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684 lines
19 KiB
C
684 lines
19 KiB
C
/*
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* Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <assert.h>
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#include "internal/cryptlib.h"
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#include "bn_lcl.h"
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#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
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/*
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* Here follows specialised variants of bn_add_words() and bn_sub_words().
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* They have the property performing operations on arrays of different sizes.
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* The sizes of those arrays is expressed through cl, which is the common
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* length ( basically, min(len(a),len(b)) ), and dl, which is the delta
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* between the two lengths, calculated as len(a)-len(b). All lengths are the
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* number of BN_ULONGs... For the operations that require a result array as
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* parameter, it must have the length cl+abs(dl). These functions should
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* probably end up in bn_asm.c as soon as there are assembler counterparts
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* for the systems that use assembler files.
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*/
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BN_ULONG bn_sub_part_words(BN_ULONG *r,
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const BN_ULONG *a, const BN_ULONG *b,
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int cl, int dl)
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{
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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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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) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[1];
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r[1] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[2];
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r[2] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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t = b[3];
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r[3] = (0 - t - c) & BN_MASK2;
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if (t != 0)
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c = 1;
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if (++dl >= 0)
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break;
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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) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[1];
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r[1] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[2];
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r[2] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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t = a[3];
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r[3] = (t - c) & BN_MASK2;
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if (t != 0)
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c = 0;
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if (--dl <= 0)
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break;
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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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/* fall thru */
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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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/* fall thru */
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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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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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r[1] = a[1];
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if (--dl <= 0)
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break;
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r[2] = a[2];
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if (--dl <= 0)
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break;
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r[3] = a[3];
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if (--dl <= 0)
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break;
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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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#endif
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#ifdef BN_RECURSION
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/*
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* Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
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* Computer Programming, Vol. 2)
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*/
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/*-
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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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*/
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/* dnX may not be positive, but n2/2+dnX has to be */
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void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
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int dna, int dnb, BN_ULONG *t)
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{
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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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# ifdef BN_MUL_COMBA
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# if 0
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if (n2 == 4) {
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bn_mul_comba4(r, a, b);
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return;
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}
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# endif
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/*
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* Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
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* [steve]
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*/
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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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# endif /* BN_MUL_COMBA */
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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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memset(&r[2 * n2 + dna + dnb], 0,
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sizeof(BN_ULONG) * -(dna + dnb));
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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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# ifdef BN_MUL_COMBA
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if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
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* 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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memset(&t[n2], 0, sizeof(*t) * 8);
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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) { /* XXX: bn_mul_comba8 could
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* take extra args to do
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* 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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memset(&t[n2], 0, sizeof(*t) * 16);
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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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# endif /* BN_MUL_COMBA */
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{
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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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memset(&t[n2], 0, sizeof(*t) * n2);
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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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/*-
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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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*/
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c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
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if (neg) { /* 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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/*-
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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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*/
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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) & BN_MASK2;
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*p = ln;
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/*
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* The overflow will stop before we over write words we should not
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* overwrite
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*/
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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) & BN_MASK2;
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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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/*
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* n+tn is the word length t needs to be n*4 is size, as does r
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*/
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/* tnX may not be negative but less than n */
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void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
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int tna, int tnb, BN_ULONG *t)
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{
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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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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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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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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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/*
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* The zero case isn't yet implemented here. The speedup would probably
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* be negligible.
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*/
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# if 0
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if (n == 4) {
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bn_mul_comba4(&(t[n2]), t, &(t[n]));
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bn_mul_comba4(r, a, b);
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bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
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memset(&r[n2 + tn * 2], 0, sizeof(*r) * (n2 - tn * 2));
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} else
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# endif
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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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memset(&r[n2 + tna + tnb], 0, sizeof(*r) * (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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/*
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* If there is only a bottom half to the number, just do it
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*/
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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) {
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bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
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i, tna - i, tnb - i, p);
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memset(&r[n2 + i * 2], 0, sizeof(*r) * (n2 - i * 2));
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} else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */
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bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
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i, tna - i, tnb - i, p);
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memset(&(r[n2 + tna + tnb]), 0,
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sizeof(BN_ULONG) * (n2 - tna - tnb));
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} else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
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memset(&r[n2], 0, sizeof(*r) * n2);
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if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
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&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
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bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
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} else {
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for (;;) {
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i /= 2;
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/*
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* these simplified conditions work exclusively because
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* difference between tna and tnb is 1 or 0
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*/
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if (i < tna || i < tnb) {
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bn_mul_part_recursive(&(r[n2]),
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&(a[n]), &(b[n]),
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i, tna - i, tnb - i, p);
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break;
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} else if (i == tna || i == tnb) {
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bn_mul_recursive(&(r[n2]),
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&(a[n]), &(b[n]),
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i, tna - i, tnb - i, p);
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break;
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}
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}
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}
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}
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}
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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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*/
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c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
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if (neg) { /* 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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/*-
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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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*/
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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) & BN_MASK2;
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*p = ln;
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/*
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* The overflow will stop before we over write words we should not
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* overwrite
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*/
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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) & BN_MASK2;
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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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/*-
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* a and b must be the same size, which is n2.
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* r needs to be n2 words and t needs to be n2*2
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*/
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void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
|
|
BN_ULONG *t)
|
|
{
|
|
int n = n2 / 2;
|
|
|
|
bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
|
|
if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
|
|
bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
|
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
|
bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
|
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
|
} else {
|
|
bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
|
|
bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
|
|
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
|
|
bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
|
|
}
|
|
}
|
|
#endif /* BN_RECURSION */
|
|
|
|
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
|
|
{
|
|
int ret = bn_mul_fixed_top(r, a, b, ctx);
|
|
|
|
bn_correct_top(r);
|
|
bn_check_top(r);
|
|
|
|
return ret;
|
|
}
|
|
|
|
int bn_mul_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
|
|
{
|
|
int ret = 0;
|
|
int top, al, bl;
|
|
BIGNUM *rr;
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
|
int i;
|
|
#endif
|
|
#ifdef BN_RECURSION
|
|
BIGNUM *t = NULL;
|
|
int j = 0, k;
|
|
#endif
|
|
|
|
bn_check_top(a);
|
|
bn_check_top(b);
|
|
bn_check_top(r);
|
|
|
|
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;
|
|
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
|
i = al - bl;
|
|
#endif
|
|
#ifdef BN_MUL_COMBA
|
|
if (i == 0) {
|
|
# if 0
|
|
if (al == 4) {
|
|
if (bn_wexpand(rr, 8) == NULL)
|
|
goto err;
|
|
rr->top = 8;
|
|
bn_mul_comba4(rr->d, a->d, b->d);
|
|
goto end;
|
|
}
|
|
# endif
|
|
if (al == 8) {
|
|
if (bn_wexpand(rr, 16) == NULL)
|
|
goto err;
|
|
rr->top = 16;
|
|
bn_mul_comba8(rr->d, a->d, b->d);
|
|
goto end;
|
|
}
|
|
}
|
|
#endif /* BN_MUL_COMBA */
|
|
#ifdef BN_RECURSION
|
|
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
|
|
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) == NULL)
|
|
goto err;
|
|
if (bn_wexpand(rr, k * 4) == NULL)
|
|
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) == NULL)
|
|
goto err;
|
|
if (bn_wexpand(rr, k * 2) == NULL)
|
|
goto err;
|
|
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
|
|
}
|
|
rr->top = top;
|
|
goto end;
|
|
}
|
|
}
|
|
#endif /* BN_RECURSION */
|
|
if (bn_wexpand(rr, top) == NULL)
|
|
goto err;
|
|
rr->top = top;
|
|
bn_mul_normal(rr->d, a->d, al, b->d, bl);
|
|
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
|
|
end:
|
|
#endif
|
|
rr->neg = a->neg ^ b->neg;
|
|
rr->flags |= BN_FLG_FIXED_TOP;
|
|
if (r != rr && BN_copy(r, rr) == NULL)
|
|
goto err;
|
|
|
|
ret = 1;
|
|
err:
|
|
bn_check_top(r);
|
|
BN_CTX_end(ctx);
|
|
return ret;
|
|
}
|
|
|
|
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
|
|
{
|
|
BN_ULONG *rr;
|
|
|
|
if (na < nb) {
|
|
int itmp;
|
|
BN_ULONG *ltmp;
|
|
|
|
itmp = na;
|
|
na = nb;
|
|
nb = itmp;
|
|
ltmp = a;
|
|
a = b;
|
|
b = ltmp;
|
|
|
|
}
|
|
rr = &(r[na]);
|
|
if (nb <= 0) {
|
|
(void)bn_mul_words(r, a, na, 0);
|
|
return;
|
|
} else
|
|
rr[0] = bn_mul_words(r, a, na, b[0]);
|
|
|
|
for (;;) {
|
|
if (--nb <= 0)
|
|
return;
|
|
rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
|
|
if (--nb <= 0)
|
|
return;
|
|
rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
|
|
if (--nb <= 0)
|
|
return;
|
|
rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
|
|
if (--nb <= 0)
|
|
return;
|
|
rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
|
|
rr += 4;
|
|
r += 4;
|
|
b += 4;
|
|
}
|
|
}
|
|
|
|
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
|
|
{
|
|
bn_mul_words(r, a, n, b[0]);
|
|
|
|
for (;;) {
|
|
if (--n <= 0)
|
|
return;
|
|
bn_mul_add_words(&(r[1]), a, n, b[1]);
|
|
if (--n <= 0)
|
|
return;
|
|
bn_mul_add_words(&(r[2]), a, n, b[2]);
|
|
if (--n <= 0)
|
|
return;
|
|
bn_mul_add_words(&(r[3]), a, n, b[3]);
|
|
if (--n <= 0)
|
|
return;
|
|
bn_mul_add_words(&(r[4]), a, n, b[4]);
|
|
r += 4;
|
|
b += 4;
|
|
}
|
|
}
|