-/* crypto/bn/bn_mul.c */
-/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
- * All rights reserved.
+/*
+ * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
*
- * This package is an SSL implementation written
- * by Eric Young (eay@cryptsoft.com).
- * The implementation was written so as to conform with Netscapes SSL.
- *
- * This library is free for commercial and non-commercial use as long as
- * the following conditions are aheared to. The following conditions
- * apply to all code found in this distribution, be it the RC4, RSA,
- * lhash, DES, etc., code; not just the SSL code. The SSL documentation
- * included with this distribution is covered by the same copyright terms
- * except that the holder is Tim Hudson (tjh@cryptsoft.com).
- *
- * Copyright remains Eric Young's, and as such any Copyright notices in
- * the code are not to be removed.
- * If this package is used in a product, Eric Young should be given attribution
- * as the author of the parts of the library used.
- * This can be in the form of a textual message at program startup or
- * in documentation (online or textual) provided with the package.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- * 3. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * "This product includes cryptographic software written by
- * Eric Young (eay@cryptsoft.com)"
- * The word 'cryptographic' can be left out if the rouines from the library
- * being used are not cryptographic related :-).
- * 4. If you include any Windows specific code (or a derivative thereof) from
- * the apps directory (application code) you must include an acknowledgement:
- * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
- *
- * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- *
- * The licence and distribution terms for any publically available version or
- * derivative of this code cannot be changed. i.e. this code cannot simply be
- * copied and put under another distribution licence
- * [including the GNU Public Licence.]
+ * Licensed under the 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
*/
-#include <stdio.h>
-#include "cryptlib.h"
+#include <assert.h>
+#include "internal/cryptlib.h"
#include "bn_lcl.h"
-/* r must be different to a and b */
-/* int BN_mmul(r, a, b) */
-int BN_mul(r, a, b)
-BIGNUM *r;
-BIGNUM *a;
-BIGNUM *b;
- {
- int i;
- int max,al,bl;
- BN_ULONG *ap,*bp,*rp;
-
- al=a->top;
- bl=b->top;
- if ((al == 0) || (bl == 0))
- {
- r->top=0;
- return(1);
- }
-
- max=(al+bl);
- if (bn_wexpand(r,max) == NULL) return(0);
- r->top=max;
- r->neg=a->neg^b->neg;
- ap=a->d;
- bp=b->d;
- rp=r->d;
-
- rp[al]=bn_mul_words(rp,ap,al,*(bp++));
- rp++;
- for (i=1; i<bl; i++)
- {
- rp[al]=bn_mul_add_words(rp,ap,al,*(bp++));
- rp++;
- }
- if (r->d[max-1] == 0) r->top--;
- return(1);
- }
-
-#if 0
-#include "stack.h"
-
-int limit=16;
-
-typedef struct bn_pool_st
- {
- int used;
- int tos;
- STACK *sk;
- } BN_POOL;
-
-BIGNUM *BN_POOL_push(bp)
-BN_POOL *bp;
- {
- BIGNUM *ret;
-
- if (bp->used >= bp->tos)
- {
- ret=BN_new();
- sk_push(bp->sk,(char *)ret);
- bp->tos++;
- bp->used++;
- }
- else
- {
- ret=(BIGNUM *)sk_value(bp->sk,bp->used);
- bp->used++;
- }
- return(ret);
- }
-
-void BN_POOL_pop(bp,num)
-BN_POOL *bp;
-int num;
- {
- bp->used-=num;
- }
-
-int BN_mul(r,a,b)
-BIGNUM *r,*a,*b;
- {
- static BN_POOL bp;
- static init=1;
-
- if (init)
- {
- bp.used=0;
- bp.tos=0;
- bp.sk=sk_new_null();
- init=0;
- }
- return(BN_mm(r,a,b,&bp));
- }
-
-/* r must be different to a and b */
-int BN_mm(m, A, B, bp)
-BIGNUM *m,*A,*B;
-BN_POOL *bp;
- {
- int i,num;
- int an,bn;
- BIGNUM *a,*b,*c,*d,*ac,*bd;
-
- an=A->top;
- bn=B->top;
- if ((an <= limit) || (bn <= limit))
- {
- return(BN_mmul(m,A,B));
- }
-
- a=BN_POOL_push(bp);
- b=BN_POOL_push(bp);
- c=BN_POOL_push(bp);
- d=BN_POOL_push(bp);
- ac=BN_POOL_push(bp);
- bd=BN_POOL_push(bp);
-
- num=(an <= bn)?an:bn;
- num=1<<(BN_num_bits_word(num-1)-1);
-
- /* Are going to now chop things into 'num' word chunks. */
- num*=BN_BITS2;
-
- BN_copy(a,A);
- BN_mask_bits(a,num);
- BN_rshift(b,A,num);
-
- BN_copy(c,B);
- BN_mask_bits(c,num);
- BN_rshift(d,B,num);
-
- BN_sub(ac ,b,a);
- BN_sub(bd,c,d);
- BN_mm(m,ac,bd,bp);
- BN_mm(ac,a,c,bp);
- BN_mm(bd,b,d,bp);
-
- BN_add(m,m,ac);
- BN_add(m,m,bd);
- BN_lshift(m,m,num);
- BN_lshift(bd,bd,num*2);
-
- BN_add(m,m,ac);
- BN_add(m,m,bd);
- BN_POOL_pop(bp,6);
- return(1);
- }
+#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
+/*
+ * 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 ( 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
+ * probably end up in bn_asm.c as soon as there are assembler counterparts
+ * for the systems that use assembler files.
+ */
+
+BN_ULONG bn_sub_part_words(BN_ULONG *r,
+ const BN_ULONG *a, const BN_ULONG *b,
+ int cl, int dl)
+{
+ BN_ULONG c, t;
+
+ assert(cl >= 0);
+ c = bn_sub_words(r, a, b, cl);
+
+ if (dl == 0)
+ return c;
+
+ r += cl;
+ a += cl;
+ b += cl;
+
+ if (dl < 0) {
+ for (;;) {
+ t = b[0];
+ r[0] = (0 - t - c) & BN_MASK2;
+ if (t != 0)
+ c = 1;
+ if (++dl >= 0)
+ break;
+
+ t = b[1];
+ r[1] = (0 - t - c) & BN_MASK2;
+ if (t != 0)
+ c = 1;
+ if (++dl >= 0)
+ break;
+
+ t = b[2];
+ r[2] = (0 - t - c) & BN_MASK2;
+ if (t != 0)
+ c = 1;
+ if (++dl >= 0)
+ break;
+
+ t = b[3];
+ r[3] = (0 - t - c) & BN_MASK2;
+ if (t != 0)
+ c = 1;
+ if (++dl >= 0)
+ break;
+
+ b += 4;
+ r += 4;
+ }
+ } else {
+ int save_dl = dl;
+ while (c) {
+ t = a[0];
+ r[0] = (t - c) & BN_MASK2;
+ if (t != 0)
+ c = 0;
+ if (--dl <= 0)
+ break;
+
+ t = a[1];
+ r[1] = (t - c) & BN_MASK2;
+ if (t != 0)
+ c = 0;
+ if (--dl <= 0)
+ break;
+
+ t = a[2];
+ r[2] = (t - c) & BN_MASK2;
+ if (t != 0)
+ c = 0;
+ if (--dl <= 0)
+ break;
+
+ t = a[3];
+ r[3] = (t - c) & BN_MASK2;
+ if (t != 0)
+ c = 0;
+ 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;
+}
#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
+ * Computer Programming, Vol. 2)
+ */
+
+/*-
+ * r is 2*n2 words in size,
+ * a and b are both n2 words in size.
+ * n2 must be a power of 2.
+ * We multiply and return the result.
+ * t must be 2*n2 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]
+ */
+/* dnX may not be positive, but n2/2+dnX has to be */
+void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
+ int dna, int dnb, BN_ULONG *t)
+{
+ int n = n2 / 2, c1, c2;
+ int tna = n + dna, tnb = n + dnb;
+ unsigned int neg, zero;
+ BN_ULONG ln, lo, *p;
+
+# ifdef BN_MUL_COMBA
+# if 0
+ if (n2 == 4) {
+ bn_mul_comba4(r, a, b);
+ return;
+ }
+# endif
+ /*
+ * Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
+ * [steve]
+ */
+ if (n2 == 8 && dna == 0 && dnb == 0) {
+ bn_mul_comba8(r, a, b);
+ return;
+ }
+# endif /* BN_MUL_COMBA */
+ /* Else do normal multiply */
+ if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
+ bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
+ if ((dna + dnb) < 0)
+ memset(&r[2 * n2 + dna + dnb], 0,
+ sizeof(BN_ULONG) * -(dna + dnb));
+ return;
+ }
+ /* r=(a[0]-a[1])*(b[1]-b[0]) */
+ c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
+ c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
+ zero = neg = 0;
+ switch (c1 * 3 + c2) {
+ case -4:
+ bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
+ bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
+ break;
+ case -3:
+ zero = 1;
+ 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); /* + */
+ neg = 1;
+ break;
+ case -1:
+ case 0:
+ case 1:
+ zero = 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:
+ zero = 1;
+ 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);
+ break;
+ }
+
+# ifdef BN_MUL_COMBA
+ if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
+ * extra args to do this well */
+ if (!zero)
+ bn_mul_comba4(&(t[n2]), t, &(t[n]));
+ else
+ memset(&t[n2], 0, sizeof(*t) * 8);
+
+ bn_mul_comba4(r, a, b);
+ bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
+ } else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could
+ * take extra args to do
+ * this well */
+ if (!zero)
+ bn_mul_comba8(&(t[n2]), t, &(t[n]));
+ else
+ memset(&t[n2], 0, sizeof(*t) * 16);
+
+ bn_mul_comba8(r, a, b);
+ bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
+ } else
+# endif /* BN_MUL_COMBA */
+ {
+ p = &(t[n2 * 2]);
+ if (!zero)
+ bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
+ else
+ memset(&t[n2], 0, sizeof(*t) * n2);
+ bn_mul_recursive(r, a, b, n, 0, 0, p);
+ bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
+ }
+
+ /*-
+ * 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) & BN_MASK2;
+ *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) & BN_MASK2;
+ *p = ln;
+ } while (ln == 0);
+ }
+ }
+}
+
+/*
+ * n+tn is the word length t needs to be n*4 is size, as does r
+ */
+/* tnX may not be negative but less than n */
+void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
+ int tna, int tnb, BN_ULONG *t)
+{
+ int i, j, n2 = n * 2;
+ int c1, c2, neg;
+ BN_ULONG ln, lo, *p;
+
+ if (n < 8) {
+ bn_mul_normal(r, a, n + tna, b, n + tnb);
+ return;
+ }
+
+ /* r=(a[0]-a[1])*(b[1]-b[0]) */
+ c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
+ c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
+ neg = 0;
+ switch (c1 * 3 + c2) {
+ case -4:
+ bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
+ 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); /* + */
+ neg = 1;
+ break;
+ 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);
+ break;
+ }
+ /*
+ * The zero case isn't yet implemented here. The speedup would probably
+ * be negligible.
+ */
+# if 0
+ if (n == 4) {
+ bn_mul_comba4(&(t[n2]), t, &(t[n]));
+ bn_mul_comba4(r, a, b);
+ bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
+ memset(&r[n2 + tn * 2], 0, sizeof(*r) * (n2 - tn * 2));
+ } else
+# endif
+ if (n == 8) {
+ bn_mul_comba8(&(t[n2]), t, &(t[n]));
+ bn_mul_comba8(r, a, b);
+ bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
+ memset(&r[n2 + tna + tnb], 0, sizeof(*r) * (n2 - tna - tnb));
+ } else {
+ p = &(t[n2 * 2]);
+ bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
+ bn_mul_recursive(r, a, b, n, 0, 0, p);
+ i = n / 2;
+ /*
+ * If there is only a bottom half to the number, just do it
+ */
+ if (tna > tnb)
+ j = tna - i;
+ else
+ j = tnb - i;
+ if (j == 0) {
+ bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
+ i, tna - i, tnb - i, p);
+ memset(&r[n2 + i * 2], 0, sizeof(*r) * (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);
+ memset(&(r[n2 + tna + tnb]), 0,
+ sizeof(BN_ULONG) * (n2 - tna - tnb));
+ } else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
+
+ memset(&r[n2], 0, sizeof(*r) * 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) & BN_MASK2;
+ *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) & BN_MASK2;
+ *p = ln;
+ } while (ln == 0);
+ }
+ }
+}
+
+/*-
+ * a and b must be the same size, which is n2.
+ * r needs to be n2 words and t needs to be n2*2
+ */
+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);
+ }
+}
+
+/*-
+ * 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]);
+ bn_add_words(lp, &(r[0]), &(l[0]), n);
+ } else {
+ 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)
+{
+ 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;
+ rr->neg = a->neg ^ b->neg;
+
+#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;
+ }
+# 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)
+ 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
+ bn_correct_top(rr);
+ 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;
+ }
+}
projects / openssl.git / blobdiff