-/* crypto/bn/bn_mul.c */
-/* 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.
+/*
+ * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
*
- * 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 OpenSSL license (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
*/
-#ifndef BN_DEBUG
-# undef NDEBUG /* avoid conflicting definitions */
-# define NDEBUG
-#endif
-
#include <assert.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
* Here follows specialised variants of bn_add_words() and bn_sub_words().
* They have the property performing operations on arrays of different sizes.
* The sizes of those arrays is expressed through cl, which is the common
- * length ( basicall, min(len(a),len(b)) ), and dl, which is the delta
+ * length ( basically, min(len(a),len(b)) ), and dl, which is the delta
* between the two lengths, calculated as len(a)-len(b). All lengths are the
* number of BN_ULONGs... For the operations that require a result array as
* parameter, it must have the length cl+abs(dl). These functions should
r[1] = a[1];
if (--dl <= 0)
break;
+ /* fall thru */
case 2:
r[2] = a[2];
if (--dl <= 0)
break;
+ /* fall thru */
case 3:
r[3] = a[3];
if (--dl <= 0)
}
#endif
-BN_ULONG bn_add_part_words(BN_ULONG *r,
- const BN_ULONG *a, const BN_ULONG *b,
- int cl, int dl)
-{
- BN_ULONG c, l, t;
-
- assert(cl >= 0);
- c = bn_add_words(r, a, b, cl);
-
- if (dl == 0)
- return c;
-
- r += cl;
- a += cl;
- b += cl;
-
- if (dl < 0) {
- int save_dl = dl;
- while (c) {
- l = (c + b[0]) & BN_MASK2;
- c = (l < c);
- r[0] = l;
- if (++dl >= 0)
- break;
-
- l = (c + b[1]) & BN_MASK2;
- c = (l < c);
- r[1] = l;
- if (++dl >= 0)
- break;
-
- l = (c + b[2]) & BN_MASK2;
- c = (l < c);
- r[2] = l;
- if (++dl >= 0)
- break;
-
- l = (c + b[3]) & BN_MASK2;
- c = (l < c);
- r[3] = l;
- if (++dl >= 0)
- break;
-
- save_dl = dl;
- b += 4;
- r += 4;
- }
- if (dl < 0) {
- if (save_dl < dl) {
- switch (dl - save_dl) {
- case 1:
- r[1] = b[1];
- if (++dl >= 0)
- break;
- case 2:
- r[2] = b[2];
- if (++dl >= 0)
- break;
- case 3:
- r[3] = b[3];
- if (++dl >= 0)
- break;
- }
- b += 4;
- r += 4;
- }
- }
- if (dl < 0) {
- for (;;) {
- r[0] = b[0];
- if (++dl >= 0)
- break;
- r[1] = b[1];
- if (++dl >= 0)
- break;
- r[2] = b[2];
- if (++dl >= 0)
- break;
- r[3] = b[3];
- if (++dl >= 0)
- break;
-
- b += 4;
- r += 4;
- }
- }
- } else {
- int save_dl = dl;
- while (c) {
- t = (a[0] + c) & BN_MASK2;
- c = (t < c);
- r[0] = t;
- if (--dl <= 0)
- break;
-
- t = (a[1] + c) & BN_MASK2;
- c = (t < c);
- r[1] = t;
- if (--dl <= 0)
- break;
-
- t = (a[2] + c) & BN_MASK2;
- c = (t < c);
- r[2] = t;
- if (--dl <= 0)
- break;
-
- t = (a[3] + c) & BN_MASK2;
- c = (t < c);
- r[3] = t;
- if (--dl <= 0)
- break;
-
- save_dl = dl;
- a += 4;
- r += 4;
- }
- if (dl > 0) {
- if (save_dl > dl) {
- switch (save_dl - dl) {
- case 1:
- r[1] = a[1];
- if (--dl <= 0)
- break;
- case 2:
- r[2] = a[2];
- if (--dl <= 0)
- break;
- case 3:
- r[3] = a[3];
- if (--dl <= 0)
- break;
- }
- a += 4;
- r += 4;
- }
- }
- if (dl > 0) {
- for (;;) {
- r[0] = a[0];
- if (--dl <= 0)
- break;
- r[1] = a[1];
- if (--dl <= 0)
- break;
- r[2] = a[2];
- if (--dl <= 0)
- break;
- r[3] = a[3];
- if (--dl <= 0)
- break;
-
- a += 4;
- r += 4;
- }
- }
- }
- return c;
-}
-
#ifdef BN_RECURSION
/*
* Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
break;
case -3:
- /* break; */
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
case -1:
case 0:
case 1:
- /* break; */
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
neg = 1;
break;
case 3:
- /* break; */
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
}
}
-
-/*-
- * a and b must be the same size, which is n2.
- * r needs to be n2 words and t needs to be n2*2
- * l is the low words of the output.
- * t needs to be n2*3
- */
-void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
- BN_ULONG *t)
-{
- int i, n;
- int c1, c2;
- int neg, oneg, zero;
- BN_ULONG ll, lc, *lp, *mp;
-
- n = n2 / 2;
-
- /* Calculate (al-ah)*(bh-bl) */
- neg = zero = 0;
- c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
- c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
- switch (c1 * 3 + c2) {
- case -4:
- bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
- bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
- break;
- case -3:
- zero = 1;
- break;
- case -2:
- bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
- bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
- neg = 1;
- break;
- case -1:
- case 0:
- case 1:
- zero = 1;
- break;
- case 2:
- bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
- bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
- neg = 1;
- break;
- case 3:
- zero = 1;
- break;
- case 4:
- bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
- bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
- break;
- }
-
- oneg = neg;
- /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
- /* r[10] = (a[1]*b[1]) */
-# ifdef BN_MUL_COMBA
- if (n == 8) {
- bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
- bn_mul_comba8(r, &(a[n]), &(b[n]));
- } else
-# endif
- {
- bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
- bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
- }
-
- /*-
- * s0 == low(al*bl)
- * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
- * We know s0 and s1 so the only unknown is high(al*bl)
- * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
- * high(al*bl) == s1 - (r[0]+l[0]+t[0])
- */
- if (l != NULL) {
- lp = &(t[n2 + n]);
- c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
- } else {
- c1 = 0;
- lp = &(r[0]);
- }
-
- if (neg)
- neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
- else {
- bn_add_words(&(t[n2]), lp, &(t[0]), n);
- neg = 0;
- }
-
- if (l != NULL) {
- bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
- } else {
- lp = &(t[n2 + n]);
- mp = &(t[n2]);
- for (i = 0; i < n; i++)
- lp[i] = ((~mp[i]) + 1) & BN_MASK2;
- }
-
- /*-
- * s[0] = low(al*bl)
- * t[3] = high(al*bl)
- * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
- * r[10] = (a[1]*b[1])
- */
- /*-
- * R[10] = al*bl
- * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
- * R[32] = ah*bh
- */
- /*-
- * R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
- * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
- * R[3]=r[1]+(carry/borrow)
- */
- if (l != NULL) {
- lp = &(t[n2]);
- c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
- } else {
- lp = &(t[n2 + n]);
- c1 = 0;
- }
- c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
- if (oneg)
- c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
- else
- c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
-
- c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
- c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
- if (oneg)
- c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
- else
- c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
-
- if (c1 != 0) { /* Add starting at r[0], could be +ve or -ve */
- i = 0;
- if (c1 > 0) {
- lc = c1;
- do {
- ll = (r[i] + lc) & BN_MASK2;
- r[i++] = ll;
- lc = (lc > ll);
- } while (lc);
- } else {
- lc = -c1;
- do {
- ll = r[i];
- r[i++] = (ll - lc) & BN_MASK2;
- lc = (lc > ll);
- } while (lc);
- }
- }
- if (c2 != 0) { /* Add starting at r[1] */
- i = n;
- if (c2 > 0) {
- lc = c2;
- do {
- ll = (r[i] + lc) & BN_MASK2;
- r[i++] = ll;
- lc = (lc > ll);
- } while (lc);
- } else {
- lc = -c2;
- do {
- ll = r[i];
- r[i++] = (ll - lc) & BN_MASK2;
- lc = (lc > ll);
- } while (lc);
- }
- }
-}
#endif /* BN_RECURSION */
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
if ((al == 0) || (bl == 0)) {
BN_zero(r);
- return (1);
+ return 1;
}
top = al + bl;
goto err;
} else
rr = r;
- rr->neg = a->neg ^ b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al - bl;
rr->top = top;
goto end;
}
-# if 0
- if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
- BIGNUM *tmp_bn = (BIGNUM *)b;
- if (bn_wexpand(tmp_bn, al) == NULL)
- goto err;
- tmp_bn->d[bl] = 0;
- bl++;
- i--;
- } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
- BIGNUM *tmp_bn = (BIGNUM *)a;
- if (bn_wexpand(tmp_bn, bl) == NULL)
- goto err;
- tmp_bn->d[al] = 0;
- al++;
- i++;
- }
- if (i == 0) {
- /* symmetric and > 4 */
- /* 16 or larger */
- j = BN_num_bits_word((BN_ULONG)al);
- j = 1 << (j - 1);
- k = j + j;
- t = BN_CTX_get(ctx);
- if (al == j) { /* exact multiple */
- if (bn_wexpand(t, k * 2) == NULL)
- goto err;
- if (bn_wexpand(rr, k * 2) == NULL)
- goto err;
- bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
- } else {
- if (bn_wexpand(t, k * 4) == NULL)
- goto err;
- if (bn_wexpand(rr, k * 4) == NULL)
- goto err;
- bn_mul_part_recursive(rr->d, a->d, b->d, al - j, j, t->d);
- }
- rr->top = top;
- goto end;
- }
-# endif
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr, top) == NULL)
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
+ rr->neg = a->neg ^ b->neg;
bn_correct_top(rr);
- if (r != rr)
- BN_copy(r, rr);
+ if (r != rr && BN_copy(r, rr) == NULL)
+ goto err;
+
ret = 1;
err:
bn_check_top(r);
BN_CTX_end(ctx);
- return (ret);
+ return ret;
}
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
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