diff options
Diffstat (limited to 'openssl/crypto/bn/bn_gf2m.c')
| -rw-r--r-- | openssl/crypto/bn/bn_gf2m.c | 1095 |
1 files changed, 1095 insertions, 0 deletions
diff --git a/openssl/crypto/bn/bn_gf2m.c b/openssl/crypto/bn/bn_gf2m.c new file mode 100644 index 000000000..306f029f2 --- /dev/null +++ b/openssl/crypto/bn/bn_gf2m.c @@ -0,0 +1,1095 @@ +/* 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" + +/* 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 +#ifdef SIXTEEN_BIT +#define SQR1(w) \ + SQR_tb[(w) >> 12 & 0xF] << 8 | SQR_tb[(w) >> 8 & 0xF] +#define SQR0(w) \ + SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] +#endif +#ifdef EIGHT_BIT +#define SQR1(w) \ + SQR_tb[(w) >> 4 & 0xF] +#define SQR0(w) \ + SQR_tb[(w) & 15] +#endif + +/* 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 EIGHT_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[4], top1b = a >> 7; + register BN_ULONG a1, a2; + + a1 = a & (0x7F); a2 = a1 << 1; + + tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2; + + s = tab[b & 0x3]; l = s; + s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 6; + s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 4; + s = tab[b >> 6 ]; l ^= s << 6; h ^= s >> 2; + + /* compensate for the top bit of a */ + + if (top1b & 01) { l ^= b << 7; h ^= b >> 1; } + + *r1 = h; *r0 = l; + } +#endif +#ifdef SIXTEEN_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[4], top1b = a >> 15; + register BN_ULONG a1, a2; + + a1 = a & (0x7FFF); a2 = a1 << 1; + + tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2; + + s = tab[b & 0x3]; l = s; + s = tab[b >> 2 & 0x3]; l ^= s << 2; h = s >> 14; + s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 12; + s = tab[b >> 6 & 0x3]; l ^= s << 6; h ^= s >> 10; + s = tab[b >> 8 & 0x3]; l ^= s << 8; h ^= s >> 8; + s = tab[b >>10 & 0x3]; l ^= s << 10; h ^= s >> 6; + s = tab[b >>12 & 0x3]; l ^= s << 12; h ^= s >> 4; + s = tab[b >>14 ]; l ^= s << 14; h ^= s >> 2; + + /* compensate for the top bit of a */ + + if (top1b & 01) { l ^= b << 15; h ^= b >> 1; } + + *r1 = h; *r0 = l; + } +#endif +#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; */ + } + + +/* 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; } + + bn_wexpand(r, at->top); + + 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 unsigned 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); + tmp_ulong = zz >> d1; + if (d0 && tmp_ulong) + 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; + const int max = BN_num_bits(p); + unsigned int *arr=NULL; + bn_check_top(a); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err; + ret = BN_GF2m_poly2arr(p, arr, max); + if (!ret || ret > max) + { + BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH); + goto err; + } + ret = BN_GF2m_mod_arr(r, a, arr); + bn_check_top(r); +err: + if (arr) OPENSSL_free(arr); + 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 unsigned 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); + unsigned int *arr=NULL; + bn_check_top(a); + bn_check_top(b); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned 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 unsigned 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) return 0; + 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); + unsigned int *arr=NULL; + + bn_check_top(a); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned 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, *u, *v, *tmp; + int ret = 0; + + bn_check_top(a); + bn_check_top(p); + + BN_CTX_start(ctx); + + b = BN_CTX_get(ctx); + c = BN_CTX_get(ctx); + u = BN_CTX_get(ctx); + v = BN_CTX_get(ctx); + if (v == NULL) goto err; + + if (!BN_one(b)) goto err; + if (!BN_GF2m_mod(u, a, p)) goto err; + if (!BN_copy(v, p)) goto err; + + if (BN_is_zero(u)) goto err; + + while (1) + { + while (!BN_is_odd(u)) + { + 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; + } + + + if (!BN_copy(r, b)) goto err; + bn_check_top(r); + ret = 1; + +err: + 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 unsigned 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 unsigned 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 unsigned 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); + unsigned int *arr=NULL; + bn_check_top(a); + bn_check_top(b); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned 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 unsigned 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); + unsigned int *arr=NULL; + bn_check_top(a); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned 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 unsigned int p[], BN_CTX *ctx) + { + int ret = 0, count = 0; + unsigned int 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); + unsigned int *arr=NULL; + bn_check_top(a); + bn_check_top(p); + if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned 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 , where a_0 is *not* zero) into an array + * of integers corresponding to the bits with non-zero coefficient. + * Up to max elements of the array will be filled. Return value is total + * number of coefficients that would be extracted if array was large enough. + */ +int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max) + { + int i, j, k = 0; + BN_ULONG mask; + + if (BN_is_zero(a) || !BN_is_bit_set(a, 0)) + /* a_0 == 0 => return error (the unsigned int array + * must be terminated by 0) + */ + 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; + } + } + + return k; + } + +/* Convert the coefficient array representation of a polynomial to a + * bit-string. The array must be terminated by 0. + */ +int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a) + { + int i; + + bn_check_top(a); + BN_zero(a); + for (i = 0; p[i] != 0; i++) + { + if (BN_set_bit(a, p[i]) == 0) + return 0; + } + BN_set_bit(a, 0); + bn_check_top(a); + + return 1; + } + |