903 lines
22 KiB
C
903 lines
22 KiB
C
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.] */
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#include <openssl/bn.h>
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#include <assert.h>
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#include <string.h>
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#include <openssl/err.h>
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#include <openssl/mem.h>
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#include "internal.h"
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#include "../../internal.h"
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#define BN_MUL_RECURSIVE_SIZE_NORMAL 16
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#define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL
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static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na,
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const BN_ULONG *b, size_t nb) {
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if (na < nb) {
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size_t itmp = na;
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na = nb;
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nb = itmp;
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const BN_ULONG *ltmp = a;
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a = b;
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b = ltmp;
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}
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BN_ULONG *rr = &(r[na]);
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if (nb == 0) {
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OPENSSL_memset(r, 0, na * sizeof(BN_ULONG));
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return;
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}
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rr[0] = bn_mul_words(r, a, na, b[0]);
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for (;;) {
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if (--nb == 0) {
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return;
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}
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rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
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if (--nb == 0) {
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return;
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}
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rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
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if (--nb == 0) {
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return;
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}
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rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
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if (--nb == 0) {
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return;
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}
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rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
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rr += 4;
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r += 4;
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b += 4;
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}
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}
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#if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM)
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// Here follows specialised variants of bn_add_words() and bn_sub_words(). They
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// have the property performing operations on arrays of different sizes. The
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// sizes of those arrays is expressed through cl, which is the common length (
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// basicall, min(len(a),len(b)) ), and dl, which is the delta between the two
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// lengths, calculated as len(a)-len(b). All lengths are the number of
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// BN_ULONGs... For the operations that require a result array as parameter,
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// it must have the length cl+abs(dl). These functions should probably end up
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// in bn_asm.c as soon as there are assembler counterparts for the systems that
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// use assembler files.
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static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
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const BN_ULONG *b, int cl, int dl) {
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BN_ULONG c, t;
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assert(cl >= 0);
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c = bn_sub_words(r, a, b, cl);
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if (dl == 0) {
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return c;
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}
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r += cl;
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a += cl;
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b += cl;
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if (dl < 0) {
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for (;;) {
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t = b[0];
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r[0] = 0 - t - c;
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if (t != 0) {
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c = 1;
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}
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if (++dl >= 0) {
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break;
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}
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t = b[1];
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r[1] = 0 - t - c;
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if (t != 0) {
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c = 1;
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}
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if (++dl >= 0) {
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break;
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}
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t = b[2];
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r[2] = 0 - t - c;
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if (t != 0) {
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c = 1;
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}
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if (++dl >= 0) {
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break;
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}
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t = b[3];
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r[3] = 0 - t - c;
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if (t != 0) {
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c = 1;
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}
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if (++dl >= 0) {
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break;
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}
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b += 4;
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r += 4;
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}
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} else {
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int save_dl = dl;
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while (c) {
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t = a[0];
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r[0] = t - c;
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if (t != 0) {
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c = 0;
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}
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if (--dl <= 0) {
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break;
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}
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t = a[1];
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r[1] = t - c;
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if (t != 0) {
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c = 0;
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}
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if (--dl <= 0) {
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break;
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}
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t = a[2];
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r[2] = t - c;
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if (t != 0) {
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c = 0;
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}
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if (--dl <= 0) {
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break;
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}
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t = a[3];
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r[3] = t - c;
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if (t != 0) {
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c = 0;
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}
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if (--dl <= 0) {
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break;
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}
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save_dl = dl;
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a += 4;
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r += 4;
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}
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if (dl > 0) {
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if (save_dl > dl) {
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switch (save_dl - dl) {
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case 1:
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r[1] = a[1];
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if (--dl <= 0) {
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break;
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}
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OPENSSL_FALLTHROUGH;
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case 2:
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r[2] = a[2];
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if (--dl <= 0) {
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break;
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}
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OPENSSL_FALLTHROUGH;
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case 3:
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r[3] = a[3];
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if (--dl <= 0) {
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break;
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}
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}
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a += 4;
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r += 4;
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}
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}
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if (dl > 0) {
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for (;;) {
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r[0] = a[0];
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if (--dl <= 0) {
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break;
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}
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r[1] = a[1];
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if (--dl <= 0) {
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break;
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}
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r[2] = a[2];
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if (--dl <= 0) {
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break;
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}
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r[3] = a[3];
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if (--dl <= 0) {
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break;
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}
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a += 4;
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r += 4;
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}
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}
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}
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return c;
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}
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#else
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// On other platforms the function is defined in asm.
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BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
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int cl, int dl);
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#endif
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// Karatsuba recursive multiplication algorithm
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// (cf. Knuth, The Art of Computer Programming, Vol. 2)
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// r is 2*n2 words in size,
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// a and b are both n2 words in size.
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// n2 must be a power of 2.
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// We multiply and return the result.
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// t must be 2*n2 words in size
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// We calculate
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// a[0]*b[0]
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// a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
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// a[1]*b[1]
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// dnX may not be positive, but n2/2+dnX has to be
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static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
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int n2, int dna, int dnb, BN_ULONG *t) {
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int n = n2 / 2, c1, c2;
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int tna = n + dna, tnb = n + dnb;
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unsigned int neg, zero;
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BN_ULONG ln, lo, *p;
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// Only call bn_mul_comba 8 if n2 == 8 and the
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// two arrays are complete [steve]
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if (n2 == 8 && dna == 0 && dnb == 0) {
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bn_mul_comba8(r, a, b);
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return;
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}
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// Else do normal multiply
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if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
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bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
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if ((dna + dnb) < 0) {
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OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,
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sizeof(BN_ULONG) * -(dna + dnb));
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}
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return;
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}
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// r=(a[0]-a[1])*(b[1]-b[0])
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c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
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c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
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zero = neg = 0;
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switch (c1 * 3 + c2) {
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case -4:
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bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
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bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
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break;
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case -3:
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zero = 1;
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break;
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case -2:
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bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
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bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); // +
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neg = 1;
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break;
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case -1:
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case 0:
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case 1:
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zero = 1;
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break;
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case 2:
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bn_sub_part_words(t, a, &(a[n]), tna, n - tna); // +
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bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
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neg = 1;
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break;
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case 3:
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zero = 1;
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break;
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case 4:
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bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
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bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
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break;
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}
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if (n == 4 && dna == 0 && dnb == 0) {
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// XXX: bn_mul_comba4 could take extra args to do this well
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if (!zero) {
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bn_mul_comba4(&(t[n2]), t, &(t[n]));
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} else {
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OPENSSL_memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
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}
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bn_mul_comba4(r, a, b);
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bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
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} else if (n == 8 && dna == 0 && dnb == 0) {
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// XXX: bn_mul_comba8 could take extra args to do this well
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if (!zero) {
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bn_mul_comba8(&(t[n2]), t, &(t[n]));
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} else {
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OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
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}
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bn_mul_comba8(r, a, b);
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bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
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} else {
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p = &(t[n2 * 2]);
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if (!zero) {
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bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
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} else {
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OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
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}
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bn_mul_recursive(r, a, b, n, 0, 0, p);
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bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
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}
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// t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
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// r[10] holds (a[0]*b[0])
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// r[32] holds (b[1]*b[1])
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c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
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if (neg) {
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// if t[32] is negative
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c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
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} else {
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// Might have a carry
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c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
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}
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// t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
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// r[10] holds (a[0]*b[0])
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// r[32] holds (b[1]*b[1])
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// c1 holds the carry bits
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c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
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if (c1) {
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p = &(r[n + n2]);
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lo = *p;
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ln = lo + c1;
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*p = ln;
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// The overflow will stop before we over write
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// words we should not overwrite
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if (ln < (BN_ULONG)c1) {
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do {
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p++;
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lo = *p;
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ln = lo + 1;
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*p = ln;
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} while (ln == 0);
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}
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}
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}
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// n+tn is the word length
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// t needs to be n*4 is size, as does r
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// tnX may not be negative but less than n
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static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,
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const BN_ULONG *b, int n, int tna, int tnb,
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BN_ULONG *t) {
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int i, j, n2 = n * 2;
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int c1, c2, neg;
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BN_ULONG ln, lo, *p;
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if (n < 8) {
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bn_mul_normal(r, a, n + tna, b, n + tnb);
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return;
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}
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// r=(a[0]-a[1])*(b[1]-b[0])
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c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
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c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
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neg = 0;
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switch (c1 * 3 + c2) {
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case -4:
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bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
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bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
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break;
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case -3:
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// break;
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case -2:
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bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
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bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); // +
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neg = 1;
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break;
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case -1:
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case 0:
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case 1:
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// break;
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case 2:
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bn_sub_part_words(t, a, &(a[n]), tna, n - tna); // +
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bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
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neg = 1;
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break;
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case 3:
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// break;
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case 4:
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bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
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bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
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break;
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}
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if (n == 8) {
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bn_mul_comba8(&(t[n2]), t, &(t[n]));
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bn_mul_comba8(r, a, b);
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bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
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OPENSSL_memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
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} else {
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p = &(t[n2 * 2]);
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bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
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bn_mul_recursive(r, a, b, n, 0, 0, p);
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i = n / 2;
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// If there is only a bottom half to the number,
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// just do it
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if (tna > tnb) {
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j = tna - i;
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} else {
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j = tnb - i;
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}
|
|
|
|
if (j == 0) {
|
|
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
|
|
OPENSSL_memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
|
|
} else if (j > 0) {
|
|
// eg, n == 16, i == 8 and tn == 11
|
|
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
|
|
OPENSSL_memset(&(r[n2 + tna + tnb]), 0,
|
|
sizeof(BN_ULONG) * (n2 - tna - tnb));
|
|
} else {
|
|
// (j < 0) eg, n == 16, i == 8 and tn == 5
|
|
OPENSSL_memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
|
|
if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
|
|
tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
|
|
bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
|
|
} else {
|
|
for (;;) {
|
|
i /= 2;
|
|
// these simplified conditions work
|
|
// exclusively because difference
|
|
// between tna and tnb is 1 or 0
|
|
if (i < tna || i < tnb) {
|
|
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i,
|
|
tnb - i, p);
|
|
break;
|
|
} else if (i == tna || i == tnb) {
|
|
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i,
|
|
p);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
|
|
// r[10] holds (a[0]*b[0])
|
|
// r[32] holds (b[1]*b[1])
|
|
|
|
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
|
|
|
|
if (neg) {
|
|
// if t[32] is negative
|
|
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
|
|
} else {
|
|
// Might have a carry
|
|
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
|
|
}
|
|
|
|
// t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
|
|
// r[10] holds (a[0]*b[0])
|
|
// r[32] holds (b[1]*b[1])
|
|
// c1 holds the carry bits
|
|
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
|
|
if (c1) {
|
|
p = &(r[n + n2]);
|
|
lo = *p;
|
|
ln = lo + c1;
|
|
*p = ln;
|
|
|
|
// The overflow will stop before we over write
|
|
// words we should not overwrite
|
|
if (ln < (BN_ULONG)c1) {
|
|
do {
|
|
p++;
|
|
lo = *p;
|
|
ln = lo + 1;
|
|
*p = ln;
|
|
} while (ln == 0);
|
|
}
|
|
}
|
|
}
|
|
|
|
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
|
|
int ret = 0;
|
|
int top, al, bl;
|
|
BIGNUM *rr;
|
|
int i;
|
|
BIGNUM *t = NULL;
|
|
int j = 0, k;
|
|
|
|
al = a->top;
|
|
bl = b->top;
|
|
|
|
if ((al == 0) || (bl == 0)) {
|
|
BN_zero(r);
|
|
return 1;
|
|
}
|
|
top = al + bl;
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((r == a) || (r == b)) {
|
|
if ((rr = BN_CTX_get(ctx)) == NULL) {
|
|
goto err;
|
|
}
|
|
} else {
|
|
rr = r;
|
|
}
|
|
rr->neg = a->neg ^ b->neg;
|
|
|
|
i = al - bl;
|
|
if (i == 0) {
|
|
if (al == 8) {
|
|
if (!bn_wexpand(rr, 16)) {
|
|
goto err;
|
|
}
|
|
rr->top = 16;
|
|
bn_mul_comba8(rr->d, a->d, b->d);
|
|
goto end;
|
|
}
|
|
}
|
|
|
|
static const int kMulNormalSize = 16;
|
|
if (al >= kMulNormalSize && bl >= kMulNormalSize) {
|
|
if (i >= -1 && i <= 1) {
|
|
/* Find out the power of two lower or equal
|
|
to the longest of the two numbers */
|
|
if (i >= 0) {
|
|
j = BN_num_bits_word((BN_ULONG)al);
|
|
}
|
|
if (i == -1) {
|
|
j = BN_num_bits_word((BN_ULONG)bl);
|
|
}
|
|
j = 1 << (j - 1);
|
|
assert(j <= al || j <= bl);
|
|
k = j + j;
|
|
t = BN_CTX_get(ctx);
|
|
if (t == NULL) {
|
|
goto err;
|
|
}
|
|
if (al > j || bl > j) {
|
|
if (!bn_wexpand(t, k * 4)) {
|
|
goto err;
|
|
}
|
|
if (!bn_wexpand(rr, k * 4)) {
|
|
goto err;
|
|
}
|
|
bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
|
|
} else {
|
|
// al <= j || bl <= j
|
|
if (!bn_wexpand(t, k * 2)) {
|
|
goto err;
|
|
}
|
|
if (!bn_wexpand(rr, k * 2)) {
|
|
goto err;
|
|
}
|
|
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
|
|
}
|
|
rr->top = top;
|
|
goto end;
|
|
}
|
|
}
|
|
|
|
if (!bn_wexpand(rr, top)) {
|
|
goto err;
|
|
}
|
|
rr->top = top;
|
|
bn_mul_normal(rr->d, a->d, al, b->d, bl);
|
|
|
|
end:
|
|
bn_correct_top(rr);
|
|
if (r != rr && !BN_copy(r, rr)) {
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
int bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
|
|
const BN_ULONG *b, size_t num_b) {
|
|
if (num_r != num_a + num_b) {
|
|
OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
|
return 0;
|
|
}
|
|
// TODO(davidben): Should this call |bn_mul_comba4| too? |BN_mul| does not
|
|
// hit that code.
|
|
if (num_a == 8 && num_b == 8) {
|
|
bn_mul_comba8(r, a, b);
|
|
} else {
|
|
bn_mul_normal(r, a, num_a, b, num_b);
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
// tmp must have 2*n words
|
|
static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n,
|
|
BN_ULONG *tmp) {
|
|
if (n == 0) {
|
|
return;
|
|
}
|
|
|
|
size_t max = n * 2;
|
|
const BN_ULONG *ap = a;
|
|
BN_ULONG *rp = r;
|
|
rp[0] = rp[max - 1] = 0;
|
|
rp++;
|
|
|
|
// Compute the contribution of a[i] * a[j] for all i < j.
|
|
if (n > 1) {
|
|
ap++;
|
|
rp[n - 1] = bn_mul_words(rp, ap, n - 1, ap[-1]);
|
|
rp += 2;
|
|
}
|
|
if (n > 2) {
|
|
for (size_t i = n - 2; i > 0; i--) {
|
|
ap++;
|
|
rp[i] = bn_mul_add_words(rp, ap, i, ap[-1]);
|
|
rp += 2;
|
|
}
|
|
}
|
|
|
|
// The final result fits in |max| words, so none of the following operations
|
|
// will overflow.
|
|
|
|
// Double |r|, giving the contribution of a[i] * a[j] for all i != j.
|
|
bn_add_words(r, r, r, max);
|
|
|
|
// Add in the contribution of a[i] * a[i] for all i.
|
|
bn_sqr_words(tmp, a, n);
|
|
bn_add_words(r, r, tmp, max);
|
|
}
|
|
|
|
// r is 2*n words in size,
|
|
// a and b are both n words in size. (There's not actually a 'b' here ...)
|
|
// n must be a power of 2.
|
|
// We multiply and return the result.
|
|
// t must be 2*n words in size
|
|
// We calculate
|
|
// a[0]*b[0]
|
|
// a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
|
|
// a[1]*b[1]
|
|
static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2,
|
|
BN_ULONG *t) {
|
|
int n = n2 / 2;
|
|
int zero, c1;
|
|
BN_ULONG ln, lo, *p;
|
|
|
|
if (n2 == 4) {
|
|
bn_sqr_comba4(r, a);
|
|
return;
|
|
} else if (n2 == 8) {
|
|
bn_sqr_comba8(r, a);
|
|
return;
|
|
}
|
|
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
|
|
bn_sqr_normal(r, a, n2, t);
|
|
return;
|
|
}
|
|
// r=(a[0]-a[1])*(a[1]-a[0])
|
|
c1 = bn_cmp_words(a, &(a[n]), n);
|
|
zero = 0;
|
|
if (c1 > 0) {
|
|
bn_sub_words(t, a, &(a[n]), n);
|
|
} else if (c1 < 0) {
|
|
bn_sub_words(t, &(a[n]), a, n);
|
|
} else {
|
|
zero = 1;
|
|
}
|
|
|
|
// The result will always be negative unless it is zero
|
|
p = &(t[n2 * 2]);
|
|
|
|
if (!zero) {
|
|
bn_sqr_recursive(&(t[n2]), t, n, p);
|
|
} else {
|
|
OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
|
|
}
|
|
bn_sqr_recursive(r, a, n, p);
|
|
bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
|
|
|
|
// t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
|
|
// r[10] holds (a[0]*b[0])
|
|
// r[32] holds (b[1]*b[1])
|
|
|
|
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
|
|
|
|
// t[32] is negative
|
|
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
|
|
|
|
// t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
|
|
// r[10] holds (a[0]*a[0])
|
|
// r[32] holds (a[1]*a[1])
|
|
// c1 holds the carry bits
|
|
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
|
|
if (c1) {
|
|
p = &(r[n + n2]);
|
|
lo = *p;
|
|
ln = lo + c1;
|
|
*p = ln;
|
|
|
|
// The overflow will stop before we over write
|
|
// words we should not overwrite
|
|
if (ln < (BN_ULONG)c1) {
|
|
do {
|
|
p++;
|
|
lo = *p;
|
|
ln = lo + 1;
|
|
*p = ln;
|
|
} while (ln == 0);
|
|
}
|
|
}
|
|
}
|
|
|
|
int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
|
|
if (!bn->top) {
|
|
return 1;
|
|
}
|
|
|
|
if (w == 0) {
|
|
BN_zero(bn);
|
|
return 1;
|
|
}
|
|
|
|
BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->top, w);
|
|
if (ll) {
|
|
if (!bn_wexpand(bn, bn->top + 1)) {
|
|
return 0;
|
|
}
|
|
bn->d[bn->top++] = ll;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
|
|
int max, al;
|
|
int ret = 0;
|
|
BIGNUM *tmp, *rr;
|
|
|
|
al = a->top;
|
|
if (al <= 0) {
|
|
r->top = 0;
|
|
r->neg = 0;
|
|
return 1;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
rr = (a != r) ? r : BN_CTX_get(ctx);
|
|
tmp = BN_CTX_get(ctx);
|
|
if (!rr || !tmp) {
|
|
goto err;
|
|
}
|
|
|
|
max = 2 * al; // Non-zero (from above)
|
|
if (!bn_wexpand(rr, max)) {
|
|
goto err;
|
|
}
|
|
|
|
if (al == 4) {
|
|
bn_sqr_comba4(rr->d, a->d);
|
|
} else if (al == 8) {
|
|
bn_sqr_comba8(rr->d, a->d);
|
|
} else {
|
|
if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
|
|
BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
|
|
bn_sqr_normal(rr->d, a->d, al, t);
|
|
} else {
|
|
int j, k;
|
|
|
|
j = BN_num_bits_word((BN_ULONG)al);
|
|
j = 1 << (j - 1);
|
|
k = j + j;
|
|
if (al == j) {
|
|
if (!bn_wexpand(tmp, k * 2)) {
|
|
goto err;
|
|
}
|
|
bn_sqr_recursive(rr->d, a->d, al, tmp->d);
|
|
} else {
|
|
if (!bn_wexpand(tmp, max)) {
|
|
goto err;
|
|
}
|
|
bn_sqr_normal(rr->d, a->d, al, tmp->d);
|
|
}
|
|
}
|
|
}
|
|
|
|
rr->neg = 0;
|
|
// If the most-significant half of the top word of 'a' is zero, then
|
|
// the square of 'a' will max-1 words.
|
|
if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
|
|
rr->top = max - 1;
|
|
} else {
|
|
rr->top = max;
|
|
}
|
|
|
|
if (rr != r && !BN_copy(r, rr)) {
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
int bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) {
|
|
if (num_r != 2 * num_a || num_a > BN_SMALL_MAX_WORDS) {
|
|
OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
|
return 0;
|
|
}
|
|
if (num_a == 4) {
|
|
bn_sqr_comba4(r, a);
|
|
} else if (num_a == 8) {
|
|
bn_sqr_comba8(r, a);
|
|
} else {
|
|
BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
|
|
bn_sqr_normal(r, a, num_a, tmp);
|
|
OPENSSL_cleanse(tmp, 2 * num_a * sizeof(BN_ULONG));
|
|
}
|
|
return 1;
|
|
}
|