diff options
Diffstat (limited to 'thirdparty/openssl/crypto/bn/bn_gf2m.c')
| -rw-r--r-- | thirdparty/openssl/crypto/bn/bn_gf2m.c | 1300 |
1 files changed, 0 insertions, 1300 deletions
diff --git a/thirdparty/openssl/crypto/bn/bn_gf2m.c b/thirdparty/openssl/crypto/bn/bn_gf2m.c deleted file mode 100644 index 2c61da1109..0000000000 --- a/thirdparty/openssl/crypto/bn/bn_gf2m.c +++ /dev/null @@ -1,1300 +0,0 @@ -/* crypto/bn/bn_gf2m.c */ -/* ==================================================================== - * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. - * - * The Elliptic Curve Public-Key Crypto Library (ECC Code) included - * herein is developed by SUN MICROSYSTEMS, INC., and is contributed - * to the OpenSSL project. - * - * The ECC Code is licensed pursuant to the OpenSSL open source - * license provided below. - * - * In addition, Sun covenants to all licensees who provide a reciprocal - * covenant with respect to their own patents if any, not to sue under - * current and future patent claims necessarily infringed by the making, - * using, practicing, selling, offering for sale and/or otherwise - * disposing of the ECC Code as delivered hereunder (or portions thereof), - * provided that such covenant shall not apply: - * 1) for code that a licensee deletes from the ECC Code; - * 2) separates from the ECC Code; or - * 3) for infringements caused by: - * i) the modification of the ECC Code or - * ii) the combination of the ECC Code with other software or - * devices where such combination causes the infringement. - * - * The software is originally written by Sheueling Chang Shantz and - * Douglas Stebila of Sun Microsystems Laboratories. - * - */ - -/* - * NOTE: This file is licensed pursuant to the OpenSSL license below and may - * be modified; but after modifications, the above covenant may no longer - * apply! In such cases, the corresponding paragraph ["In addition, Sun - * covenants ... causes the infringement."] and this note can be edited out; - * but please keep the Sun copyright notice and attribution. - */ - -/* ==================================================================== - * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. - * - * 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 above 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 acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" - * - * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to - * endorse or promote products derived from this software without - * prior written permission. For written permission, please contact - * openssl-core@openssl.org. - * - * 5. Products derived from this software may not be called "OpenSSL" - * nor may "OpenSSL" appear in their names without prior written - * permission of the OpenSSL Project. - * - * 6. Redistributions of any form whatsoever must retain the following - * acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit (http://www.openssl.org/)" - * - * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY - * EXPRESSED 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 OpenSSL PROJECT OR - * ITS 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. - * ==================================================================== - * - * This product includes cryptographic software written by Eric Young - * (eay@cryptsoft.com). This product includes software written by Tim - * Hudson (tjh@cryptsoft.com). - * - */ - -#include <assert.h> -#include <limits.h> -#include <stdio.h> -#include "cryptlib.h" -#include "bn_lcl.h" - -#ifndef OPENSSL_NO_EC2M - -/* - * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should - * fail. - */ -# define MAX_ITERATIONS 50 - -static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21, - 64, 65, 68, 69, 80, 81, 84, 85 -}; - -/* Platform-specific macros to accelerate squaring. */ -# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) -# define SQR1(w) \ - SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \ - SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \ - SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \ - SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF] -# define SQR0(w) \ - SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \ - SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \ - SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ - SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] -# endif -# ifdef THIRTY_TWO_BIT -# define SQR1(w) \ - SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \ - SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF] -# define SQR0(w) \ - SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ - SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] -# endif - -# if !defined(OPENSSL_BN_ASM_GF2m) -/* - * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is - * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that - * the variables have the right amount of space allocated. - */ -# ifdef THIRTY_TWO_BIT -static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, - const BN_ULONG b) -{ - register BN_ULONG h, l, s; - BN_ULONG tab[8], top2b = a >> 30; - register BN_ULONG a1, a2, a4; - - a1 = a & (0x3FFFFFFF); - a2 = a1 << 1; - a4 = a2 << 1; - - tab[0] = 0; - tab[1] = a1; - tab[2] = a2; - tab[3] = a1 ^ a2; - tab[4] = a4; - tab[5] = a1 ^ a4; - tab[6] = a2 ^ a4; - tab[7] = a1 ^ a2 ^ a4; - - s = tab[b & 0x7]; - l = s; - s = tab[b >> 3 & 0x7]; - l ^= s << 3; - h = s >> 29; - s = tab[b >> 6 & 0x7]; - l ^= s << 6; - h ^= s >> 26; - s = tab[b >> 9 & 0x7]; - l ^= s << 9; - h ^= s >> 23; - s = tab[b >> 12 & 0x7]; - l ^= s << 12; - h ^= s >> 20; - s = tab[b >> 15 & 0x7]; - l ^= s << 15; - h ^= s >> 17; - s = tab[b >> 18 & 0x7]; - l ^= s << 18; - h ^= s >> 14; - s = tab[b >> 21 & 0x7]; - l ^= s << 21; - h ^= s >> 11; - s = tab[b >> 24 & 0x7]; - l ^= s << 24; - h ^= s >> 8; - s = tab[b >> 27 & 0x7]; - l ^= s << 27; - h ^= s >> 5; - s = tab[b >> 30]; - l ^= s << 30; - h ^= s >> 2; - - /* compensate for the top two bits of a */ - - if (top2b & 01) { - l ^= b << 30; - h ^= b >> 2; - } - if (top2b & 02) { - l ^= b << 31; - h ^= b >> 1; - } - - *r1 = h; - *r0 = l; -} -# endif -# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) -static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, - const BN_ULONG b) -{ - register BN_ULONG h, l, s; - BN_ULONG tab[16], top3b = a >> 61; - register BN_ULONG a1, a2, a4, a8; - - a1 = a & (0x1FFFFFFFFFFFFFFFULL); - a2 = a1 << 1; - a4 = a2 << 1; - a8 = a4 << 1; - - tab[0] = 0; - tab[1] = a1; - tab[2] = a2; - tab[3] = a1 ^ a2; - tab[4] = a4; - tab[5] = a1 ^ a4; - tab[6] = a2 ^ a4; - tab[7] = a1 ^ a2 ^ a4; - tab[8] = a8; - tab[9] = a1 ^ a8; - tab[10] = a2 ^ a8; - tab[11] = a1 ^ a2 ^ a8; - tab[12] = a4 ^ a8; - tab[13] = a1 ^ a4 ^ a8; - tab[14] = a2 ^ a4 ^ a8; - tab[15] = a1 ^ a2 ^ a4 ^ a8; - - s = tab[b & 0xF]; - l = s; - s = tab[b >> 4 & 0xF]; - l ^= s << 4; - h = s >> 60; - s = tab[b >> 8 & 0xF]; - l ^= s << 8; - h ^= s >> 56; - s = tab[b >> 12 & 0xF]; - l ^= s << 12; - h ^= s >> 52; - s = tab[b >> 16 & 0xF]; - l ^= s << 16; - h ^= s >> 48; - s = tab[b >> 20 & 0xF]; - l ^= s << 20; - h ^= s >> 44; - s = tab[b >> 24 & 0xF]; - l ^= s << 24; - h ^= s >> 40; - s = tab[b >> 28 & 0xF]; - l ^= s << 28; - h ^= s >> 36; - s = tab[b >> 32 & 0xF]; - l ^= s << 32; - h ^= s >> 32; - s = tab[b >> 36 & 0xF]; - l ^= s << 36; - h ^= s >> 28; - s = tab[b >> 40 & 0xF]; - l ^= s << 40; - h ^= s >> 24; - s = tab[b >> 44 & 0xF]; - l ^= s << 44; - h ^= s >> 20; - s = tab[b >> 48 & 0xF]; - l ^= s << 48; - h ^= s >> 16; - s = tab[b >> 52 & 0xF]; - l ^= s << 52; - h ^= s >> 12; - s = tab[b >> 56 & 0xF]; - l ^= s << 56; - h ^= s >> 8; - s = tab[b >> 60]; - l ^= s << 60; - h ^= s >> 4; - - /* compensate for the top three bits of a */ - - if (top3b & 01) { - l ^= b << 61; - h ^= b >> 3; - } - if (top3b & 02) { - l ^= b << 62; - h ^= b >> 2; - } - if (top3b & 04) { - l ^= b << 63; - h ^= b >> 1; - } - - *r1 = h; - *r0 = l; -} -# endif - -/* - * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, - * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST - * ensure that the variables have the right amount of space allocated. - */ -static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, - const BN_ULONG b1, const BN_ULONG b0) -{ - BN_ULONG m1, m0; - /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ - bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1); - bn_GF2m_mul_1x1(r + 1, r, a0, b0); - bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); - /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ - r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ - r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ -} -# else -void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, - BN_ULONG b0); -# endif - -/* - * Add polynomials a and b and store result in r; r could be a or b, a and b - * could be equal; r is the bitwise XOR of a and b. - */ -int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) -{ - int i; - const BIGNUM *at, *bt; - - bn_check_top(a); - bn_check_top(b); - - if (a->top < b->top) { - at = b; - bt = a; - } else { - at = a; - bt = b; - } - - if (bn_wexpand(r, at->top) == NULL) - return 0; - - for (i = 0; i < bt->top; i++) { - r->d[i] = at->d[i] ^ bt->d[i]; - } - for (; i < at->top; i++) { - r->d[i] = at->d[i]; - } - - r->top = at->top; - bn_correct_top(r); - - return 1; -} - -/*- - * Some functions allow for representation of the irreducible polynomials - * as an int[], say p. The irreducible f(t) is then of the form: - * t^p[0] + t^p[1] + ... + t^p[k] - * where m = p[0] > p[1] > ... > p[k] = 0. - */ - -/* Performs modular reduction of a and store result in r. r could be a. */ -int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) -{ - int j, k; - int n, dN, d0, d1; - BN_ULONG zz, *z; - - bn_check_top(a); - - if (!p[0]) { - /* reduction mod 1 => return 0 */ - BN_zero(r); - return 1; - } - - /* - * Since the algorithm does reduction in the r value, if a != r, copy the - * contents of a into r so we can do reduction in r. - */ - if (a != r) { - if (!bn_wexpand(r, a->top)) - return 0; - for (j = 0; j < a->top; j++) { - r->d[j] = a->d[j]; - } - r->top = a->top; - } - z = r->d; - - /* start reduction */ - dN = p[0] / BN_BITS2; - for (j = r->top - 1; j > dN;) { - zz = z[j]; - if (z[j] == 0) { - j--; - continue; - } - z[j] = 0; - - for (k = 1; p[k] != 0; k++) { - /* reducing component t^p[k] */ - n = p[0] - p[k]; - d0 = n % BN_BITS2; - d1 = BN_BITS2 - d0; - n /= BN_BITS2; - z[j - n] ^= (zz >> d0); - if (d0) - z[j - n - 1] ^= (zz << d1); - } - - /* reducing component t^0 */ - n = dN; - d0 = p[0] % BN_BITS2; - d1 = BN_BITS2 - d0; - z[j - n] ^= (zz >> d0); - if (d0) - z[j - n - 1] ^= (zz << d1); - } - - /* final round of reduction */ - while (j == dN) { - - d0 = p[0] % BN_BITS2; - zz = z[dN] >> d0; - if (zz == 0) - break; - d1 = BN_BITS2 - d0; - - /* clear up the top d1 bits */ - if (d0) - z[dN] = (z[dN] << d1) >> d1; - else - z[dN] = 0; - z[0] ^= zz; /* reduction t^0 component */ - - for (k = 1; p[k] != 0; k++) { - BN_ULONG tmp_ulong; - - /* reducing component t^p[k] */ - n = p[k] / BN_BITS2; - d0 = p[k] % BN_BITS2; - d1 = BN_BITS2 - d0; - z[n] ^= (zz << d0); - if (d0 && (tmp_ulong = zz >> d1)) - z[n + 1] ^= tmp_ulong; - } - - } - - bn_correct_top(r); - return 1; -} - -/* - * Performs modular reduction of a by p and store result in r. r could be a. - * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper - * function is only provided for convenience; for best performance, use the - * BN_GF2m_mod_arr function. - */ -int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) -{ - int ret = 0; - int arr[6]; - bn_check_top(a); - bn_check_top(p); - ret = BN_GF2m_poly2arr(p, arr, sizeof(arr) / sizeof(arr[0])); - if (!ret || ret > (int)(sizeof(arr) / sizeof(arr[0]))) { - BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH); - return 0; - } - ret = BN_GF2m_mod_arr(r, a, arr); - bn_check_top(r); - return ret; -} - -/* - * Compute the product of two polynomials a and b, reduce modulo p, and store - * the result in r. r could be a or b; a could be b. - */ -int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, - const int p[], BN_CTX *ctx) -{ - int zlen, i, j, k, ret = 0; - BIGNUM *s; - BN_ULONG x1, x0, y1, y0, zz[4]; - - bn_check_top(a); - bn_check_top(b); - - if (a == b) { - return BN_GF2m_mod_sqr_arr(r, a, p, ctx); - } - - BN_CTX_start(ctx); - if ((s = BN_CTX_get(ctx)) == NULL) - goto err; - - zlen = a->top + b->top + 4; - if (!bn_wexpand(s, zlen)) - goto err; - s->top = zlen; - - for (i = 0; i < zlen; i++) - s->d[i] = 0; - - for (j = 0; j < b->top; j += 2) { - y0 = b->d[j]; - y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1]; - for (i = 0; i < a->top; i += 2) { - x0 = a->d[i]; - x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1]; - bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); - for (k = 0; k < 4; k++) - s->d[i + j + k] ^= zz[k]; - } - } - - bn_correct_top(s); - if (BN_GF2m_mod_arr(r, s, p)) - ret = 1; - bn_check_top(r); - - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Compute the product of two polynomials a and b, reduce modulo p, and store - * the result in r. r could be a or b; a could equal b. This function calls - * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is - * only provided for convenience; for best performance, use the - * BN_GF2m_mod_mul_arr function. - */ -int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, - const BIGNUM *p, BN_CTX *ctx) -{ - int ret = 0; - const int max = BN_num_bits(p) + 1; - int *arr = NULL; - bn_check_top(a); - bn_check_top(b); - bn_check_top(p); - if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) - goto err; - ret = BN_GF2m_poly2arr(p, arr, max); - if (!ret || ret > max) { - BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH); - goto err; - } - ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); - bn_check_top(r); - err: - if (arr) - OPENSSL_free(arr); - return ret; -} - -/* Square a, reduce the result mod p, and store it in a. r could be a. */ -int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], - BN_CTX *ctx) -{ - int i, ret = 0; - BIGNUM *s; - - bn_check_top(a); - BN_CTX_start(ctx); - if ((s = BN_CTX_get(ctx)) == NULL) - goto err; - if (!bn_wexpand(s, 2 * a->top)) - goto err; - - for (i = a->top - 1; i >= 0; i--) { - s->d[2 * i + 1] = SQR1(a->d[i]); - s->d[2 * i] = SQR0(a->d[i]); - } - - s->top = 2 * a->top; - bn_correct_top(s); - if (!BN_GF2m_mod_arr(r, s, p)) - goto err; - bn_check_top(r); - ret = 1; - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Square a, reduce the result mod p, and store it in a. r could be a. This - * function calls down to the BN_GF2m_mod_sqr_arr implementation; this - * wrapper function is only provided for convenience; for best performance, - * use the BN_GF2m_mod_sqr_arr function. - */ -int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) -{ - int ret = 0; - const int max = BN_num_bits(p) + 1; - int *arr = NULL; - - bn_check_top(a); - bn_check_top(p); - if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) - goto err; - ret = BN_GF2m_poly2arr(p, arr, max); - if (!ret || ret > max) { - BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH); - goto err; - } - ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); - bn_check_top(r); - err: - if (arr) - OPENSSL_free(arr); - return ret; -} - -/* - * Invert a, reduce modulo p, and store the result in r. r could be a. Uses - * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D., - * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic - * Curve Cryptography Over Binary Fields". - */ -int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) -{ - BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; - int ret = 0; - - bn_check_top(a); - bn_check_top(p); - - BN_CTX_start(ctx); - - if ((b = BN_CTX_get(ctx)) == NULL) - goto err; - if ((c = BN_CTX_get(ctx)) == NULL) - goto err; - if ((u = BN_CTX_get(ctx)) == NULL) - goto err; - if ((v = BN_CTX_get(ctx)) == NULL) - goto err; - - if (!BN_GF2m_mod(u, a, p)) - goto err; - if (BN_is_zero(u)) - goto err; - - if (!BN_copy(v, p)) - goto err; -# if 0 - if (!BN_one(b)) - goto err; - - while (1) { - while (!BN_is_odd(u)) { - if (BN_is_zero(u)) - goto err; - if (!BN_rshift1(u, u)) - goto err; - if (BN_is_odd(b)) { - if (!BN_GF2m_add(b, b, p)) - goto err; - } - if (!BN_rshift1(b, b)) - goto err; - } - - if (BN_abs_is_word(u, 1)) - break; - - if (BN_num_bits(u) < BN_num_bits(v)) { - tmp = u; - u = v; - v = tmp; - tmp = b; - b = c; - c = tmp; - } - - if (!BN_GF2m_add(u, u, v)) - goto err; - if (!BN_GF2m_add(b, b, c)) - goto err; - } -# else - { - int i; - int ubits = BN_num_bits(u); - int vbits = BN_num_bits(v); /* v is copy of p */ - int top = p->top; - BN_ULONG *udp, *bdp, *vdp, *cdp; - - if (!bn_wexpand(u, top)) - goto err; - udp = u->d; - for (i = u->top; i < top; i++) - udp[i] = 0; - u->top = top; - if (!bn_wexpand(b, top)) - goto err; - bdp = b->d; - bdp[0] = 1; - for (i = 1; i < top; i++) - bdp[i] = 0; - b->top = top; - if (!bn_wexpand(c, top)) - goto err; - cdp = c->d; - for (i = 0; i < top; i++) - cdp[i] = 0; - c->top = top; - vdp = v->d; /* It pays off to "cache" *->d pointers, - * because it allows optimizer to be more - * aggressive. But we don't have to "cache" - * p->d, because *p is declared 'const'... */ - while (1) { - while (ubits && !(udp[0] & 1)) { - BN_ULONG u0, u1, b0, b1, mask; - - u0 = udp[0]; - b0 = bdp[0]; - mask = (BN_ULONG)0 - (b0 & 1); - b0 ^= p->d[0] & mask; - for (i = 0; i < top - 1; i++) { - u1 = udp[i + 1]; - udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2; - u0 = u1; - b1 = bdp[i + 1] ^ (p->d[i + 1] & mask); - bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2; - b0 = b1; - } - udp[i] = u0 >> 1; - bdp[i] = b0 >> 1; - ubits--; - } - - if (ubits <= BN_BITS2) { - if (udp[0] == 0) /* poly was reducible */ - goto err; - if (udp[0] == 1) - break; - } - - if (ubits < vbits) { - i = ubits; - ubits = vbits; - vbits = i; - tmp = u; - u = v; - v = tmp; - tmp = b; - b = c; - c = tmp; - udp = vdp; - vdp = v->d; - bdp = cdp; - cdp = c->d; - } - for (i = 0; i < top; i++) { - udp[i] ^= vdp[i]; - bdp[i] ^= cdp[i]; - } - if (ubits == vbits) { - BN_ULONG ul; - int utop = (ubits - 1) / BN_BITS2; - - while ((ul = udp[utop]) == 0 && utop) - utop--; - ubits = utop * BN_BITS2 + BN_num_bits_word(ul); - } - } - bn_correct_top(b); - } -# endif - - if (!BN_copy(r, b)) - goto err; - bn_check_top(r); - ret = 1; - - err: -# ifdef BN_DEBUG /* BN_CTX_end would complain about the - * expanded form */ - bn_correct_top(c); - bn_correct_top(u); - bn_correct_top(v); -# endif - BN_CTX_end(ctx); - return ret; -} - -/* - * Invert xx, reduce modulo p, and store the result in r. r could be xx. - * This function calls down to the BN_GF2m_mod_inv implementation; this - * wrapper function is only provided for convenience; for best performance, - * use the BN_GF2m_mod_inv function. - */ -int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], - BN_CTX *ctx) -{ - BIGNUM *field; - int ret = 0; - - bn_check_top(xx); - BN_CTX_start(ctx); - if ((field = BN_CTX_get(ctx)) == NULL) - goto err; - if (!BN_GF2m_arr2poly(p, field)) - goto err; - - ret = BN_GF2m_mod_inv(r, xx, field, ctx); - bn_check_top(r); - - err: - BN_CTX_end(ctx); - return ret; -} - -# ifndef OPENSSL_SUN_GF2M_DIV -/* - * Divide y by x, reduce modulo p, and store the result in r. r could be x - * or y, x could equal y. - */ -int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, - const BIGNUM *p, BN_CTX *ctx) -{ - BIGNUM *xinv = NULL; - int ret = 0; - - bn_check_top(y); - bn_check_top(x); - bn_check_top(p); - - BN_CTX_start(ctx); - xinv = BN_CTX_get(ctx); - if (xinv == NULL) - goto err; - - if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) - goto err; - if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) - goto err; - bn_check_top(r); - ret = 1; - - err: - BN_CTX_end(ctx); - return ret; -} -# else -/* - * Divide y by x, reduce modulo p, and store the result in r. r could be x - * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from - * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the - * Great Divide". - */ -int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, - const BIGNUM *p, BN_CTX *ctx) -{ - BIGNUM *a, *b, *u, *v; - int ret = 0; - - bn_check_top(y); - bn_check_top(x); - bn_check_top(p); - - BN_CTX_start(ctx); - - a = BN_CTX_get(ctx); - b = BN_CTX_get(ctx); - u = BN_CTX_get(ctx); - v = BN_CTX_get(ctx); - if (v == NULL) - goto err; - - /* reduce x and y mod p */ - if (!BN_GF2m_mod(u, y, p)) - goto err; - if (!BN_GF2m_mod(a, x, p)) - goto err; - if (!BN_copy(b, p)) - goto err; - - while (!BN_is_odd(a)) { - if (!BN_rshift1(a, a)) - goto err; - if (BN_is_odd(u)) - if (!BN_GF2m_add(u, u, p)) - goto err; - if (!BN_rshift1(u, u)) - goto err; - } - - do { - if (BN_GF2m_cmp(b, a) > 0) { - if (!BN_GF2m_add(b, b, a)) - goto err; - if (!BN_GF2m_add(v, v, u)) - goto err; - do { - if (!BN_rshift1(b, b)) - goto err; - if (BN_is_odd(v)) - if (!BN_GF2m_add(v, v, p)) - goto err; - if (!BN_rshift1(v, v)) - goto err; - } while (!BN_is_odd(b)); - } else if (BN_abs_is_word(a, 1)) - break; - else { - if (!BN_GF2m_add(a, a, b)) - goto err; - if (!BN_GF2m_add(u, u, v)) - goto err; - do { - if (!BN_rshift1(a, a)) - goto err; - if (BN_is_odd(u)) - if (!BN_GF2m_add(u, u, p)) - goto err; - if (!BN_rshift1(u, u)) - goto err; - } while (!BN_is_odd(a)); - } - } while (1); - - if (!BN_copy(r, u)) - goto err; - bn_check_top(r); - ret = 1; - - err: - BN_CTX_end(ctx); - return ret; -} -# endif - -/* - * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx - * * or yy, xx could equal yy. This function calls down to the - * BN_GF2m_mod_div implementation; this wrapper function is only provided for - * convenience; for best performance, use the BN_GF2m_mod_div function. - */ -int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, - const int p[], BN_CTX *ctx) -{ - BIGNUM *field; - int ret = 0; - - bn_check_top(yy); - bn_check_top(xx); - - BN_CTX_start(ctx); - if ((field = BN_CTX_get(ctx)) == NULL) - goto err; - if (!BN_GF2m_arr2poly(p, field)) - goto err; - - ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); - bn_check_top(r); - - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Compute the bth power of a, reduce modulo p, and store the result in r. r - * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE - * P1363. - */ -int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, - const int p[], BN_CTX *ctx) -{ - int ret = 0, i, n; - BIGNUM *u; - - bn_check_top(a); - bn_check_top(b); - - if (BN_is_zero(b)) - return (BN_one(r)); - - if (BN_abs_is_word(b, 1)) - return (BN_copy(r, a) != NULL); - - BN_CTX_start(ctx); - if ((u = BN_CTX_get(ctx)) == NULL) - goto err; - - if (!BN_GF2m_mod_arr(u, a, p)) - goto err; - - n = BN_num_bits(b) - 1; - for (i = n - 1; i >= 0; i--) { - if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) - goto err; - if (BN_is_bit_set(b, i)) { - if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) - goto err; - } - } - if (!BN_copy(r, u)) - goto err; - bn_check_top(r); - ret = 1; - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Compute the bth power of a, reduce modulo p, and store the result in r. r - * could be a. This function calls down to the BN_GF2m_mod_exp_arr - * implementation; this wrapper function is only provided for convenience; - * for best performance, use the BN_GF2m_mod_exp_arr function. - */ -int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, - const BIGNUM *p, BN_CTX *ctx) -{ - int ret = 0; - const int max = BN_num_bits(p) + 1; - int *arr = NULL; - bn_check_top(a); - bn_check_top(b); - bn_check_top(p); - if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) - goto err; - ret = BN_GF2m_poly2arr(p, arr, max); - if (!ret || ret > max) { - BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH); - goto err; - } - ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); - bn_check_top(r); - err: - if (arr) - OPENSSL_free(arr); - return ret; -} - -/* - * Compute the square root of a, reduce modulo p, and store the result in r. - * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363. - */ -int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], - BN_CTX *ctx) -{ - int ret = 0; - BIGNUM *u; - - bn_check_top(a); - - if (!p[0]) { - /* reduction mod 1 => return 0 */ - BN_zero(r); - return 1; - } - - BN_CTX_start(ctx); - if ((u = BN_CTX_get(ctx)) == NULL) - goto err; - - if (!BN_set_bit(u, p[0] - 1)) - goto err; - ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); - bn_check_top(r); - - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Compute the square root of a, reduce modulo p, and store the result in r. - * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr - * implementation; this wrapper function is only provided for convenience; - * for best performance, use the BN_GF2m_mod_sqrt_arr function. - */ -int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) -{ - int ret = 0; - const int max = BN_num_bits(p) + 1; - int *arr = NULL; - bn_check_top(a); - bn_check_top(p); - if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) - goto err; - ret = BN_GF2m_poly2arr(p, arr, max); - if (!ret || ret > max) { - BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH); - goto err; - } - ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); - bn_check_top(r); - err: - if (arr) - OPENSSL_free(arr); - return ret; -} - -/* - * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns - * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363. - */ -int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], - BN_CTX *ctx) -{ - int ret = 0, count = 0, j; - BIGNUM *a, *z, *rho, *w, *w2, *tmp; - - bn_check_top(a_); - - if (!p[0]) { - /* reduction mod 1 => return 0 */ - BN_zero(r); - return 1; - } - - BN_CTX_start(ctx); - a = BN_CTX_get(ctx); - z = BN_CTX_get(ctx); - w = BN_CTX_get(ctx); - if (w == NULL) - goto err; - - if (!BN_GF2m_mod_arr(a, a_, p)) - goto err; - - if (BN_is_zero(a)) { - BN_zero(r); - ret = 1; - goto err; - } - - if (p[0] & 0x1) { /* m is odd */ - /* compute half-trace of a */ - if (!BN_copy(z, a)) - goto err; - for (j = 1; j <= (p[0] - 1) / 2; j++) { - if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) - goto err; - if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) - goto err; - if (!BN_GF2m_add(z, z, a)) - goto err; - } - - } else { /* m is even */ - - rho = BN_CTX_get(ctx); - w2 = BN_CTX_get(ctx); - tmp = BN_CTX_get(ctx); - if (tmp == NULL) - goto err; - do { - if (!BN_rand(rho, p[0], 0, 0)) - goto err; - if (!BN_GF2m_mod_arr(rho, rho, p)) - goto err; - BN_zero(z); - if (!BN_copy(w, rho)) - goto err; - for (j = 1; j <= p[0] - 1; j++) { - if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) - goto err; - if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) - goto err; - if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) - goto err; - if (!BN_GF2m_add(z, z, tmp)) - goto err; - if (!BN_GF2m_add(w, w2, rho)) - goto err; - } - count++; - } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); - if (BN_is_zero(w)) { - BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS); - goto err; - } - } - - if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) - goto err; - if (!BN_GF2m_add(w, z, w)) - goto err; - if (BN_GF2m_cmp(w, a)) { - BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION); - goto err; - } - - if (!BN_copy(r, z)) - goto err; - bn_check_top(r); - - ret = 1; - - err: - BN_CTX_end(ctx); - return ret; -} - -/* - * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns - * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr - * implementation; this wrapper function is only provided for convenience; - * for best performance, use the BN_GF2m_mod_solve_quad_arr function. - */ -int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, - BN_CTX *ctx) -{ - int ret = 0; - const int max = BN_num_bits(p) + 1; - int *arr = NULL; - bn_check_top(a); - bn_check_top(p); - if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) - goto err; - ret = BN_GF2m_poly2arr(p, arr, max); - if (!ret || ret > max) { - BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH); - goto err; - } - ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); - bn_check_top(r); - err: - if (arr) - OPENSSL_free(arr); - return ret; -} - -/* - * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i * - * x^i) into an array of integers corresponding to the bits with non-zero - * coefficient. Array is terminated with -1. Up to max elements of the array - * will be filled. Return value is total number of array elements that would - * be filled if array was large enough. - */ -int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) -{ - int i, j, k = 0; - BN_ULONG mask; - - if (BN_is_zero(a)) - return 0; - - for (i = a->top - 1; i >= 0; i--) { - if (!a->d[i]) - /* skip word if a->d[i] == 0 */ - continue; - mask = BN_TBIT; - for (j = BN_BITS2 - 1; j >= 0; j--) { - if (a->d[i] & mask) { - if (k < max) - p[k] = BN_BITS2 * i + j; - k++; - } - mask >>= 1; - } - } - - if (k < max) { - p[k] = -1; - k++; - } - - return k; -} - -/* - * Convert the coefficient array representation of a polynomial to a - * bit-string. The array must be terminated by -1. - */ -int BN_GF2m_arr2poly(const int p[], BIGNUM *a) -{ - int i; - - bn_check_top(a); - BN_zero(a); - for (i = 0; p[i] != -1; i++) { - if (BN_set_bit(a, p[i]) == 0) - return 0; - } - bn_check_top(a); - - return 1; -} - -#endif |