| /* |
| * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved. |
| * |
| * Licensed under the Apache License 2.0 (the "License"). You may not use |
| * this file except in compliance with the License. You can obtain a copy |
| * in the file LICENSE in the source distribution or at |
| * https://www.openssl.org/source/license.html |
| */ |
| |
| #include <assert.h> |
| #include "internal/cryptlib.h" |
| #include "bn_local.h" |
| |
| #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; |
| /* fall thru */ |
| case 2: |
| r[2] = a[2]; |
| if (--dl <= 0) |
| break; |
| /* fall thru */ |
| 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 |
| |
| #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: |
| 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: |
| 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: |
| 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); |
| } |
| } |
| #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; |
| } |
| } |
