
+ }
+ }
+
+ // wend is the size of the current window
+ j = wend + 1;
+ // add the 'bytes above'
+ if (!start) {
+ for (i = 0; i < j; i++) {
+ if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ // wvalue will be an odd number < 2^window
+ if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx)) {
+ goto err;
+ }
+
+ // move the 'window' down further
+ wstart -= wend + 1;
+ start = 0;
+ if (wstart < 0) {
+ break;
+ }
+ }
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ BN_RECP_CTX_free(&recp);
+ return ret;
+}
+
+int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
+ BN_CTX *ctx) {
+ if (BN_is_odd(m)) {
+ return BN_mod_exp_mont(r, a, p, m, ctx, NULL);
+ }
+
+ return mod_exp_recp(r, a, p, m, ctx);
+}
+
+int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx, const BN_MONT_CTX *mont) {
+ if (!BN_is_odd(m)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return 0;
+ }
+ int bits = BN_num_bits(p);
+ if (bits == 0) {
+ // x**0 mod 1 is still zero.
+ if (BN_is_one(m)) {
+ BN_zero(rr);
+ return 1;
+ }
+ return BN_one(rr);
+ }
+
+ int ret = 0;
+ BIGNUM *val[TABLE_SIZE];
+ BN_MONT_CTX *new_mont = NULL;
+
+ BN_CTX_start(ctx);
+ BIGNUM *d = BN_CTX_get(ctx);
+ BIGNUM *r = BN_CTX_get(ctx);
+ val[0] = BN_CTX_get(ctx);
+ if (!d || !r || !val[0]) {
+ goto err;
+ }
+
+ // Allocate a montgomery context if it was not supplied by the caller.
+ if (mont == NULL) {
+ new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
+ if (new_mont == NULL) {
+ goto err;
+ }
+ mont = new_mont;
+ }
+
+ const BIGNUM *aa;
+ if (a->neg || BN_ucmp(a, m) >= 0) {
+ if (!BN_nnmod(val[0], a, m, ctx)) {
+ goto err;
+ }
+ aa = val[0];
+ } else {
+ aa = a;
+ }
+
+ if (BN_is_zero(aa)) {
+ BN_zero(rr);
+ ret = 1;
+ goto err;
+ }
+
+ // We exponentiate by looking at sliding windows of the exponent and
+ // precomputing powers of |aa|. Windows may be shifted so they always end on a
+ // set bit, so only precompute odd powers. We compute val[i] = aa^(2*i + 1)
+ // for i = 0 to 2^(window-1), all in Montgomery form.
+ int window = BN_window_bits_for_exponent_size(bits);
+ if (!BN_to_montgomery(val[0], aa, mont, ctx)) {
+ goto err;
+ }
+ if (window > 1) {
+ if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx)) {
+ goto err;
+ }
+ for (int i = 1; i < 1 << (window - 1); i++) {
+ val[i] = BN_CTX_get(ctx);
+ if (val[i] == NULL ||
+ !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ if (!bn_one_to_montgomery(r, mont, ctx)) {
+ goto err;
+ }
+
+ int r_is_one = 1;
+ int wstart = bits - 1; // The top bit of the window.
+ for (;;) {
+ if (!BN_is_bit_set(p, wstart)) {
+ if (!r_is_one && !BN_mod_mul_montgomery(r, r, r, mont, ctx)) {
+ goto err;
+ }
+ if (wstart == 0) {
+ break;
+ }
+ wstart--;
+ continue;
+ }
+
+ // We now have wstart on a set bit. Find the largest window we can use.
+ int wvalue = 1;
+ int wsize = 0;
+ for (int i = 1; i < window && i <= wstart; i++) {
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wsize);
+ wvalue |= 1;
+ wsize = i;
+ }
+ }
+
+ // Shift |r| to the end of the window.
+ if (!r_is_one) {
+ for (int i = 0; i < wsize + 1; i++) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ assert(wvalue & 1);
+ assert(wvalue < (1 << window));
+ if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx)) {
+ goto err;
+ }
+
+ r_is_one = 0;
+ if (wstart == wsize) {
+ break;
+ }
+ wstart -= wsize + 1;
+ }
+
+ if (!BN_from_montgomery(rr, r, mont, ctx)) {
+ goto err;
+ }
+ ret = 1;
+
+err:
+ BN_MONT_CTX_free(new_mont);
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int bn_mod_exp_mont_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
+ size_t num_a, const BN_ULONG *p, size_t num_p,
+ const BN_MONT_CTX *mont) {
+ size_t num_n = mont->N.width;
+ if (num_n != num_a || num_n != num_r || num_n > BN_SMALL_MAX_WORDS) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+ if (!BN_is_odd(&mont->N)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return 0;
+ }
+ unsigned bits = 0;
+ if (num_p != 0) {
+ bits = BN_num_bits_word(p[num_p - 1]) + (num_p - 1) * BN_BITS2;
+ }
+ if (bits == 0) {
+ OPENSSL_memset(r, 0, num_r * sizeof(BN_ULONG));
+ if (!BN_is_one(&mont->N)) {
+ r[0] = 1;
+ }
+ return 1;
+ }
+
+ // We exponentiate by looking at sliding windows of the exponent and
+ // precomputing powers of |a|. Windows may be shifted so they always end on a
+ // set bit, so only precompute odd powers. We compute val[i] = a^(2*i + 1) for
+ // i = 0 to 2^(window-1), all in Montgomery form.
+ unsigned window = BN_window_bits_for_exponent_size(bits);
+ if (window > TABLE_BITS_SMALL) {
+ window = TABLE_BITS_SMALL; // Tolerate excessively large |p|.
+ }
+ int ret = 0;
+ BN_ULONG val[TABLE_SIZE_SMALL][BN_SMALL_MAX_WORDS];
+ OPENSSL_memcpy(val[0], a, num_n * sizeof(BN_ULONG));
+ if (window > 1) {
+ BN_ULONG d[BN_SMALL_MAX_WORDS];
+ if (!bn_mod_mul_montgomery_small(d, num_n, val[0], num_n, val[0], num_n,
+ mont)) {
+ goto err;
+ }
+ for (unsigned i = 1; i < 1u << (window - 1); i++) {
+ if (!bn_mod_mul_montgomery_small(val[i], num_n, val[i - 1], num_n, d,
+ num_n, mont)) {
+ goto err;
+ }
+ }
+ }
+
+ if (!bn_one_to_montgomery_small(r, num_r, mont)) {
+ goto err;
+ }
+
+ int r_is_one = 1;
+ unsigned wstart = bits - 1; // The top bit of the window.
+ for (;;) {
+ if (!bn_is_bit_set_words(p, num_p, wstart)) {
+ if (!r_is_one &&
+ !bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) {
+ goto err;
+ }
+ if (wstart == 0) {
+ break;
+ }
+ wstart--;
+ continue;
+ }
+
+ // We now have wstart on a set bit. Find the largest window we can use.
+ unsigned wvalue = 1;
+ unsigned wsize = 0;
+ for (unsigned i = 1; i < window && i <= wstart; i++) {
+ if (bn_is_bit_set_words(p, num_p, wstart - i)) {
+ wvalue <<= (i - wsize);
+ wvalue |= 1;
+ wsize = i;
+ }
+ }
+
+ // Shift |r| to the end of the window.
+ if (!r_is_one) {
+ for (unsigned i = 0; i < wsize + 1; i++) {
+ if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, r, num_r, mont)) {
+ goto err;
+ }
+ }
+ }
+
+ assert(wvalue & 1);
+ assert(wvalue < (1u << window));
+ if (!bn_mod_mul_montgomery_small(r, num_r, r, num_r, val[wvalue >> 1],
+ num_n, mont)) {
+ goto err;
+ }
+
+ r_is_one = 0;
+ if (wstart == wsize) {
+ break;
+ }
+ wstart -= wsize + 1;
+ }
+
+ ret = 1;
+
+err:
+ OPENSSL_cleanse(val, sizeof(val));
+ return ret;
+}
+
+int bn_mod_inverse_prime_mont_small(BN_ULONG *r, size_t num_r,
+ const BN_ULONG *a, size_t num_a,
+ const BN_MONT_CTX *mont) {
+ const BN_ULONG *p = mont->N.d;
+ size_t num_p = mont->N.width;
+ if (num_p > BN_SMALL_MAX_WORDS || num_p == 0) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return 0;
+ }
+
+ // Per Fermat's Little Theorem, a^-1 = a^(p-2) (mod p) for p prime.
+ BN_ULONG p_minus_two[BN_SMALL_MAX_WORDS];
+ OPENSSL_memcpy(p_minus_two, p, num_p * sizeof(BN_ULONG));
+ if (p_minus_two[0] >= 2) {
+ p_minus_two[0] -= 2;
+ } else {
+ p_minus_two[0] -= 2;
+ for (size_t i = 1; i < num_p; i++) {
+ if (p_minus_two[i]-- != 0) {
+ break;
+ }
+ }
+ }
+
+ return bn_mod_exp_mont_small(r, num_r, a, num_a, p_minus_two, num_p, mont);
+}
+
+
+// |BN_mod_exp_mont_consttime| stores the precomputed powers in a specific
+// layout so that accessing any of these table values shows the same access
+// pattern as far as cache lines are concerned. The following functions are
+// used to transfer a BIGNUM from/to that table.
+
+static void copy_to_prebuf(const BIGNUM *b, int top, unsigned char *buf,
+ int idx, int window) {
+ int i, j;
+ const int width = 1 << window;
+ BN_ULONG *table = (BN_ULONG *) buf;
+
+ if (top > b->width) {
+ top = b->width; // this works because 'buf' is explicitly zeroed
+ }
+
+ for (i = 0, j = idx; i < top; i++, j += width) {
+ table[j] = b->d[i];
+ }
+}
+
+static int copy_from_prebuf(BIGNUM *b, int top, unsigned char *buf, int idx,
+ int window) {
+ int i, j;
+ const int width = 1 << window;
+ volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
+
+ if (!bn_wexpand(b, top)) {
+ return 0;
+ }
+
+ if (window <= 3) {
+ for (i = 0; i < top; i++, table += width) {
+ BN_ULONG acc = 0;
+
+ for (j = 0; j < width; j++) {
+ acc |= table[j] & ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
+ }
+
+ b->d[i] = acc;
+ }
+ } else {
+ int xstride = 1 << (window - 2);
+ BN_ULONG y0, y1, y2, y3;
+
+ i = idx >> (window - 2); // equivalent of idx / xstride
+ idx &= xstride - 1; // equivalent of idx % xstride
+
+ y0 = (BN_ULONG)0 - (constant_time_eq_int(i, 0) & 1);
+ y1 = (BN_ULONG)0 - (constant_time_eq_int(i, 1) & 1);
+ y2 = (BN_ULONG)0 - (constant_time_eq_int(i, 2) & 1);
+ y3 = (BN_ULONG)0 - (constant_time_eq_int(i, 3) & 1);
+
+ for (i = 0; i < top; i++, table += width) {
+ BN_ULONG acc = 0;
+
+ for (j = 0; j < xstride; j++) {
+ acc |= ((table[j + 0 * xstride] & y0) | (table[j + 1 * xstride] & y1) |
+ (table[j + 2 * xstride] & y2) | (table[j + 3 * xstride] & y3)) &
+ ((BN_ULONG)0 - (constant_time_eq_int(j, idx) & 1));
+ }
+
+ b->d[i] = acc;
+ }
+ }
+
+ b->width = top;
+ return 1;
+}
+
+// BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
+// line width of the target processor is at least the following value.
+#define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH (64)
+#define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK \
+ (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
+
+// Window sizes optimized for fixed window size modular exponentiation
+// algorithm (BN_mod_exp_mont_consttime).
+//
+// To achieve the security goals of BN_mode_exp_mont_consttime, the maximum
+// size of the window must not exceed
+// log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH).
+//
+// Window size thresholds are defined for cache line sizes of 32 and 64, cache
+// line sizes where log_2(32)=5 and log_2(64)=6 respectively. A window size of
+// 7 should only be used on processors that have a 128 byte or greater cache
+// line size.
+#if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
+
+#define BN_window_bits_for_ctime_exponent_size(b) \
+ ((b) > 937 ? 6 : (b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1)
+#define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
+
+#elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
+
+#define BN_window_bits_for_ctime_exponent_size(b) \
+ ((b) > 306 ? 5 : (b) > 89 ? 4 : (b) > 22 ? 3 : 1)
+#define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
+
+#endif
+
+// Given a pointer value, compute the next address that is a cache line
+// multiple.
+#define MOD_EXP_CTIME_ALIGN(x_) \
+ ((unsigned char *)(x_) + \
+ (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - \
+ (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
+
+// This variant of BN_mod_exp_mont() uses fixed windows and the special
+// precomputation memory layout to limit data-dependency to a minimum
+// to protect secret exponents (cf. the hyper-threading timing attacks
+// pointed out by Colin Percival,
+// http://www.daemonology.net/hyperthreading-considered-harmful/)
+int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx,
+ const BN_MONT_CTX *mont) {
+ int i, ret = 0, window, wvalue;
+ BN_MONT_CTX *new_mont = NULL;
+
+ int numPowers;
+ unsigned char *powerbufFree = NULL;
+ int powerbufLen = 0;
+ unsigned char *powerbuf = NULL;
+ BIGNUM tmp, am;
+ BIGNUM *new_a = NULL;
+
+ if (!BN_is_odd(m)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return 0;
+ }
+
+ // Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
+ // whether the top bits are zero.
+ int max_bits = p->width * BN_BITS2;
+ int bits = max_bits;
+ if (bits == 0) {
+ // x**0 mod 1 is still zero.
+ if (BN_is_one(m)) {
+ BN_zero(rr);
+ return 1;
+ }
+ return BN_one(rr);
+ }
+
+ // Allocate a montgomery context if it was not supplied by the caller.
+ if (mont == NULL) {
+ new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
+ if (new_mont == NULL) {
+ goto err;
+ }
+ mont = new_mont;
+ }
+
+ // Use the width in |mont->N|, rather than the copy in |m|. The assembly
+ // implementation assumes it can use |top| to size R.
+ int top = mont->N.width;
+
+ if (a->neg || BN_ucmp(a, m) >= 0) {
+ new_a = BN_new();
+ if (new_a == NULL ||
+ !BN_nnmod(new_a, a, m, ctx)) {
+ goto err;
+ }
+ a = new_a;
+ }
+
+#ifdef RSAZ_ENABLED
+ // If the size of the operands allow it, perform the optimized
+ // RSAZ exponentiation. For further information see
+ // crypto/bn/rsaz_exp.c and accompanying assembly modules.
+ if ((16 == a->width) && (16 == p->width) && (BN_num_bits(m) == 1024) &&
+ rsaz_avx2_eligible()) {
+ if (!bn_wexpand(rr, 16)) {
+ goto err;
+ }
+ RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d, mont->n0[0]);
+ rr->width = 16;
+ rr->neg = 0;
+ ret = 1;
+ goto err;
+ }
+#endif
+
+ // Get the window size to use with size of p.
+ window = BN_window_bits_for_ctime_exponent_size(bits);
+#if defined(OPENSSL_BN_ASM_MONT5)
+ if (window >= 5) {
+ window = 5; // ~5% improvement for RSA2048 sign, and even for RSA4096
+ // reserve space for mont->N.d[] copy
+ powerbufLen += top * sizeof(mont->N.d[0]);
+ }
+#endif
+
+ // Allocate a buffer large enough to hold all of the pre-computed
+ // powers of am, am itself and tmp.
+ numPowers = 1 << window;
+ powerbufLen +=
+ sizeof(m->d[0]) *
+ (top * numPowers + ((2 * top) > numPowers ? (2 * top) : numPowers));
+#ifdef alloca
+ if (powerbufLen < 3072) {
+ powerbufFree = alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
+ } else
+#endif
+ {
+ if ((powerbufFree = OPENSSL_malloc(
+ powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) {
+ goto err;
+ }
+ }
+
+ powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
+ OPENSSL_memset(powerbuf, 0, powerbufLen);
+
+#ifdef alloca
+ if (powerbufLen < 3072) {
+ powerbufFree = NULL;
+ }
+#endif
+
+ // lay down tmp and am right after powers table
+ tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
+ am.d = tmp.d + top;
+ tmp.width = am.width = 0;
+ tmp.dmax = am.dmax = top;
+ tmp.neg = am.neg = 0;
+ tmp.flags = am.flags = BN_FLG_STATIC_DATA;
+
+ if (!bn_one_to_montgomery(&tmp, mont, ctx)) {
+ goto err;
+ }
+
+ // prepare a^1 in Montgomery domain
+ assert(!a->neg);
+ assert(BN_ucmp(a, m) < 0);
+ if (!BN_to_montgomery(&am, a, mont, ctx)) {
+ goto err;
+ }
+
+#if defined(OPENSSL_BN_ASM_MONT5)
+ // This optimization uses ideas from http://eprint.iacr.org/2011/239,
+ // specifically optimization of cache-timing attack countermeasures
+ // and pre-computation optimization.
+
+ // Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
+ // 512-bit RSA is hardly relevant, we omit it to spare size...
+ if (window == 5 && top > 1) {
+ const BN_ULONG *n0 = mont->n0;
+ BN_ULONG *np;
+
+ // BN_to_montgomery can contaminate words above .top
+ // [in BN_DEBUG[_DEBUG] build]...
+ for (i = am.width; i < top; i++) {
+ am.d[i] = 0;
+ }
+ for (i = tmp.width; i < top; i++) {
+ tmp.d[i] = 0;
+ }
+
+ // copy mont->N.d[] to improve cache locality
+ for (np = am.d + top, i = 0; i < top; i++) {
+ np[i] = mont->N.d[i];
+ }
+
+ bn_scatter5(tmp.d, top, powerbuf, 0);
+ bn_scatter5(am.d, am.width, powerbuf, 1);
+ bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, 2);
+
+ // same as above, but uses squaring for 1/2 of operations
+ for (i = 4; i < 32; i *= 2) {
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ }
+ for (i = 3; i < 8; i += 2) {
+ int j;
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ for (j = 2 * i; j < 32; j *= 2) {
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, j);
+ }
+ }
+ for (; i < 16; i += 2) {
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, 2 * i);
+ }
+ for (; i < 32; i += 2) {
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ }
+
+ bits--;
+ for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--) {
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+ bn_gather5(tmp.d, top, powerbuf, wvalue);
+
+ // At this point |bits| is 4 mod 5 and at least -1. (|bits| is the first bit
+ // that has not been read yet.)
+ assert(bits >= -1 && (bits == -1 || bits % 5 == 4));
+
+ // Scan the exponent one window at a time starting from the most
+ // significant bits.
+ if (top & 7) {
+ while (bits >= 0) {
+ for (wvalue = 0, i = 0; i < 5; i++, bits--) {
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
+ }
+ } else {
+ const uint8_t *p_bytes = (const uint8_t *)p->d;
+ assert(bits < max_bits);
+ // |p = 0| has been handled as a special case, so |max_bits| is at least
+ // one word.
+ assert(max_bits >= 64);
+
+ // If the first bit to be read lands in the last byte, unroll the first
+ // iteration to avoid reading past the bounds of |p->d|. (After the first
+ // iteration, we are guaranteed to be past the last byte.) Note |bits|
+ // here is the top bit, inclusive.
+ if (bits - 4 >= max_bits - 8) {
+ // Read five bits from |bits-4| through |bits|, inclusive.
+ wvalue = p_bytes[p->width * BN_BYTES - 1];
+ wvalue >>= (bits - 4) & 7;
+ wvalue &= 0x1f;
+ bits -= 5;
+ bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
+ }
+ while (bits >= 0) {
+ // Read five bits from |bits-4| through |bits|, inclusive.
+ int first_bit = bits - 4;
+ uint16_t val;
+ OPENSSL_memcpy(&val, p_bytes + (first_bit >> 3), sizeof(val));
+ val >>= first_bit & 7;
+ val &= 0x1f;
+ bits -= 5;
+ bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, val);
+ }
+ }
+
+ ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
+ tmp.width = top;
+ if (ret) {
+ if (!BN_copy(rr, &tmp)) {
+ ret = 0;
+ }
+ goto err; // non-zero ret means it's not error
+ }
+ } else
+#endif
+ {
+ copy_to_prebuf(&tmp, top, powerbuf, 0, window);
+ copy_to_prebuf(&am, top, powerbuf, 1, window);
+
+ // If the window size is greater than 1, then calculate
+ // val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
+ // (even powers could instead be computed as (a^(i/2))^2
+ // to use the slight performance advantage of sqr over mul).
+ if (window > 1) {
+ if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx)) {
+ goto err;
+ }
+
+ copy_to_prebuf(&tmp, top, powerbuf, 2, window);
+
+ for (i = 3; i < numPowers; i++) {
+ // Calculate a^i = a^(i-1) * a
+ if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx)) {
+ goto err;
+ }
+
+ copy_to_prebuf(&tmp, top, powerbuf, i, window);
+ }
+ }
+
+ bits--;
+ for (wvalue = 0, i = bits % window; i >= 0; i--, bits--) {
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+ if (!copy_from_prebuf(&tmp, top, powerbuf, wvalue, window)) {
+ goto err;
+ }
+
+ // Scan the exponent one window at a time starting from the most
+ // significant bits.
+ while (bits >= 0) {
+ wvalue = 0; // The 'value' of the window
+
+ // Scan the window, squaring the result as we go
+ for (i = 0; i < window; i++, bits--) {
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx)) {
+ goto err;
+ }
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+
+ // Fetch the appropriate pre-computed value from the pre-buf
+ if (!copy_from_prebuf(&am, top, powerbuf, wvalue, window)) {
+ goto err;
+ }
+
+ // Multiply the result into the intermediate result
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx)) {
+ goto err;
+ }
+ }
+ }
+
+ // Convert the final result from montgomery to standard format
+ if (!BN_from_montgomery(rr, &tmp, mont, ctx)) {
+ goto err;
+ }
+ ret = 1;
+
+err:
+ BN_MONT_CTX_free(new_mont);
+ BN_clear_free(new_a);
+ OPENSSL_free(powerbufFree);
+ return (ret);
+}
+
+int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
+ const BIGNUM *m, BN_CTX *ctx,
+ const BN_MONT_CTX *mont) {
+ BIGNUM a_bignum;
+ BN_init(&a_bignum);
+
+ int ret = 0;
+
+ if (!BN_set_word(&a_bignum, a)) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ ret = BN_mod_exp_mont(rr, &a_bignum, p, m, ctx, mont);
+
+err:
+ BN_free(&a_bignum);
+
+ return ret;
+}
+
+#define TABLE_SIZE 32
+
+int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
+ const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
+ BN_CTX *ctx, const BN_MONT_CTX *mont) {
+ BIGNUM tmp;
+ BN_init(&tmp);
+
+ int ret = 0;
+ BN_MONT_CTX *new_mont = NULL;
+
+ // Allocate a montgomery context if it was not supplied by the caller.
+ if (mont == NULL) {
+ new_mont = BN_MONT_CTX_new_for_modulus(m, ctx);
+ if (new_mont == NULL) {
+ goto err;
+ }
+ mont = new_mont;
+ }
+
+ // BN_mod_mul_montgomery removes one Montgomery factor, so passing one
+ // Montgomery-encoded and one non-Montgomery-encoded value gives a
+ // non-Montgomery-encoded result.
+ if (!BN_mod_exp_mont(rr, a1, p1, m, ctx, mont) ||
+ !BN_mod_exp_mont(&tmp, a2, p2, m, ctx, mont) ||
+ !BN_to_montgomery(rr, rr, mont, ctx) ||
+ !BN_mod_mul_montgomery(rr, rr, &tmp, mont, ctx)) {
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ BN_MONT_CTX_free(new_mont);
+ BN_free(&tmp);
+
+ return ret;
+}
git://repos.xcallymotion.com / motion2.git / blobdiff