diff options
Diffstat (limited to 'openssl/crypto/bn/bn_gf2m.c')
| -rw-r--r-- | openssl/crypto/bn/bn_gf2m.c | 2110 |
1 files changed, 1145 insertions, 965 deletions
diff --git a/openssl/crypto/bn/bn_gf2m.c b/openssl/crypto/bn/bn_gf2m.c index 8a4dc20ad..aeee49a01 100644 --- a/openssl/crypto/bn/bn_gf2m.c +++ b/openssl/crypto/bn/bn_gf2m.c @@ -27,12 +27,13 @@ * */ -/* 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. */ +/* + * 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. @@ -42,7 +43,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * 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 @@ -96,1018 +97,1197 @@ #ifndef OPENSSL_NO_EC2M -/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */ -#define MAX_ITERATIONS 50 +/* + * 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 +}; -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) \ +# 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) \ +# 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) \ +# 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) \ +# 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 +# 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. +# 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. +# 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 +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 +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); - 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. - * +{ + 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 + * 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 +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 +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; - } - +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) 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_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) + 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) + 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_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, ubits = BN_num_bits(u), - vbits = BN_num_bits(v), /* v is copy of p */ - top = p->top; - BN_ULONG *udp,*bdp,*vdp,*cdp; - - bn_wexpand(u,top); udp = u->d; - for (i=u->top;i<top;i++) udp[i] = 0; - u->top = top; - bn_wexpand(b,top); bdp = b->d; - bdp[0] = 1; - for (i=1;i<top;i++) bdp[i] = 0; - b->top = top; - bn_wexpand(c,top); 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 && 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. +{ + 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, ubits = BN_num_bits(u), vbits = BN_num_bits(v), /* v is copy + * of p */ + top = p->top; + BN_ULONG *udp, *bdp, *vdp, *cdp; + + bn_wexpand(u, top); + udp = u->d; + for (i = u->top; i < top; i++) + udp[i] = 0; + u->top = top; + bn_wexpand(b, top); + bdp = b->d; + bdp[0] = 1; + for (i = 1; i < top; i++) + bdp[i] = 0; + b->top = top; + bn_wexpand(c, top); + 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 && 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 +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 *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(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_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_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_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_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 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_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_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 +{ + 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; - } +{ + 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 |