--- /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) 1998-2001 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 <openssl/err.h>
+
+#include "internal.h"
+
+
+static BN_ULONG word_is_odd_mask(BN_ULONG a) { return (BN_ULONG)0 - (a & 1); }
+
+static void maybe_rshift1_words(BN_ULONG *a, BN_ULONG mask, BN_ULONG *tmp,
+ size_t num) {
+ bn_rshift1_words(tmp, a, num);
+ bn_select_words(a, mask, tmp, a, num);
+}
+
+static void maybe_rshift1_words_carry(BN_ULONG *a, BN_ULONG carry,
+ BN_ULONG mask, BN_ULONG *tmp,
+ size_t num) {
+ maybe_rshift1_words(a, mask, tmp, num);
+ if (num != 0) {
+ carry &= mask;
+ a[num - 1] |= carry << (BN_BITS2-1);
+ }
+}
+
+static BN_ULONG maybe_add_words(BN_ULONG *a, BN_ULONG mask, const BN_ULONG *b,
+ BN_ULONG *tmp, size_t num) {
+ BN_ULONG carry = bn_add_words(tmp, a, b, num);
+ bn_select_words(a, mask, tmp, a, num);
+ return carry & mask;
+}
+
+static int bn_gcd_consttime(BIGNUM *r, unsigned *out_shift, const BIGNUM *x,
+ const BIGNUM *y, BN_CTX *ctx) {
+ size_t width = x->width > y->width ? x->width : y->width;
+ if (width == 0) {
+ *out_shift = 0;
+ BN_zero(r);
+ return 1;
+ }
+
+ // This is a constant-time implementation of Stein's algorithm (binary GCD).
+ int ret = 0;
+ BN_CTX_start(ctx);
+ BIGNUM *u = BN_CTX_get(ctx);
+ BIGNUM *v = BN_CTX_get(ctx);
+ BIGNUM *tmp = BN_CTX_get(ctx);
+ if (u == NULL || v == NULL || tmp == NULL ||
+ !BN_copy(u, x) ||
+ !BN_copy(v, y) ||
+ !bn_resize_words(u, width) ||
+ !bn_resize_words(v, width) ||
+ !bn_resize_words(tmp, width)) {
+ goto err;
+ }
+
+ // Each loop iteration halves at least one of |u| and |v|. Thus we need at
+ // most the combined bit width of inputs for at least one value to be zero.
+ unsigned x_bits = x->width * BN_BITS2, y_bits = y->width * BN_BITS2;
+ unsigned num_iters = x_bits + y_bits;
+ if (num_iters < x_bits) {
+ OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
+ goto err;
+ }
+
+ unsigned shift = 0;
+ for (unsigned i = 0; i < num_iters; i++) {
+ BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
+
+ // If both |u| and |v| are odd, subtract the smaller from the larger.
+ BN_ULONG u_less_than_v =
+ (BN_ULONG)0 - bn_sub_words(tmp->d, u->d, v->d, width);
+ bn_select_words(u->d, both_odd & ~u_less_than_v, tmp->d, u->d, width);
+ bn_sub_words(tmp->d, v->d, u->d, width);
+ bn_select_words(v->d, both_odd & u_less_than_v, tmp->d, v->d, width);
+
+ // At least one of |u| and |v| is now even.
+ BN_ULONG u_is_odd = word_is_odd_mask(u->d[0]);
+ BN_ULONG v_is_odd = word_is_odd_mask(v->d[0]);
+ assert(!(u_is_odd & v_is_odd));
+
+ // If both are even, the final GCD gains a factor of two.
+ shift += 1 & (~u_is_odd & ~v_is_odd);
+
+ // Halve any which are even.
+ maybe_rshift1_words(u->d, ~u_is_odd, tmp->d, width);
+ maybe_rshift1_words(v->d, ~v_is_odd, tmp->d, width);
+ }
+
+ // One of |u| or |v| is zero at this point. The algorithm usually makes |u|
+ // zero, unless |y| was already zero on input. Fix this by combining the
+ // values.
+ assert(BN_is_zero(u) || BN_is_zero(v));
+ for (size_t i = 0; i < width; i++) {
+ v->d[i] |= u->d[i];
+ }
+
+ *out_shift = shift;
+ ret = bn_set_words(r, v->d, width);
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int BN_gcd(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) {
+ unsigned shift;
+ return bn_gcd_consttime(r, &shift, x, y, ctx) &&
+ BN_lshift(r, r, shift);
+}
+
+int bn_is_relatively_prime(int *out_relatively_prime, const BIGNUM *x,
+ const BIGNUM *y, BN_CTX *ctx) {
+ int ret = 0;
+ BN_CTX_start(ctx);
+ unsigned shift;
+ BIGNUM *gcd = BN_CTX_get(ctx);
+ if (gcd == NULL ||
+ !bn_gcd_consttime(gcd, &shift, x, y, ctx)) {
+ goto err;
+ }
+
+ // Check that 2^|shift| * |gcd| is one.
+ if (gcd->width == 0) {
+ *out_relatively_prime = 0;
+ } else {
+ BN_ULONG mask = shift | (gcd->d[0] ^ 1);
+ for (int i = 1; i < gcd->width; i++) {
+ mask |= gcd->d[i];
+ }
+ *out_relatively_prime = mask == 0;
+ }
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
+ BN_CTX_start(ctx);
+ unsigned shift;
+ BIGNUM *gcd = BN_CTX_get(ctx);
+ int ret = gcd != NULL &&
+ bn_mul_consttime(r, a, b, ctx) &&
+ bn_gcd_consttime(gcd, &shift, a, b, ctx) &&
+ bn_div_consttime(r, NULL, r, gcd, ctx) &&
+ bn_rshift_secret_shift(r, r, shift, ctx);
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, const BIGNUM *a,
+ const BIGNUM *n, BN_CTX *ctx) {
+ *out_no_inverse = 0;
+ if (BN_is_negative(a) || BN_ucmp(a, n) >= 0) {
+ OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
+ return 0;
+ }
+ if (BN_is_zero(a)) {
+ if (BN_is_one(n)) {
+ BN_zero(r);
+ return 1;
+ }
+ *out_no_inverse = 1;
+ OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
+ return 0;
+ }
+
+ // This is a constant-time implementation of the extended binary GCD
+ // algorithm. It is adapted from the Handbook of Applied Cryptography, section
+ // 14.4.3, algorithm 14.51, and modified to bound coefficients and avoid
+ // negative numbers.
+ //
+ // For more details and proof of correctness, see
+ // https://github.com/mit-plv/fiat-crypto/pull/333. In particular, see |step|
+ // and |mod_inverse_consttime| for the algorithm in Gallina and see
+ // |mod_inverse_consttime_spec| for the correctness result.
+
+ if (!BN_is_odd(a) && !BN_is_odd(n)) {
+ *out_no_inverse = 1;
+ OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
+ return 0;
+ }
+
+ // This function exists to compute the RSA private exponent, where |a| is one
+ // word. We'll thus use |a_width| when available.
+ size_t n_width = n->width, a_width = a->width;
+ if (a_width > n_width) {
+ a_width = n_width;
+ }
+
+ int ret = 0;
+ BN_CTX_start(ctx);
+ BIGNUM *u = BN_CTX_get(ctx);
+ BIGNUM *v = BN_CTX_get(ctx);
+ BIGNUM *A = BN_CTX_get(ctx);
+ BIGNUM *B = BN_CTX_get(ctx);
+ BIGNUM *C = BN_CTX_get(ctx);
+ BIGNUM *D = BN_CTX_get(ctx);
+ BIGNUM *tmp = BN_CTX_get(ctx);
+ BIGNUM *tmp2 = BN_CTX_get(ctx);
+ if (u == NULL || v == NULL || A == NULL || B == NULL || C == NULL ||
+ D == NULL || tmp == NULL || tmp2 == NULL ||
+ !BN_copy(u, a) ||
+ !BN_copy(v, n) ||
+ !BN_one(A) ||
+ !BN_one(D) ||
+ // For convenience, size |u| and |v| equivalently.
+ !bn_resize_words(u, n_width) ||
+ !bn_resize_words(v, n_width) ||
+ // |A| and |C| are bounded by |m|.
+ !bn_resize_words(A, n_width) ||
+ !bn_resize_words(C, n_width) ||
+ // |B| and |D| are bounded by |a|.
+ !bn_resize_words(B, a_width) ||
+ !bn_resize_words(D, a_width) ||
+ // |tmp| and |tmp2| may be used at either size.
+ !bn_resize_words(tmp, n_width) ||
+ !bn_resize_words(tmp2, n_width)) {
+ goto err;
+ }
+
+ // Each loop iteration halves at least one of |u| and |v|. Thus we need at
+ // most the combined bit width of inputs for at least one value to be zero.
+ unsigned a_bits = a_width * BN_BITS2, n_bits = n_width * BN_BITS2;
+ unsigned num_iters = a_bits + n_bits;
+ if (num_iters < a_bits) {
+ OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
+ goto err;
+ }
+
+ // Before and after each loop iteration, the following hold:
+ //
+ // u = A*a - B*n
+ // v = D*n - C*a
+ // 0 < u <= a
+ // 0 <= v <= n
+ // 0 <= A < n
+ // 0 <= B <= a
+ // 0 <= C < n
+ // 0 <= D <= a
+ //
+ // After each loop iteration, u and v only get smaller, and at least one of
+ // them shrinks by at least a factor of two.
+ for (unsigned i = 0; i < num_iters; i++) {
+ BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
+
+ // If both |u| and |v| are odd, subtract the smaller from the larger.
+ BN_ULONG v_less_than_u =
+ (BN_ULONG)0 - bn_sub_words(tmp->d, v->d, u->d, n_width);
+ bn_select_words(v->d, both_odd & ~v_less_than_u, tmp->d, v->d, n_width);
+ bn_sub_words(tmp->d, u->d, v->d, n_width);
+ bn_select_words(u->d, both_odd & v_less_than_u, tmp->d, u->d, n_width);
+
+ // If we updated one of the values, update the corresponding coefficient.
+ BN_ULONG carry = bn_add_words(tmp->d, A->d, C->d, n_width);
+ carry -= bn_sub_words(tmp2->d, tmp->d, n->d, n_width);
+ bn_select_words(tmp->d, carry, tmp->d, tmp2->d, n_width);
+ bn_select_words(A->d, both_odd & v_less_than_u, tmp->d, A->d, n_width);
+ bn_select_words(C->d, both_odd & ~v_less_than_u, tmp->d, C->d, n_width);
+
+ bn_add_words(tmp->d, B->d, D->d, a_width);
+ bn_sub_words(tmp2->d, tmp->d, a->d, a_width);
+ bn_select_words(tmp->d, carry, tmp->d, tmp2->d, a_width);
+ bn_select_words(B->d, both_odd & v_less_than_u, tmp->d, B->d, a_width);
+ bn_select_words(D->d, both_odd & ~v_less_than_u, tmp->d, D->d, a_width);
+
+ // Our loop invariants hold at this point. Additionally, exactly one of |u|
+ // and |v| is now even.
+ BN_ULONG u_is_even = ~word_is_odd_mask(u->d[0]);
+ BN_ULONG v_is_even = ~word_is_odd_mask(v->d[0]);
+ assert(u_is_even != v_is_even);
+
+ // Halve the even one and adjust the corresponding coefficient.
+ maybe_rshift1_words(u->d, u_is_even, tmp->d, n_width);
+ BN_ULONG A_or_B_is_odd =
+ word_is_odd_mask(A->d[0]) | word_is_odd_mask(B->d[0]);
+ BN_ULONG A_carry =
+ maybe_add_words(A->d, A_or_B_is_odd & u_is_even, n->d, tmp->d, n_width);
+ BN_ULONG B_carry =
+ maybe_add_words(B->d, A_or_B_is_odd & u_is_even, a->d, tmp->d, a_width);
+ maybe_rshift1_words_carry(A->d, A_carry, u_is_even, tmp->d, n_width);
+ maybe_rshift1_words_carry(B->d, B_carry, u_is_even, tmp->d, a_width);
+
+ maybe_rshift1_words(v->d, v_is_even, tmp->d, n_width);
+ BN_ULONG C_or_D_is_odd =
+ word_is_odd_mask(C->d[0]) | word_is_odd_mask(D->d[0]);
+ BN_ULONG C_carry =
+ maybe_add_words(C->d, C_or_D_is_odd & v_is_even, n->d, tmp->d, n_width);
+ BN_ULONG D_carry =
+ maybe_add_words(D->d, C_or_D_is_odd & v_is_even, a->d, tmp->d, a_width);
+ maybe_rshift1_words_carry(C->d, C_carry, v_is_even, tmp->d, n_width);
+ maybe_rshift1_words_carry(D->d, D_carry, v_is_even, tmp->d, a_width);
+ }
+
+ assert(BN_is_zero(v));
+ if (!BN_is_one(u)) {
+ *out_no_inverse = 1;
+ OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
+ goto err;
+ }
+
+ ret = BN_copy(r, A) != NULL;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
+ const BIGNUM *n, BN_CTX *ctx) {
+ *out_no_inverse = 0;
+
+ if (!BN_is_odd(n)) {
+ OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return 0;
+ }
+
+ if (BN_is_negative(a) || BN_cmp(a, n) >= 0) {
+ OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
+ return 0;
+ }
+
+ BIGNUM *A, *B, *X, *Y;
+ int ret = 0;
+ int sign;
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ if (Y == NULL) {
+ goto err;
+ }
+
+ BIGNUM *R = out;
+
+ BN_zero(Y);
+ if (!BN_one(X) || BN_copy(B, a) == NULL || BN_copy(A, n) == NULL) {
+ goto err;
+ }
+ A->neg = 0;
+ sign = -1;
+ // From B = a mod |n|, A = |n| it follows that
+ //
+ // 0 <= B < A,
+ // -sign*X*a == B (mod |n|),
+ // sign*Y*a == A (mod |n|).
+
+ // Binary inversion algorithm; requires odd modulus. This is faster than the
+ // general algorithm if the modulus is sufficiently small (about 400 .. 500
+ // bits on 32-bit systems, but much more on 64-bit systems)
+ int shift;
+
+ while (!BN_is_zero(B)) {
+ // 0 < B < |n|,
+ // 0 < A <= |n|,
+ // (1) -sign*X*a == B (mod |n|),
+ // (2) sign*Y*a == A (mod |n|)
+
+ // Now divide B by the maximum possible power of two in the integers,
+ // and divide X by the same value mod |n|.
+ // When we're done, (1) still holds.
+ shift = 0;
+ while (!BN_is_bit_set(B, shift)) {
+ // note that 0 < B
+ shift++;
+
+ if (BN_is_odd(X)) {
+ if (!BN_uadd(X, X, n)) {
+ goto err;
+ }
+ }
+ // now X is even, so we can easily divide it by two
+ if (!BN_rshift1(X, X)) {
+ goto err;
+ }
+ }
+ if (shift > 0) {
+ if (!BN_rshift(B, B, shift)) {
+ goto err;
+ }
+ }
+
+ // Same for A and Y. Afterwards, (2) still holds.
+ shift = 0;
+ while (!BN_is_bit_set(A, shift)) {
+ // note that 0 < A
+ shift++;
+
+ if (BN_is_odd(Y)) {
+ if (!BN_uadd(Y, Y, n)) {
+ goto err;
+ }
+ }
+ // now Y is even
+ if (!BN_rshift1(Y, Y)) {
+ goto err;
+ }
+ }
+ if (shift > 0) {
+ if (!BN_rshift(A, A, shift)) {
+ goto err;
+ }
+ }
+
+ // We still have (1) and (2).
+ // Both A and B are odd.
+ // The following computations ensure that
+ //
+ // 0 <= B < |n|,
+ // 0 < A < |n|,
+ // (1) -sign*X*a == B (mod |n|),
+ // (2) sign*Y*a == A (mod |n|),
+ //
+ // and that either A or B is even in the next iteration.
+ if (BN_ucmp(B, A) >= 0) {
+ // -sign*(X + Y)*a == B - A (mod |n|)
+ if (!BN_uadd(X, X, Y)) {
+ goto err;
+ }
+ // NB: we could use BN_mod_add_quick(X, X, Y, n), but that
+ // actually makes the algorithm slower
+ if (!BN_usub(B, B, A)) {
+ goto err;
+ }
+ } else {
+ // sign*(X + Y)*a == A - B (mod |n|)
+ if (!BN_uadd(Y, Y, X)) {
+ goto err;
+ }
+ // as above, BN_mod_add_quick(Y, Y, X, n) would slow things down
+ if (!BN_usub(A, A, B)) {
+ goto err;
+ }
+ }
+ }
+
+ if (!BN_is_one(A)) {
+ *out_no_inverse = 1;
+ OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
+ goto err;
+ }
+
+ // The while loop (Euclid's algorithm) ends when
+ // A == gcd(a,n);
+ // we have
+ // sign*Y*a == A (mod |n|),
+ // where Y is non-negative.
+
+ if (sign < 0) {
+ if (!BN_sub(Y, n, Y)) {
+ goto err;
+ }
+ }
+ // Now Y*a == A (mod |n|).
+
+ // Y*a == 1 (mod |n|)
+ if (!Y->neg && BN_ucmp(Y, n) < 0) {
+ if (!BN_copy(R, Y)) {
+ goto err;
+ }
+ } else {
+ if (!BN_nnmod(R, Y, n, ctx)) {
+ goto err;
+ }
+ }
+
+ ret = 1;
+
+err:
+ BN_CTX_end(ctx);
+ return ret;
+}
+
+BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
+ BN_CTX *ctx) {
+ BIGNUM *new_out = NULL;
+ if (out == NULL) {
+ new_out = BN_new();
+ if (new_out == NULL) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_MALLOC_FAILURE);
+ return NULL;
+ }
+ out = new_out;
+ }
+
+ int ok = 0;
+ BIGNUM *a_reduced = NULL;
+ if (a->neg || BN_ucmp(a, n) >= 0) {
+ a_reduced = BN_dup(a);
+ if (a_reduced == NULL) {
+ goto err;
+ }
+ if (!BN_nnmod(a_reduced, a_reduced, n, ctx)) {
+ goto err;
+ }
+ a = a_reduced;
+ }
+
+ int no_inverse;
+ if (!BN_is_odd(n)) {
+ if (!bn_mod_inverse_consttime(out, &no_inverse, a, n, ctx)) {
+ goto err;
+ }
+ } else if (!BN_mod_inverse_odd(out, &no_inverse, a, n, ctx)) {
+ goto err;
+ }
+
+ ok = 1;
+
+err:
+ if (!ok) {
+ BN_free(new_out);
+ out = NULL;
+ }
+ BN_free(a_reduced);
+ return out;
+}
+
+int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
+ const BN_MONT_CTX *mont, BN_CTX *ctx) {
+ *out_no_inverse = 0;
+
+ if (BN_is_negative(a) || BN_cmp(a, &mont->N) >= 0) {
+ OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
+ return 0;
+ }
+
+ int ret = 0;
+ BIGNUM blinding_factor;
+ BN_init(&blinding_factor);
+
+ if (!BN_rand_range_ex(&blinding_factor, 1, &mont->N) ||
+ !BN_mod_mul_montgomery(out, &blinding_factor, a, mont, ctx) ||
+ !BN_mod_inverse_odd(out, out_no_inverse, out, &mont->N, ctx) ||
+ !BN_mod_mul_montgomery(out, &blinding_factor, out, mont, ctx)) {
+ OPENSSL_PUT_ERROR(BN, ERR_R_BN_LIB);
+ goto err;
+ }
+
+ ret = 1;
+
+err:
+ BN_free(&blinding_factor);
+ return ret;
+}
+
+int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
+ BN_CTX *ctx, const BN_MONT_CTX *mont_p) {
+ BN_CTX_start(ctx);
+ BIGNUM *p_minus_2 = BN_CTX_get(ctx);
+ int ok = p_minus_2 != NULL &&
+ BN_copy(p_minus_2, p) &&
+ BN_sub_word(p_minus_2, 2) &&
+ BN_mod_exp_mont(out, a, p_minus_2, p, ctx, mont_p);
+ BN_CTX_end(ctx);
+ return ok;
+}
+
+int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
+ BN_CTX *ctx, const BN_MONT_CTX *mont_p) {
+ BN_CTX_start(ctx);
+ BIGNUM *p_minus_2 = BN_CTX_get(ctx);
+ int ok = p_minus_2 != NULL &&
+ BN_copy(p_minus_2, p) &&
+ BN_sub_word(p_minus_2, 2) &&
+ BN_mod_exp_mont_consttime(out, a, p_minus_2, p, ctx, mont_p);
+ BN_CTX_end(ctx);
+ return ok;
+}
git://repos.xcallymotion.com / motion2.git / blobdiff