-/* crypto/bn/bn_gcd.c */
-/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
- * All rights reserved.
+/*
+ * Copyright 1995-2018 The OpenSSL Project Authors. 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.]
+ * Licensed under the Apache License 2.0 (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
*/
-#include <stdio.h>
-#include "cryptlib.h"
-#include "bn_lcl.h"
-
-static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
-int BN_gcd(BIGNUM *r, BIGNUM *in_a, BIGNUM *in_b, BN_CTX *ctx)
- {
- BIGNUM *a,*b,*t;
- int ret=0;
-
- bn_check_top(in_a);
- bn_check_top(in_b);
-
- a= &(ctx->bn[ctx->tos]);
- b= &(ctx->bn[ctx->tos+1]);
-
- if (BN_copy(a,in_a) == NULL) goto err;
- if (BN_copy(b,in_b) == NULL) goto err;
-
- if (BN_cmp(a,b) < 0) { t=a; a=b; b=t; }
- t=euclid(a,b);
- if (t == NULL) goto err;
-
- if (BN_copy(r,t) == NULL) goto err;
- ret=1;
-err:
- return(ret);
- }
-
-static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
- {
- BIGNUM *t;
- int shifts=0;
-
- bn_check_top(a);
- bn_check_top(b);
-
- for (;;)
- {
- if (BN_is_zero(b))
- break;
-
- if (BN_is_odd(a))
- {
- if (BN_is_odd(b))
- {
- if (!BN_sub(a,a,b)) goto err;
- if (!BN_rshift1(a,a)) goto err;
- if (BN_cmp(a,b) < 0)
- { t=a; a=b; b=t; }
- }
- else /* a odd - b even */
- {
- if (!BN_rshift1(b,b)) goto err;
- if (BN_cmp(a,b) < 0)
- { t=a; a=b; b=t; }
- }
- }
- else /* a is even */
- {
- if (BN_is_odd(b))
- {
- if (!BN_rshift1(a,a)) goto err;
- if (BN_cmp(a,b) < 0)
- { t=a; a=b; b=t; }
- }
- else /* a even - b even */
- {
- if (!BN_rshift1(a,a)) goto err;
- if (!BN_rshift1(b,b)) goto err;
- shifts++;
- }
- }
- }
- if (shifts)
- {
- if (!BN_lshift(a,a,shifts)) goto err;
- }
- return(a);
-err:
- return(NULL);
- }
+#include "internal/cryptlib.h"
+#include "bn_local.h"
+
+/*
+ * bn_mod_inverse_no_branch is a special version of BN_mod_inverse. It does
+ * not contain branches that may leak sensitive information.
+ *
+ * This is a static function, we ensure all callers in this file pass valid
+ * arguments: all passed pointers here are non-NULL.
+ */
+static ossl_inline
+BIGNUM *bn_mod_inverse_no_branch(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n,
+ BN_CTX *ctx, int *pnoinv)
+{
+ BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
+ BIGNUM *ret = NULL;
+ int sign;
+
+ bn_check_top(a);
+ bn_check_top(n);
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ D = BN_CTX_get(ctx);
+ M = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ T = BN_CTX_get(ctx);
+ if (T == NULL)
+ goto err;
+
+ if (in == NULL)
+ R = BN_new();
+ else
+ R = in;
+ if (R == NULL)
+ goto err;
+
+ BN_one(X);
+ BN_zero(Y);
+ if (BN_copy(B, a) == NULL)
+ goto err;
+ if (BN_copy(A, n) == NULL)
+ goto err;
+ A->neg = 0;
+
+ if (B->neg || (BN_ucmp(B, A) >= 0)) {
+ /*
+ * Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ {
+ BIGNUM local_B;
+ bn_init(&local_B);
+ BN_with_flags(&local_B, B, BN_FLG_CONSTTIME);
+ if (!BN_nnmod(B, &local_B, A, ctx))
+ goto err;
+ /* Ensure local_B goes out of scope before any further use of B */
+ }
+ }
+ 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|).
+ */
+
+ while (!BN_is_zero(B)) {
+ BIGNUM *tmp;
+
+ /*-
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /*
+ * Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ {
+ BIGNUM local_A;
+ bn_init(&local_A);
+ BN_with_flags(&local_A, A, BN_FLG_CONSTTIME);
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (!BN_div(D, M, &local_A, B, ctx))
+ goto err;
+ /* Ensure local_A goes out of scope before any further use of A */
+ }
+
+ /*-
+ * Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp = A; /* keep the BIGNUM object, the value does not
+ * matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A = B;
+ B = M;
+ /* ... so we have 0 <= B < A again */
+
+ /*-
+ * Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * sign*Y*a + D*sign*X*a == B (mod |n|),
+ * i.e.
+ * sign*(Y + D*X)*a == B (mod |n|).
+ *
+ * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ if (!BN_mul(tmp, D, X, ctx))
+ goto err;
+ if (!BN_add(tmp, tmp, Y))
+ goto err;
+
+ M = Y; /* keep the BIGNUM object, the value does not
+ * matter */
+ Y = X;
+ X = tmp;
+ sign = -sign;
+ }
+
+ /*-
+ * 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|). */
+
+ if (BN_is_one(A)) {
+ /* 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;
+ }
+ } else {
+ *pnoinv = 1;
+ /* caller sets the BN_R_NO_INVERSE error */
+ goto err;
+ }
+
+ ret = R;
+ *pnoinv = 0;
+
+ err:
+ if ((ret == NULL) && (in == NULL))
+ BN_free(R);
+ BN_CTX_end(ctx);
+ bn_check_top(ret);
+ return ret;
+}
+
+/*
+ * This is an internal function, we assume all callers pass valid arguments:
+ * all pointers passed here are assumed non-NULL.
+ */
+BIGNUM *int_bn_mod_inverse(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
+ int *pnoinv)
+{
+ BIGNUM *A, *B, *X, *Y, *M, *D, *T, *R = NULL;
+ BIGNUM *ret = NULL;
+ int sign;
+
+ /* This is invalid input so we don't worry about constant time here */
+ if (BN_abs_is_word(n, 1) || BN_is_zero(n)) {
+ *pnoinv = 1;
+ return NULL;
+ }
+
+ *pnoinv = 0;
+
+ if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0)
+ || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0)) {
+ return bn_mod_inverse_no_branch(in, a, n, ctx, pnoinv);
+ }
+
+ bn_check_top(a);
+ bn_check_top(n);
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ D = BN_CTX_get(ctx);
+ M = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ T = BN_CTX_get(ctx);
+ if (T == NULL)
+ goto err;
+
+ if (in == NULL)
+ R = BN_new();
+ else
+ R = in;
+ if (R == NULL)
+ goto err;
+
+ BN_one(X);
+ BN_zero(Y);
+ if (BN_copy(B, a) == NULL)
+ goto err;
+ if (BN_copy(A, n) == NULL)
+ goto err;
+ A->neg = 0;
+ if (B->neg || (BN_ucmp(B, A) >= 0)) {
+ if (!BN_nnmod(B, B, A, ctx))
+ goto err;
+ }
+ 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|).
+ */
+
+ if (BN_is_odd(n) && (BN_num_bits(n) <= 2048)) {
+ /*
+ * 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;
+ }
+ }
+ } else {
+ /* general inversion algorithm */
+
+ while (!BN_is_zero(B)) {
+ BIGNUM *tmp;
+
+ /*-
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (BN_num_bits(A) == BN_num_bits(B)) {
+ if (!BN_one(D))
+ goto err;
+ if (!BN_sub(M, A, B))
+ goto err;
+ } else if (BN_num_bits(A) == BN_num_bits(B) + 1) {
+ /* A/B is 1, 2, or 3 */
+ if (!BN_lshift1(T, B))
+ goto err;
+ if (BN_ucmp(A, T) < 0) {
+ /* A < 2*B, so D=1 */
+ if (!BN_one(D))
+ goto err;
+ if (!BN_sub(M, A, B))
+ goto err;
+ } else {
+ /* A >= 2*B, so D=2 or D=3 */
+ if (!BN_sub(M, A, T))
+ goto err;
+ if (!BN_add(D, T, B))
+ goto err; /* use D (:= 3*B) as temp */
+ if (BN_ucmp(A, D) < 0) {
+ /* A < 3*B, so D=2 */
+ if (!BN_set_word(D, 2))
+ goto err;
+ /*
+ * M (= A - 2*B) already has the correct value
+ */
+ } else {
+ /* only D=3 remains */
+ if (!BN_set_word(D, 3))
+ goto err;
+ /*
+ * currently M = A - 2*B, but we need M = A - 3*B
+ */
+ if (!BN_sub(M, M, B))
+ goto err;
+ }
+ }
+ } else {
+ if (!BN_div(D, M, A, B, ctx))
+ goto err;
+ }
+
+ /*-
+ * Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp = A; /* keep the BIGNUM object, the value does not matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A = B;
+ B = M;
+ /* ... so we have 0 <= B < A again */
+
+ /*-
+ * Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * sign*Y*a + D*sign*X*a == B (mod |n|),
+ * i.e.
+ * sign*(Y + D*X)*a == B (mod |n|).
+ *
+ * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ /*
+ * most of the time D is very small, so we can optimize tmp := D*X+Y
+ */
+ if (BN_is_one(D)) {
+ if (!BN_add(tmp, X, Y))
+ goto err;
+ } else {
+ if (BN_is_word(D, 2)) {
+ if (!BN_lshift1(tmp, X))
+ goto err;
+ } else if (BN_is_word(D, 4)) {
+ if (!BN_lshift(tmp, X, 2))
+ goto err;
+ } else if (D->top == 1) {
+ if (!BN_copy(tmp, X))
+ goto err;
+ if (!BN_mul_word(tmp, D->d[0]))
+ goto err;
+ } else {
+ if (!BN_mul(tmp, D, X, ctx))
+ goto err;
+ }
+ if (!BN_add(tmp, tmp, Y))
+ goto err;
+ }
+
+ M = Y; /* keep the BIGNUM object, the value does not matter */
+ Y = X;
+ X = tmp;
+ sign = -sign;
+ }
+ }
+
+ /*-
+ * 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|). */
+
+ if (BN_is_one(A)) {
+ /* 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;
+ }
+ } else {
+ *pnoinv = 1;
+ goto err;
+ }
+ ret = R;
+ err:
+ if ((ret == NULL) && (in == NULL))
+ BN_free(R);
+ BN_CTX_end(ctx);
+ bn_check_top(ret);
+ return ret;
+}
/* solves ax == 1 (mod n) */
-BIGNUM *BN_mod_inverse(BIGNUM *in, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
- {
- BIGNUM *A,*B,*X,*Y,*M,*D,*R;
- BIGNUM *T,*ret=NULL;
- int sign;
-
- bn_check_top(a);
- bn_check_top(n);
-
- A= &(ctx->bn[ctx->tos]);
- B= &(ctx->bn[ctx->tos+1]);
- X= &(ctx->bn[ctx->tos+2]);
- D= &(ctx->bn[ctx->tos+3]);
- M= &(ctx->bn[ctx->tos+4]);
- Y= &(ctx->bn[ctx->tos+5]);
- ctx->tos+=6;
- if (in == NULL)
- R=BN_new();
- else
- R=in;
- if (R == NULL) goto err;
-
- BN_zero(X);
- BN_one(Y);
- if (BN_copy(A,a) == NULL) goto err;
- if (BN_copy(B,n) == NULL) goto err;
- sign=1;
-
- while (!BN_is_zero(B))
- {
- if (!BN_div(D,M,A,B,ctx)) goto err;
- T=A;
- A=B;
- B=M;
- /* T has a struct, M does not */
-
- if (!BN_mul(T,D,X,ctx)) goto err;
- if (!BN_add(T,T,Y)) goto err;
- M=Y;
- Y=X;
- X=T;
- sign= -sign;
- }
- if (sign < 0)
- {
- if (!BN_sub(Y,n,Y)) goto err;
- }
-
- if (BN_is_one(A))
- { if (!BN_mod(R,Y,n,ctx)) goto err; }
- else
- {
- BNerr(BN_F_BN_MOD_INVERSE,BN_R_NO_INVERSE);
- goto err;
- }
- ret=R;
-err:
- if ((ret == NULL) && (in == NULL)) BN_free(R);
- ctx->tos-=6;
- return(ret);
- }
+BIGNUM *BN_mod_inverse(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+{
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *rv;
+ int noinv = 0;
+
+ if (ctx == NULL) {
+ ctx = new_ctx = BN_CTX_new_ex(NULL);
+ if (ctx == NULL) {
+ BNerr(BN_F_BN_MOD_INVERSE, ERR_R_MALLOC_FAILURE);
+ return NULL;
+ }
+ }
+
+ rv = int_bn_mod_inverse(in, a, n, ctx, &noinv);
+ if (noinv)
+ BNerr(BN_F_BN_MOD_INVERSE, BN_R_NO_INVERSE);
+ BN_CTX_free(new_ctx);
+ return rv;
+}
+
+/*-
+ * This function is based on the constant-time GCD work by Bernstein and Yang:
+ * https://eprint.iacr.org/2019/266
+ * Generalized fast GCD function to allow even inputs.
+ * The algorithm first finds the shared powers of 2 between
+ * the inputs, and removes them, reducing at least one of the
+ * inputs to an odd value. Then it proceeds to calculate the GCD.
+ * Before returning the resulting GCD, we take care of adding
+ * back the powers of two removed at the beginning.
+ * Note 1: we assume the bit length of both inputs is public information,
+ * since access to top potentially leaks this information.
+ */
+int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
+{
+ BIGNUM *g, *temp = NULL;
+ BN_ULONG mask = 0;
+ int i, j, top, rlen, glen, m, bit = 1, delta = 1, cond = 0, shifts = 0, ret = 0;
+
+ /* Note 2: zero input corner cases are not constant-time since they are
+ * handled immediately. An attacker can run an attack under this
+ * assumption without the need of side-channel information. */
+ if (BN_is_zero(in_b)) {
+ ret = BN_copy(r, in_a) != NULL;
+ r->neg = 0;
+ return ret;
+ }
+ if (BN_is_zero(in_a)) {
+ ret = BN_copy(r, in_b) != NULL;
+ r->neg = 0;
+ return ret;
+ }
+
+ bn_check_top(in_a);
+ bn_check_top(in_b);
+
+ BN_CTX_start(ctx);
+ temp = BN_CTX_get(ctx);
+ g = BN_CTX_get(ctx);
+
+ /* make r != 0, g != 0 even, so BN_rshift is not a potential nop */
+ if (g == NULL
+ || !BN_lshift1(g, in_b)
+ || !BN_lshift1(r, in_a))
+ goto err;
+
+ /* find shared powers of two, i.e. "shifts" >= 1 */
+ for (i = 0; i < r->dmax && i < g->dmax; i++) {
+ mask = ~(r->d[i] | g->d[i]);
+ for (j = 0; j < BN_BITS2; j++) {
+ bit &= mask;
+ shifts += bit;
+ mask >>= 1;
+ }
+ }
+
+ /* subtract shared powers of two; shifts >= 1 */
+ if (!BN_rshift(r, r, shifts)
+ || !BN_rshift(g, g, shifts))
+ goto err;
+
+ /* expand to biggest nword, with room for a possible extra word */
+ top = 1 + ((r->top >= g->top) ? r->top : g->top);
+ if (bn_wexpand(r, top) == NULL
+ || bn_wexpand(g, top) == NULL
+ || bn_wexpand(temp, top) == NULL)
+ goto err;
+
+ /* re arrange inputs s.t. r is odd */
+ BN_consttime_swap((~r->d[0]) & 1, r, g, top);
+
+ /* compute the number of iterations */
+ rlen = BN_num_bits(r);
+ glen = BN_num_bits(g);
+ m = 4 + 3 * ((rlen >= glen) ? rlen : glen);
+
+ for (i = 0; i < m; i++) {
+ /* conditionally flip signs if delta is positive and g is odd */
+ cond = (-delta >> (8 * sizeof(delta) - 1)) & g->d[0] & 1
+ /* make sure g->top > 0 (i.e. if top == 0 then g == 0 always) */
+ & (~((g->top - 1) >> (sizeof(g->top) * 8 - 1)));
+ delta = (-cond & -delta) | ((cond - 1) & delta);
+ r->neg ^= cond;
+ /* swap */
+ BN_consttime_swap(cond, r, g, top);
+
+ /* elimination step */
+ delta++;
+ if (!BN_add(temp, g, r))
+ goto err;
+ BN_consttime_swap(g->d[0] & 1 /* g is odd */
+ /* make sure g->top > 0 (i.e. if top == 0 then g == 0 always) */
+ & (~((g->top - 1) >> (sizeof(g->top) * 8 - 1))),
+ g, temp, top);
+ if (!BN_rshift1(g, g))
+ goto err;
+ }
+
+ /* remove possible negative sign */
+ r->neg = 0;
+ /* add powers of 2 removed, then correct the artificial shift */
+ if (!BN_lshift(r, r, shifts)
+ || !BN_rshift1(r, r))
+ goto err;
+
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ bn_check_top(r);
+ return ret;
+}
projects / openssl.git / blobdiff