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Diffstat (limited to 'security/nss/lib/freebl/mpi/mp_gf2m.c')
| -rw-r--r-- | security/nss/lib/freebl/mpi/mp_gf2m.c | 570 |
1 files changed, 570 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/mp_gf2m.c b/security/nss/lib/freebl/mpi/mp_gf2m.c new file mode 100644 index 000000000..93d419611 --- /dev/null +++ b/security/nss/lib/freebl/mpi/mp_gf2m.c @@ -0,0 +1,570 @@ +/* + * Version: MPL 1.1/GPL 2.0/LGPL 2.1 + * + * The contents of this file are subject to the Mozilla Public License Version + * 1.1 (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * Software distributed under the License is distributed on an "AS IS" basis, + * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License + * for the specific language governing rights and limitations under the + * License. + * + * The Original Code is the Multi-precision Binary Polynomial Arithmetic + * Library. + * + * The Initial Developer of the Original Code is Sun Microsystems, Inc. + * Portions created by Sun Microsystems, Inc. are Copyright (C) 2003 + * Sun Microsystems, Inc. All Rights Reserved. + * + * Contributor(s): + * Sheueling Chang Shantz <sheueling.chang@sun.com> and + * Douglas Stebila <douglas@stebila.ca> of Sun Laboratories. + * + * Alternatively, the contents of this file may be used under the terms of + * either the GNU General Public License Version 2 or later (the "GPL"), or + * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), + * in which case the provisions of the GPL or the LGPL are applicable instead + * of those above. If you wish to allow use of your version of this file only + * under the terms of either the GPL or the LGPL, and not to allow others to + * use your version of this file under the terms of the MPL, indicate your + * decision by deleting the provisions above and replace them with the notice + * and other provisions required by the GPL or the LGPL. If you do not delete + * the provisions above, a recipient may use your version of this file under + * the terms of any one of the MPL, the GPL or the LGPL. + * + */ + +#include "mp_gf2m.h" +#include "mplogic.h" +#include "mpi-priv.h" + +static const mp_digit SQR_tb[16] = +{ + 0, 1, 4, 5, 16, 17, 20, 21, + 64, 65, 68, 69, 80, 81, 84, 85 +}; + +#if defined(MP_USE_UINT_DIGIT) +#define MP_DIGIT_BITS 32 + +/* Platform-specific macros for fast binary polynomial squaring. */ + +#define gf2m_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 gf2m_SQR0(w) \ + SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ + SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] + +/* Multiply two binary polynomials mp_digits a, b. + * Result is a polynomial with degree < 2 * MP_DIGIT_BITS - 1. + * Output in two mp_digits rh, rl. + */ +static void +s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b) +{ + register mp_digit h, l, s; + mp_digit tab[8], top2b = a >> 30; + register mp_digit 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; } + + *rh = h; *rl = l; +} +#endif + +#if defined(MP_USE_LONG_DIGIT) || defined(MP_USE_LONG_LONG_DIGIT) +#define MP_DIGIT_BITS 64 +#define MP_TOP_BIT + +/* Platform-specific fast binary polynomial squaring. */ +#define gf2m_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 gf2m_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] + +/* Multiply two binary polynomials mp_digits a, b, output in rh, rl */ +static void +s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b) +{ + register mp_digit h, l, s; + mp_digit tab[16], top3b = a >> 61; + register mp_digit a1, a2, a4, a8; + + a1 = a & (0x1FFFFFFFFFFFFFFF); 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; } + + *rh = h; *rl = l; +} +#endif + +#if 0 /* to be used later */ +/* Compute xor-multiply of two binary polynomials (a1, a0) x (b1, b0) + * result is a binary polynomial in 4 mp_digits r[4]. + * The caller MUST ensure that r has the right amount of space allocated. + */ +static void +s_bmul_2x2(mp_digit *r, const mp_digit a1, const mp_digit a0, const mp_digit b1, + const mp_digit b0) +{ + mp_digit m1, m0; + /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ + s_bmul_1x1(r+3, r+2, a1, b1); + s_bmul_1x1(r+1, r, a0, b0); + s_bmul_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; */ +} +#endif /* 0 */ + +/* Compute addition of two binary polynomials a and b, + * store result in c; c could be a or b, a and b could be equal; + * c is the bitwise XOR of a and b. + */ +mp_err +mp_badd(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_digit *pa, *pb, *pc; + mp_size ix; + mp_size used_pa, used_pb; + mp_err res = MP_OKAY; + + /* Add all digits up to the precision of b. If b had more + * precision than a initially, swap a, b first + */ + if (MP_USED(a) >= MP_USED(b)) { + pa = MP_DIGITS(a); + pb = MP_DIGITS(b); + used_pa = MP_USED(a); + used_pb = MP_USED(b); + } else { + pa = MP_DIGITS(b); + pb = MP_DIGITS(a); + used_pa = MP_USED(b); + used_pb = MP_USED(a); + } + + /* Make sure c has enough precision for the output value */ + MP_CHECKOK( s_mp_pad(c, used_pa) ); + + /* Do word-by-word xor */ + pc = MP_DIGITS(c); + for (ix = 0; ix < used_pb; ix++) { + (*pc++) = (*pa++) ^ (*pb++); + } + + /* Finish the rest of digits until we're actually done */ + for (; ix < used_pa; ++ix) { + *pc++ = *pa++; + } + + MP_USED(c) = used_pa; + MP_SIGN(c) = ZPOS; + s_mp_clamp(c); + +CLEANUP: + return res; +} + +#define s_mp_div2(a) MP_CHECKOK( mpl_rsh((a), (a), 1) ); + +/* Compute binary polynomial multiply d = a * b */ +static void +s_bmul_d(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d) +{ + mp_digit a_i, a0b0, a1b1, carry = 0; + while (a_len--) { + a_i = *a++; + s_bmul_1x1(&a1b1, &a0b0, a_i, b); + *d++ = a0b0 ^ carry; + carry = a1b1; + } + *d = carry; +} + +/* Compute binary polynomial xor multiply accumulate d ^= a * b */ +static void +s_bmul_d_add(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d) +{ + mp_digit a_i, a0b0, a1b1, carry = 0; + while (a_len--) { + a_i = *a++; + s_bmul_1x1(&a1b1, &a0b0, a_i, b); + *d++ ^= a0b0 ^ carry; + carry = a1b1; + } + *d ^= carry; +} + +/* Compute binary polynomial xor multiply c = a * b. + * All parameters may be identical. + */ +mp_err +mp_bmul(const mp_int *a, const mp_int *b, mp_int *c) +{ + mp_digit *pb, b_i; + mp_int tmp; + mp_size ib, a_used, b_used; + mp_err res = MP_OKAY; + + ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); + + if (a == c) { + MP_CHECKOK( mp_init_copy(&tmp, a) ); + if (a == b) + b = &tmp; + a = &tmp; + } else if (b == c) { + MP_CHECKOK( mp_init_copy(&tmp, b) ); + b = &tmp; + } else MP_DIGITS(&tmp) = 0; + + if (MP_USED(a) < MP_USED(b)) { + const mp_int *xch = b; /* switch a and b if b longer */ + b = a; + a = xch; + } + + MP_USED(c) = 1; MP_DIGIT(c, 0) = 0; + MP_CHECKOK( s_mp_pad(c, USED(a) + USED(b)) ); + + pb = MP_DIGITS(b); + s_bmul_d(MP_DIGITS(a), MP_USED(a), *pb++, MP_DIGITS(c)); + + /* Outer loop: Digits of b */ + a_used = MP_USED(a); + b_used = MP_USED(b); + for (ib = 1; ib < b_used; ib++) { + b_i = *pb++; + + /* Inner product: Digits of a */ + if (b_i) + s_bmul_d_add(MP_DIGITS(a), a_used, b_i, MP_DIGITS(c) + ib); + else + MP_DIGIT(c, ib + a_used) = b_i; + } + + s_mp_clamp(c); + + SIGN(c) = ZPOS; + +CLEANUP: + mp_clear(&tmp); + return res; +} + + +/* Compute modular reduction of a and store result in r. + * r could be a. + * For modular arithmetic, the irreducible polynomial f(t) is represented + * as an array of int[], where f(t) is of the form: + * f(t) = t^p[0] + t^p[1] + ... + t^p[k] + * where m = p[0] > p[1] > ... > p[k] = 0. + */ +int +mp_bmod(const mp_int *a, const unsigned int p[], mp_int *r) +{ + int j, k; + int n, dN, d0, d1; + mp_digit zz, *z, tmp; + mp_size used; + mp_err res = MP_OKAY; + + /* The algorithm does the reduction in place in r, + * if a != r, copy a into r first so reduction can be done in r + */ + if (a != r) { + MP_CHECKOK( mp_copy(a, r) ); + } + z = MP_DIGITS(r); + + /* start reduction */ + dN = p[0] / MP_DIGIT_BITS; + used = MP_USED(r); + + for (j = used - 1; j > dN;) { + + zz = z[j]; + if (zz == 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 % MP_DIGIT_BITS; + d1 = MP_DIGIT_BITS - d0; + n /= MP_DIGIT_BITS; + z[j-n] ^= (zz>>d0); + if (d0) + z[j-n-1] ^= (zz<<d1); + } + + /* reducing component t^0 */ + n = dN; + d0 = p[0] % MP_DIGIT_BITS; + d1 = MP_DIGIT_BITS - d0; + z[j-n] ^= (zz >> d0); + if (d0) + z[j-n-1] ^= (zz << d1); + + } + + /* final round of reduction */ + while (j == dN) { + + d0 = p[0] % MP_DIGIT_BITS; + zz = z[dN] >> d0; + if (zz == 0) break; + d1 = MP_DIGIT_BITS - d0; + + /* clear up the top d1 bits */ + if (d0) z[dN] = (z[dN] << d1) >> d1; + *z ^= zz; /* reduction t^0 component */ + + for (k = 1; p[k] > 0; k++) { + /* reducing component t^p[k]*/ + n = p[k] / MP_DIGIT_BITS; + d0 = p[k] % MP_DIGIT_BITS; + d1 = MP_DIGIT_BITS - d0; + z[n] ^= (zz << d0); + tmp = zz >> d1; + if (d0 && tmp) + z[n+1] ^= tmp; + } + } + + s_mp_clamp(r); +CLEANUP: + return res; +} + +/* Compute the product of two polynomials a and b, reduce modulo p, + * Store the result in r. r could be a or b; a could be b. + */ +mp_err +mp_bmulmod(const mp_int *a, const mp_int *b, const unsigned int p[], mp_int *r) +{ + mp_err res; + + if (a == b) return mp_bsqrmod(a, p, r); + if ((res = mp_bmul(a, b, r) ) != MP_OKAY) + return res; + return mp_bmod(r, p, r); +} + +/* Compute binary polynomial squaring c = a*a mod p . + * Parameter r and a can be identical. + */ + +mp_err +mp_bsqrmod(const mp_int *a, const unsigned int p[], mp_int *r) +{ + mp_digit *pa, *pr, a_i; + mp_int tmp; + mp_size ia, a_used; + mp_err res; + + ARGCHK(a != NULL && r != NULL, MP_BADARG); + + if (a == r) { + MP_CHECKOK( mp_init_copy(&tmp, a) ); + a = &tmp; + } else MP_DIGITS(&tmp) = 0; + + MP_USED(r) = 1; MP_DIGIT(r, 0) = 0; + MP_CHECKOK( s_mp_pad(r, 2*USED(a)) ); + + pa = MP_DIGITS(a); + pr = MP_DIGITS(r); + a_used = MP_USED(a); + + for (ia = 0; ia < a_used; ia++) { + a_i = *pa++; + *pr++ = gf2m_SQR0(a_i); + *pr++ = gf2m_SQR1(a_i); + } + + MP_CHECKOK( mp_bmod(r, p, r) ); + s_mp_clamp(r); + SIGN(r) = ZPOS; + +CLEANUP: + mp_clear(&tmp); + return res; +} + +/* Compute binary polynomial y/x mod p, y divided by x, reduce modulo p. + * Store the result in r. r could be x or y, and 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 +mp_bdivmod(const mp_int *y, const mp_int *x, const mp_int *pp, + const unsigned int p[], mp_int *r) +{ + mp_int aa, bb, uu; + mp_int *a, *b, *u, *v; + mp_err res = MP_OKAY; + + MP_CHECKOK( mp_init_copy(&aa, x) ); + MP_CHECKOK( mp_init_copy(&uu, y) ); + MP_CHECKOK( mp_init_copy(&bb, pp) ); + MP_CHECKOK( s_mp_pad(r, USED(pp)) ); + MP_USED(r) = 1; MP_DIGIT(r, 0) = 0; + + a = &aa; b= &bb; u=&uu; v=r; + /* reduce x and y mod p */ + MP_CHECKOK( mp_bmod(a, p, a) ); + MP_CHECKOK( mp_bmod(u, p, u) ); + + while (!mp_isodd(a)) { + s_mp_div2(a); + if (mp_isodd(u)) { + MP_CHECKOK( mp_badd(u, pp, u) ); + } + s_mp_div_2(u); + } + + do { + if (mp_cmp_mag(b, a) > 0) { + MP_CHECKOK( mp_badd(b, a, b) ); + MP_CHECKOK( mp_badd(v, u, v) ); + do { + s_mp_div2(b); + if (mp_isodd(v)) { + MP_CHECKOK( mp_badd(v, pp, v) ); + } + s_mp_div2(v); + } while (!mp_isodd(b)); + } + else if ((MP_DIGIT(a,0) == 1) && (MP_USED(a) == 1)) + break; + else { + MP_CHECKOK( mp_badd(a, b, a) ); + MP_CHECKOK( mp_badd(u, v, u) ); + do { + s_mp_div2(a); + if (mp_isodd(u)) { + MP_CHECKOK( mp_badd(u, pp, u) ); + } + s_mp_div2(u); + } while (!mp_isodd(a)); + } + } while (1); + + MP_CHECKOK( mp_copy(u, r) ); + +CLEANUP: + return res; + +} + +/* Convert the bit-string representation of a polynomial a 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 +mp_bpoly2arr(const mp_int *a, unsigned int p[], int max) +{ + int i, j, k; + mp_digit top_bit, mask; + + top_bit = 1; + top_bit <<= MP_DIGIT_BIT - 1; + + for (k = 0; k < max; k++) p[k] = 0; + k = 0; + + for (i = MP_USED(a) - 1; i >= 0; i--) { + mask = top_bit; + for (j = MP_DIGIT_BIT - 1; j >= 0; j--) { + if (MP_DIGITS(a)[i] & mask) { + if (k < max) p[k] = MP_DIGIT_BIT * 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. + */ +mp_err +mp_barr2poly(const unsigned int p[], mp_int *a) +{ + + mp_err res = MP_OKAY; + int i; + + mp_zero(a); + for (i = 0; p[i] > 0; i++) { + MP_CHECKOK( mpl_set_bit(a, p[i], 1) ); + } + MP_CHECKOK( mpl_set_bit(a, 0, 1) ); + +CLEANUP: + return MP_OKAY; +} |