| /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| * All rights reserved. |
| * |
| * This package is an SSL implementation written |
| * by Eric Young (eay@cryptsoft.com). |
| * The implementation was written so as to conform with Netscapes SSL. |
| * |
| * This library is free for commercial and non-commercial use as long as |
| * the following conditions are aheared to. The following conditions |
| * apply to all code found in this distribution, be it the RC4, RSA, |
| * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| * included with this distribution is covered by the same copyright terms |
| * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| * |
| * Copyright remains Eric Young's, and as such any Copyright notices in |
| * the code are not to be removed. |
| * If this package is used in a product, Eric Young should be given attribution |
| * as the author of the parts of the library used. |
| * This can be in the form of a textual message at program startup or |
| * in documentation (online or textual) provided with the package. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * 3. All advertising materials mentioning features or use of this software |
| * must display the following acknowledgement: |
| * "This product includes cryptographic software written by |
| * Eric Young (eay@cryptsoft.com)" |
| * The word 'cryptographic' can be left out if the rouines from the library |
| * being used are not cryptographic related :-). |
| * 4. If you include any Windows specific code (or a derivative thereof) from |
| * the apps directory (application code) you must include an acknowledgement: |
| * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| * |
| * 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.] */ |
| |
| #include <openssl/bn.h> |
| |
| #include <assert.h> |
| #include <string.h> |
| |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| |
| #include "internal.h" |
| #include "../../internal.h" |
| |
| |
| #define BN_MUL_RECURSIVE_SIZE_NORMAL 16 |
| #define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL |
| |
| |
| static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na, |
| const BN_ULONG *b, size_t nb) { |
| if (na < nb) { |
| size_t itmp = na; |
| na = nb; |
| nb = itmp; |
| const BN_ULONG *ltmp = a; |
| a = b; |
| b = ltmp; |
| } |
| BN_ULONG *rr = &(r[na]); |
| if (nb == 0) { |
| OPENSSL_memset(r, 0, na * sizeof(BN_ULONG)); |
| return; |
| } |
| 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; |
| } |
| } |
| |
| #if !defined(OPENSSL_X86) || defined(OPENSSL_NO_ASM) |
| // Here follows specialised variants of bn_add_words() and bn_sub_words(). They |
| // have the property performing operations on arrays of different sizes. The |
| // sizes of those arrays is expressed through cl, which is the common length ( |
| // basicall, min(len(a),len(b)) ), and dl, which is the delta 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. |
| |
| static 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; |
| if (t != 0) { |
| c = 1; |
| } |
| if (++dl >= 0) { |
| break; |
| } |
| |
| t = b[1]; |
| r[1] = 0 - t - c; |
| if (t != 0) { |
| c = 1; |
| } |
| if (++dl >= 0) { |
| break; |
| } |
| |
| t = b[2]; |
| r[2] = 0 - t - c; |
| if (t != 0) { |
| c = 1; |
| } |
| if (++dl >= 0) { |
| break; |
| } |
| |
| t = b[3]; |
| r[3] = 0 - t - c; |
| 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; |
| if (t != 0) { |
| c = 0; |
| } |
| if (--dl <= 0) { |
| break; |
| } |
| |
| t = a[1]; |
| r[1] = t - c; |
| if (t != 0) { |
| c = 0; |
| } |
| if (--dl <= 0) { |
| break; |
| } |
| |
| t = a[2]; |
| r[2] = t - c; |
| if (t != 0) { |
| c = 0; |
| } |
| if (--dl <= 0) { |
| break; |
| } |
| |
| t = a[3]; |
| r[3] = t - c; |
| 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; |
| } |
| OPENSSL_FALLTHROUGH; |
| case 2: |
| r[2] = a[2]; |
| if (--dl <= 0) { |
| break; |
| } |
| OPENSSL_FALLTHROUGH; |
| 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; |
| } |
| #else |
| // On other platforms the function is defined in asm. |
| BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int cl, int dl); |
| #endif |
| |
| // 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 |
| static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const 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; |
| |
| // 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; |
| } |
| |
| // 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) { |
| OPENSSL_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; |
| } |
| |
| 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 { |
| OPENSSL_memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG)); |
| } |
| |
| 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 { |
| OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG)); |
| } |
| |
| bn_mul_comba8(r, a, b); |
| bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n])); |
| } else { |
| p = &(t[n2 * 2]); |
| if (!zero) { |
| bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p); |
| } else { |
| OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG)); |
| } |
| 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; |
| *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); |
| } |
| } |
| } |
| |
| // 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 |
| static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a, |
| const 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; |
| } |
| |
| 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); |
| OPENSSL_memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (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); |
| 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; |
| } |
