diff options
Diffstat (limited to 'release/src/router/matrixssl/src/crypto/peersec/mpi.c')
| -rw-r--r-- | release/src/router/matrixssl/src/crypto/peersec/mpi.c | 3667 |
1 files changed, 0 insertions, 3667 deletions
diff --git a/release/src/router/matrixssl/src/crypto/peersec/mpi.c b/release/src/router/matrixssl/src/crypto/peersec/mpi.c deleted file mode 100644 index c37353d3..00000000 --- a/release/src/router/matrixssl/src/crypto/peersec/mpi.c +++ /dev/null @@ -1,3667 +0,0 @@ -/* - * mpi.c - * Release $Name: MATRIXSSL_1_8_8_OPEN $ - * - * multiple-precision integer library - */ -/* - * Copyright (c) PeerSec Networks, 2002-2009. All Rights Reserved. - * The latest version of this code is available at http://www.matrixssl.org - * - * This software is open source; you can redistribute it and/or modify - * it under the terms of the GNU General Public License as published by - * the Free Software Foundation; either version 2 of the License, or - * (at your option) any later version. - * - * This General Public License does NOT permit incorporating this software - * into proprietary programs. If you are unable to comply with the GPL, a - * commercial license for this software may be purchased from PeerSec Networks - * at http://www.peersec.com - * - * This program is distributed in WITHOUT ANY WARRANTY; without even the - * implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. - * See the GNU General Public License for more details. - * - * You should have received a copy of the GNU General Public License - * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA - * http://www.gnu.org/copyleft/gpl.html - */ -/******************************************************************************/ - -#include "../cryptoLayer.h" -#include <stdarg.h> - -#ifndef USE_MPI2 - -static int32 mp_exptmod_fast (psPool_t *pool, mp_int * G, mp_int * X, - mp_int * P, mp_int * Y, int32 redmode); - -/******************************************************************************/ -/* - FUTURE - 1. Convert the mp_init and mp_clear functions to not use malloc + free, - but to use static storage within the bignum variable instead - but - how to handle grow()? Maybe use a simple memory allocator - 2. verify stack usage of all functions and use of MP_LOW_MEM: - fast_mp_montgomery_reduce - fast_s_mp_mul_digs - fast_s_mp_sqr - fast_s_mp_mul_high_digs - 3. HAC stands for Handbook of Applied Cryptography - http://www.cacr.math.uwaterloo.ca/hac/ -*/ -/******************************************************************************/ -/* - Utility functions -*/ -void psZeromem(void *dst, size_t len) -{ - unsigned char *mem = (unsigned char *)dst; - - if (dst == NULL) { - return; - } - while (len-- > 0) { - *mem++ = 0; - } -} - -void psBurnStack(unsigned long len) -{ - unsigned char buf[32]; - - psZeromem(buf, sizeof(buf)); - if (len > (unsigned long)sizeof(buf)) { - psBurnStack(len - sizeof(buf)); - } -} - -/******************************************************************************/ -/* - Multiple precision integer functions - Note: we don't use va_args here to prevent portability issues. -*/ -int32 _mp_init_multi(psPool_t *pool, mp_int *mp0, mp_int *mp1, mp_int *mp2, - mp_int *mp3, mp_int *mp4, mp_int *mp5, - mp_int *mp6, mp_int *mp7) -{ - mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ - int32 n = 0; /* Number of ok inits */ - mp_int *tempArray[9]; - - tempArray[0] = mp0; - tempArray[1] = mp1; - tempArray[2] = mp2; - tempArray[3] = mp3; - tempArray[4] = mp4; - tempArray[5] = mp5; - tempArray[6] = mp6; - tempArray[7] = mp7; - tempArray[8] = NULL; - - while (tempArray[n] != NULL) { - if (mp_init(pool, tempArray[n]) != MP_OKAY) { - res = MP_MEM; - break; - } - n++; - } - - if (res == MP_MEM) { - n = 0; - while (tempArray[n] != NULL) { - mp_clear(tempArray[n]); - n++; - } - } - return res; /* Assumed ok, if error flagged above. */ -} -/******************************************************************************/ -/* - Reads a unsigned char array, assumes the msb is stored first [big endian] - */ -int32 mp_read_unsigned_bin (mp_int * a, unsigned char *b, int32 c) -{ - int32 res; - -/* - Make sure there are at least two digits. - */ - if (a->alloc < 2) { - if ((res = mp_grow(a, 2)) != MP_OKAY) { - return res; - } - } - -/* - Zero the int32. - */ - mp_zero (a); - -/* - read the bytes in - */ - while (c-- > 0) { - if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) { - return res; - } - -#ifndef MP_8BIT - a->dp[0] |= *b++; - a->used += 1; -#else - a->dp[0] = (*b & MP_MASK); - a->dp[1] |= ((*b++ >> 7U) & 1); - a->used += 2; -#endif /* MP_8BIT */ - } - mp_clamp (a); - return MP_OKAY; -} - -/******************************************************************************/ -/* - Compare two ints (signed) - */ -int32 mp_cmp (mp_int * a, mp_int * b) -{ -/* - compare based on sign - */ - if (a->sign != b->sign) { - if (a->sign == MP_NEG) { - return MP_LT; - } else { - return MP_GT; - } - } - -/* - compare digits - */ - if (a->sign == MP_NEG) { - /* if negative compare opposite direction */ - return mp_cmp_mag(b, a); - } else { - return mp_cmp_mag(a, b); - } -} - -/******************************************************************************/ -/* - Store in unsigned [big endian] format. -*/ -int32 mp_to_unsigned_bin(psPool_t *pool, mp_int * a, unsigned char *b) -{ - int32 x, res; - mp_int t; - - if ((res = mp_init_copy(pool, &t, a)) != MP_OKAY) { - return res; - } - - x = 0; - while (mp_iszero (&t) == 0) { -#ifndef MP_8BIT - b[x++] = (unsigned char) (t.dp[0] & 255); -#else - b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7)); -#endif /* MP_8BIT */ - if ((res = mp_div_2d (pool, &t, 8, &t, NULL)) != MP_OKAY) { - mp_clear (&t); - return res; - } - } - bn_reverse (b, x); - mp_clear (&t); - return MP_OKAY; -} - -void _mp_clear_multi(mp_int *mp0, mp_int *mp1, mp_int *mp2, mp_int *mp3, - mp_int *mp4, mp_int *mp5, mp_int *mp6, mp_int *mp7) -{ - int32 n = 0; /* Number of ok inits */ - - mp_int *tempArray[9]; - - tempArray[0] = mp0; - tempArray[1] = mp1; - tempArray[2] = mp2; - tempArray[3] = mp3; - tempArray[4] = mp4; - tempArray[5] = mp5; - tempArray[6] = mp6; - tempArray[7] = mp7; - tempArray[8] = NULL; - - for (n = 0; tempArray[n] != NULL; n++) { - mp_clear(tempArray[n]); - } -} - -/******************************************************************************/ -/* - Init a new mp_int. -*/ -int32 mp_init (psPool_t *pool, mp_int * a) -{ - int32 i; -/* - allocate memory required and clear it - */ - a->dp = OPT_CAST(mp_digit) psMalloc(pool, sizeof (mp_digit) * MP_PREC); - if (a->dp == NULL) { - return MP_MEM; - } - -/* - set the digits to zero - */ - for (i = 0; i < MP_PREC; i++) { - a->dp[i] = 0; - } -/* - set the used to zero, allocated digits to the default precision and sign - to positive - */ - a->used = 0; - a->alloc = MP_PREC; - a->sign = MP_ZPOS; - - return MP_OKAY; -} - -/******************************************************************************/ -/* - clear one (frees). - */ -void mp_clear (mp_int * a) -{ - int32 i; -/* - only do anything if a hasn't been freed previously - */ - if (a->dp != NULL) { -/* - first zero the digits - */ - for (i = 0; i < a->used; i++) { - a->dp[i] = 0; - } - - /* free ram */ - psFree (a->dp); - -/* - reset members to make debugging easier - */ - a->dp = NULL; - a->alloc = a->used = 0; - a->sign = MP_ZPOS; - } -} - -/******************************************************************************/ -/* - Get the size for an unsigned equivalent. - */ -int32 mp_unsigned_bin_size (mp_int * a) -{ - int32 size = mp_count_bits (a); - - return (size / 8 + ((size & 7) != 0 ? 1 : 0)); -} - -/******************************************************************************/ -/* - Trim unused digits - - This is used to ensure that leading zero digits are trimed and the - leading "used" digit will be non-zero. Typically very fast. Also fixes - the sign if there are no more leading digits -*/ -void mp_clamp (mp_int * a) -{ -/* - decrease used while the most significant digit is zero. - */ - while (a->used > 0 && a->dp[a->used - 1] == 0) { - --(a->used); - } - -/* - reset the sign flag if used == 0 - */ - if (a->used == 0) { - a->sign = MP_ZPOS; - } -} - -/******************************************************************************/ -/* - Shift left by a certain bit count. - */ -int32 mp_mul_2d (mp_int * a, int32 b, mp_int * c) -{ - mp_digit d; - int32 res; - -/* - Copy - */ - if (a != c) { - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } - } - - if (c->alloc < (int32)(c->used + b/DIGIT_BIT + 1)) { - if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } - } - -/* - Shift by as many digits in the bit count - */ - if (b >= (int32)DIGIT_BIT) { - if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { - return res; - } - } - -/* - shift any bit count < DIGIT_BIT - */ - d = (mp_digit) (b % DIGIT_BIT); - if (d != 0) { - register mp_digit *tmpc, shift, mask, r, rr; - register int32 x; - -/* - bitmask for carries - */ - mask = (((mp_digit)1) << d) - 1; - -/* - shift for msbs - */ - shift = DIGIT_BIT - d; - - /* alias */ - tmpc = c->dp; - - /* carry */ - r = 0; - for (x = 0; x < c->used; x++) { -/* - get the higher bits of the current word - */ - rr = (*tmpc >> shift) & mask; - -/* - shift the current word and OR in the carry - */ - *tmpc = ((*tmpc << d) | r) & MP_MASK; - ++tmpc; - -/* - set the carry to the carry bits of the current word - */ - r = rr; - } - -/* - set final carry - */ - if (r != 0) { - c->dp[(c->used)++] = r; - } - } - mp_clamp (c); - return MP_OKAY; -} - -/******************************************************************************/ -/* - Set to zero. - */ -void mp_zero (mp_int * a) -{ - int n; - mp_digit *tmp; - - a->sign = MP_ZPOS; - a->used = 0; - - tmp = a->dp; - for (n = 0; n < a->alloc; n++) { - *tmp++ = 0; - } -} - -#ifdef MP_LOW_MEM -#define TAB_SIZE 32 -#else -#define TAB_SIZE 256 -#endif /* MP_LOW_MEM */ - -/******************************************************************************/ -/* - Compare maginitude of two ints (unsigned). - */ -int32 mp_cmp_mag (mp_int * a, mp_int * b) -{ - int32 n; - mp_digit *tmpa, *tmpb; - -/* - compare based on # of non-zero digits - */ - if (a->used > b->used) { - return MP_GT; - } - - if (a->used < b->used) { - return MP_LT; - } - - /* alias for a */ - tmpa = a->dp + (a->used - 1); - - /* alias for b */ - tmpb = b->dp + (a->used - 1); - -/* - compare based on digits - */ - for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { - if (*tmpa > *tmpb) { - return MP_GT; - } - - if (*tmpa < *tmpb) { - return MP_LT; - } - } - return MP_EQ; -} - -/******************************************************************************/ -/* - computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 - - Uses a left-to-right k-ary sliding window to compute the modular - exponentiation. The value of k changes based on the size of the exponent. - - Uses Montgomery or Diminished Radix reduction [whichever appropriate] -*/ -int32 mp_exptmod(psPool_t *pool, mp_int * G, mp_int * X, mp_int * P, mp_int * Y) -{ - -/* - modulus P must be positive - */ - if (P->sign == MP_NEG) { - return MP_VAL; - } - -/* - if exponent X is negative we have to recurse - */ - if (X->sign == MP_NEG) { - mp_int tmpG, tmpX; - int32 err; - -/* - first compute 1/G mod P - */ - if ((err = mp_init(pool, &tmpG)) != MP_OKAY) { - return err; - } - if ((err = mp_invmod(pool, G, P, &tmpG)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } - -/* - now get |X| - */ - if ((err = mp_init(pool, &tmpX)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } - if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { - mp_clear(&tmpG); - mp_clear(&tmpX); - return err; - } - -/* - and now compute (1/G)**|X| instead of G**X [X < 0] - */ - err = mp_exptmod(pool, &tmpG, &tmpX, P, Y); - mp_clear(&tmpG); - mp_clear(&tmpX); - return err; - } - -/* - if the modulus is odd or dr != 0 use the fast method - */ - if (mp_isodd (P) == 1) { - return mp_exptmod_fast (pool, G, X, P, Y, 0); - } else { -/* - no exptmod for evens - */ - return MP_VAL; - } -} - -/******************************************************************************/ -/* - Call only from mp_exptmod to make sure this fast version qualifies -*/ -static int32 mp_exptmod_fast(psPool_t *pool, mp_int * G, mp_int * X, - mp_int * P, mp_int * Y, int32 redmode) -{ - mp_int M[TAB_SIZE], res; - mp_digit buf, mp; - int32 err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; - - -/* - use a pointer to the reduction algorithm. This allows us to use - one of many reduction algorithms without modding the guts of - the code with if statements everywhere. - */ - int32 (*redux)(mp_int*,mp_int*,mp_digit); - -/* - find window size - */ - x = mp_count_bits (X); - if (x <= 7) { - winsize = 2; - } else if (x <= 36) { - winsize = 3; - } else if (x <= 140) { - winsize = 4; - } else if (x <= 450) { - winsize = 5; - } else if (x <= 1303) { - winsize = 6; - } else if (x <= 3529) { - winsize = 7; - } else { - winsize = 8; - } - -#ifdef MP_LOW_MEM - if (winsize > 5) { - winsize = 5; - } -#endif - -/* - init M array - init first cell - */ - if ((err = mp_init(pool, &M[1])) != MP_OKAY) { - return err; - } - -/* - now init the second half of the array - */ - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - if ((err = mp_init(pool, &M[x])) != MP_OKAY) { - for (y = 1<<(winsize-1); y < x; y++) { - mp_clear(&M[y]); - } - mp_clear(&M[1]); - return err; - } - } - - -/* - now setup montgomery - */ - if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) { - goto LBL_M; - } - -/* - automatically pick the comba one if available - */ - if (((P->used * 2 + 1) < MP_WARRAY) && - P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - redux = fast_mp_montgomery_reduce; - } else { -/* - use slower baseline Montgomery method - */ - redux = mp_montgomery_reduce; - } - -/* - setup result - */ - if ((err = mp_init(pool, &res)) != MP_OKAY) { - goto LBL_M; - } - -/* - create M table. The first half of the table is not computed - though accept for M[0] and M[1] -*/ - -/* - now we need R mod m - */ - if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) { - goto LBL_RES; - } - -/* - now set M[1] to G * R mod m - */ - if ((err = mp_mulmod(pool, G, &res, P, &M[1])) != MP_OKAY) { - goto LBL_RES; - } - -/* - compute the value at M[1<<(winsize-1)] by squaring - M[1] (winsize-1) times -*/ - if ((err = mp_copy(&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - - for (x = 0; x < (winsize - 1); x++) { - if ((err = mp_sqr(pool, &M[1 << (winsize - 1)], - &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - -/* - create upper table - */ - for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { - if ((err = mp_mul(pool, &M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&M[x], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - -/* - set initial mode and bit cnt - */ - mode = 0; - bitcnt = 1; - buf = 0; - digidx = X->used - 1; - bitcpy = 0; - bitbuf = 0; - - for (;;) { -/* - grab next digit as required - */ - if (--bitcnt == 0) { - /* if digidx == -1 we are out of digits so break */ - if (digidx == -1) { - break; - } - /* read next digit and reset bitcnt */ - buf = X->dp[digidx--]; - bitcnt = (int)DIGIT_BIT; - } - - /* grab the next msb from the exponent */ - y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1; - buf <<= (mp_digit)1; - -/* - if the bit is zero and mode == 0 then we ignore it - These represent the leading zero bits before the first 1 bit - in the exponent. Technically this opt is not required but it - does lower the # of trivial squaring/reductions used -*/ - if (mode == 0 && y == 0) { - continue; - } - -/* - if the bit is zero and mode == 1 then we square - */ - if (mode == 1 && y == 0) { - if ((err = mp_sqr (pool, &res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - continue; - } - -/* - else we add it to the window - */ - bitbuf |= (y << (winsize - ++bitcpy)); - mode = 2; - - if (bitcpy == winsize) { -/* - ok window is filled so square as required and multiply - square first - */ - for (x = 0; x < winsize; x++) { - if ((err = mp_sqr(pool, &res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* then multiply */ - if ((err = mp_mul(pool, &res, &M[bitbuf], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - -/* - empty window and reset - */ - bitcpy = 0; - bitbuf = 0; - mode = 1; - } - } - -/* - if bits remain then square/multiply - */ - if (mode == 2 && bitcpy > 0) { - /* square then multiply if the bit is set */ - for (x = 0; x < bitcpy; x++) { - if ((err = mp_sqr(pool, &res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - -/* - get next bit of the window - */ - bitbuf <<= 1; - if ((bitbuf & (1 << winsize)) != 0) { -/* - then multiply - */ - if ((err = mp_mul(pool, &res, &M[1], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - } - } - -/* - fixup result if Montgomery reduction is used - recall that any value in a Montgomery system is - actually multiplied by R mod n. So we have - to reduce one more time to cancel out the factor of R. -*/ - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - -/* - swap res with Y - */ - mp_exch(&res, Y); - err = MP_OKAY; -LBL_RES:mp_clear(&res); -LBL_M: - mp_clear(&M[1]); - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - mp_clear(&M[x]); - } - return err; -} - -/******************************************************************************/ -/* - Grow as required - */ -int32 mp_grow (mp_int * a, int32 size) -{ - int32 i; - mp_digit *tmp; - -/* - If the alloc size is smaller alloc more ram. - */ - if (a->alloc < size) { -/* - ensure there are always at least MP_PREC digits extra on top - */ - size += (MP_PREC * 2) - (size % MP_PREC); - -/* - Reallocate the array a->dp - - We store the return in a temporary variable in case the operation - failed we don't want to overwrite the dp member of a. -*/ - tmp = OPT_CAST(mp_digit) psRealloc(a->dp, sizeof (mp_digit) * size); - if (tmp == NULL) { -/* - reallocation failed but "a" is still valid [can be freed] - */ - return MP_MEM; - } - -/* - reallocation succeeded so set a->dp - */ - a->dp = tmp; - -/* - zero excess digits - */ - i = a->alloc; - a->alloc = size; - for (; i < a->alloc; i++) { - a->dp[i] = 0; - } - } - return MP_OKAY; -} - -/******************************************************************************/ -/* - b = |a| - - Simple function copies the input and fixes the sign to positive -*/ -int32 mp_abs (mp_int * a, mp_int * b) -{ - int32 res; - -/* - copy a to b - */ - if (a != b) { - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; - } - } - -/* - Force the sign of b to positive - */ - b->sign = MP_ZPOS; - - return MP_OKAY; -} - -/******************************************************************************/ -/* - Creates "a" then copies b into it - */ -int32 mp_init_copy(psPool_t *pool, mp_int * a, mp_int * b) -{ - int32 res; - - if ((res = mp_init(pool, a)) != MP_OKAY) { - return res; - } - return mp_copy (b, a); -} - -/******************************************************************************/ -/* - Reverse an array, used for radix code - */ -void bn_reverse (unsigned char *s, int32 len) -{ - int32 ix, iy; - unsigned char t; - - ix = 0; - iy = len - 1; - while (ix < iy) { - t = s[ix]; - s[ix] = s[iy]; - s[iy] = t; - ++ix; - --iy; - } -} - -/******************************************************************************/ -/* - Shift right by a certain bit count (store quotient in c, optional - remainder in d) - */ -int32 mp_div_2d(psPool_t *pool, mp_int * a, int32 b, mp_int * c, mp_int * d) -{ - mp_digit D, r, rr; - int32 x, res; - mp_int t; - -/* - If the shift count is <= 0 then we do no work - */ - if (b <= 0) { - res = mp_copy (a, c); - if (d != NULL) { - mp_zero (d); - } - return res; - } - - if ((res = mp_init(pool, &t)) != MP_OKAY) { - return res; - } - -/* - Get the remainder - */ - if (d != NULL) { - if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - } - - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - mp_clear (&t); - return res; - } - -/* - Shift by as many digits in the bit count - */ - if (b >= (int32)DIGIT_BIT) { - mp_rshd (c, b / DIGIT_BIT); - } - - /* shift any bit count < DIGIT_BIT */ - D = (mp_digit) (b % DIGIT_BIT); - if (D != 0) { - register mp_digit *tmpc, mask, shift; - - /* mask */ - mask = (((mp_digit)1) << D) - 1; - - /* shift for lsb */ - shift = DIGIT_BIT - D; - - /* alias */ - tmpc = c->dp + (c->used - 1); - - /* carry */ - r = 0; - for (x = c->used - 1; x >= 0; x--) { -/* - Get the lower bits of this word in a temp. - */ - rr = *tmpc & mask; - -/* - shift the current word and mix in the carry bits from the previous word - */ - *tmpc = (*tmpc >> D) | (r << shift); - --tmpc; - -/* - set the carry to the carry bits of the current word found above - */ - r = rr; - } - } - mp_clamp (c); - if (d != NULL) { - mp_exch (&t, d); - } - mp_clear (&t); - return MP_OKAY; -} - -/******************************************************************************/ -/* - copy, b = a - */ -int32 mp_copy (mp_int * a, mp_int * b) -{ - int32 res, n; - -/* - If dst == src do nothing - */ - if (a == b) { - return MP_OKAY; - } - -/* - Grow dest - */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } - -/* - Zero b and copy the parameters over - */ - { - register mp_digit *tmpa, *tmpb; - - /* pointer aliases */ - /* source */ - tmpa = a->dp; - - /* destination */ - tmpb = b->dp; - - /* copy all the digits */ - for (n = 0; n < a->used; n++) { - *tmpb++ = *tmpa++; - } - - /* clear high digits */ - for (; n < b->used; n++) { - *tmpb++ = 0; - } - } - -/* - copy used count and sign - */ - b->used = a->used; - b->sign = a->sign; - return MP_OKAY; -} - -/******************************************************************************/ -/* - Returns the number of bits in an int32 - */ -int32 mp_count_bits (mp_int * a) -{ - int32 r; - mp_digit q; - -/* - Shortcut - */ - if (a->used == 0) { - return 0; - } - -/* - Get number of digits and add that. - */ - r = (a->used - 1) * DIGIT_BIT; - -/* - Take the last digit and count the bits in it. - */ - q = a->dp[a->used - 1]; - while (q > ((mp_digit) 0)) { - ++r; - q >>= ((mp_digit) 1); - } - return r; -} - -/******************************************************************************/ -/* - Shift left a certain amount of digits. - */ -int32 mp_lshd (mp_int * a, int32 b) -{ - int32 x, res; - -/* - If its less than zero return. - */ - if (b <= 0) { - return MP_OKAY; - } - -/* - Grow to fit the new digits. - */ - if (a->alloc < a->used + b) { - if ((res = mp_grow (a, a->used + b)) != MP_OKAY) { - return res; - } - } - - { - register mp_digit *top, *bottom; - -/* - Increment the used by the shift amount then copy upwards. - */ - a->used += b; - - /* top */ - top = a->dp + a->used - 1; - - /* base */ - bottom = a->dp + a->used - 1 - b; - -/* - Much like mp_rshd this is implemented using a sliding window - except the window goes the otherway around. Copying from - the bottom to the top. see bn_mp_rshd.c for more info. - */ - for (x = a->used - 1; x >= b; x--) { - *top-- = *bottom--; - } - - /* zero the lower digits */ - top = a->dp; - for (x = 0; x < b; x++) { - *top++ = 0; - } - } - return MP_OKAY; -} - -/******************************************************************************/ -/* - Set to a digit. - */ -void mp_set (mp_int * a, mp_digit b) -{ - mp_zero (a); - a->dp[0] = b & MP_MASK; - a->used = (a->dp[0] != 0) ? 1 : 0; -} - -/******************************************************************************/ -/* - Swap the elements of two integers, for cases where you can't simply swap - the mp_int pointers around -*/ -void mp_exch (mp_int * a, mp_int * b) -{ - mp_int t; - - t = *a; - *a = *b; - *b = t; -} - -/******************************************************************************/ -/* - High level multiplication (handles sign) - */ -int32 mp_mul(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c) -{ - int32 res, neg; - int32 digs = a->used + b->used + 1; - - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - -/* Can we use the fast multiplier? - - The fast multiplier can be used if the output will have less than - MP_WARRAY digits and the number of digits won't affect carry propagation -*/ - if ((digs < MP_WARRAY) && MIN(a->used, b->used) <= - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - res = fast_s_mp_mul_digs(pool, a, b, c, digs); - } else { - res = s_mp_mul(pool, a, b, c); - } - c->sign = (c->used > 0) ? neg : MP_ZPOS; - return res; -} - -/******************************************************************************/ -/* - c = a mod b, 0 <= c < b - */ -int32 mp_mod(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c) -{ - mp_int t; - int32 res; - - if ((res = mp_init(pool, &t)) != MP_OKAY) { - return res; - } - - if ((res = mp_div (pool, a, b, NULL, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - - if (t.sign != b->sign) { - res = mp_add (b, &t, c); - } else { - res = MP_OKAY; - mp_exch (&t, c); - } - - mp_clear (&t); - return res; -} - -/******************************************************************************/ -/* - shifts with subtractions when the result is greater than b. - - The method is slightly modified to shift B unconditionally upto just under - the leading bit of b. This saves alot of multiple precision shifting. -*/ -int32 mp_montgomery_calc_normalization (mp_int * a, mp_int * b) -{ - int32 x, bits, res; - -/* - How many bits of last digit does b use - */ - bits = mp_count_bits (b) % DIGIT_BIT; - - if (b->used > 1) { - if ((res = mp_2expt(a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { - return res; - } - } else { - mp_set(a, 1); - bits = 1; - } - -/* - Now compute C = A * B mod b - */ - for (x = bits - 1; x < (int32)DIGIT_BIT; x++) { - if ((res = mp_mul_2(a, a)) != MP_OKAY) { - return res; - } - if (mp_cmp_mag(a, b) != MP_LT) { - if ((res = s_mp_sub(a, b, a)) != MP_OKAY) { - return res; - } - } - } - - return MP_OKAY; -} - -/******************************************************************************/ -/* - d = a * b (mod c) - */ -int32 mp_mulmod(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, mp_int * d) -{ - int32 res; - mp_int t; - - if ((res = mp_init(pool, &t)) != MP_OKAY) { - return res; - } - - if ((res = mp_mul (pool, a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (pool, &t, c, d); - mp_clear (&t); - return res; -} - -/******************************************************************************/ -/* - Computes b = a*a - */ -#ifdef USE_SMALL_WORD -int32 mp_sqr (psPool_t *pool, mp_int * a, mp_int * b) -{ - int32 res; - -/* - Can we use the fast comba multiplier? - */ - if ((a->used * 2 + 1) < MP_WARRAY && a->used < - (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { - res = fast_s_mp_sqr (pool, a, b); - } else { - res = s_mp_sqr (pool, a, b); - } - b->sign = MP_ZPOS; - return res; -} -#endif /* USE_SMALL_WORD */ - -/******************************************************************************/ -/* - Computes xR**-1 == x (mod N) via Montgomery Reduction. - - This is an optimized implementation of montgomery_reduce - which uses the comba method to quickly calculate the columns of the - reduction. - - Based on Algorithm 14.32 on pp.601 of HAC. -*/ - -int32 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -{ - int32 ix, res, olduse; - mp_word W[MP_WARRAY]; - -/* - Get old used count - */ - olduse = x->used; - -/* - Grow a as required - */ - if (x->alloc < n->used + 1) { - if ((res = mp_grow(x, n->used + 1)) != MP_OKAY) { - return res; - } - } - -/* - First we have to get the digits of the input into - an array of double precision words W[...] - */ - { - register mp_word *_W; - register mp_digit *tmpx; - -/* - Alias for the W[] array - */ - _W = W; - -/* - Alias for the digits of x - */ - tmpx = x->dp; - -/* - Copy the digits of a into W[0..a->used-1] - */ - for (ix = 0; ix < x->used; ix++) { - *_W++ = *tmpx++; - } - -/* - Zero the high words of W[a->used..m->used*2] - */ - for (; ix < n->used * 2 + 1; ix++) { - *_W++ = 0; - } - } - -/* - Now we proceed to zero successive digits from the least - significant upwards. - */ - for (ix = 0; ix < n->used; ix++) { -/* - mu = ai * m' mod b - - We avoid a double precision multiplication (which isn't required) by - casting the value down to a mp_digit. Note this requires that - W[ix-1] have the carry cleared (see after the inner loop) - */ - register mp_digit mu; - mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); - -/* - a = a + mu * m * b**i - - This is computed in place and on the fly. The multiplication by b**i - is handled by offseting which columns the results are added to. - - Note the comba method normally doesn't handle carries in the inner loop - In this case we fix the carry from the previous column since the - Montgomery reduction requires digits of the result (so far) [see above] - to work. This is handled by fixing up one carry after the inner loop. - The carry fixups are done in order so after these loops the first - m->used words of W[] have the carries fixed - */ - { - register int32 iy; - register mp_digit *tmpn; - register mp_word *_W; - -/* - Alias for the digits of the modulus - */ - tmpn = n->dp; - -/* - Alias for the columns set by an offset of ix - */ - _W = W + ix; - -/* - inner loop - */ - for (iy = 0; iy < n->used; iy++) { - *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); - } - } - -/* - Now fix carry for next digit, W[ix+1] - */ - W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); - } - -/* - Now we have to propagate the carries and shift the words downward [all those - least significant digits we zeroed]. - */ - { - register mp_digit *tmpx; - register mp_word *_W, *_W1; - -/* - Now fix rest of carries - */ - -/* - alias for current word - */ - _W1 = W + ix; - -/* - alias for next word, where the carry goes - */ - _W = W + ++ix; - - for (; ix <= n->used * 2 + 1; ix++) { - *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); - } - -/* - copy out, A = A/b**n - - The result is A/b**n but instead of converting from an - array of mp_word to mp_digit than calling mp_rshd - we just copy them in the right order - */ - -/* - alias for destination word - */ - tmpx = x->dp; - -/* - alias for shifted double precision result - */ - _W = W + n->used; - - for (ix = 0; ix < n->used + 1; ix++) { - *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); - } - -/* - zero oldused digits, if the input a was larger than - m->used+1 we'll have to clear the digits - */ - for (; ix < olduse; ix++) { - *tmpx++ = 0; - } - } - -/* - Set the max used and clamp - */ - x->used = n->used + 1; - mp_clamp(x); - -/* - if A >= m then A = A - m - */ - if (mp_cmp_mag(x, n) != MP_LT) { - return s_mp_sub(x, n, x); - } - return MP_OKAY; -} - -/******************************************************************************/ -/* - High level addition (handles signs) - */ -int32 mp_add (mp_int * a, mp_int * b, mp_int * c) -{ - int32 sa, sb, res; - -/* - Get sign of both inputs - */ - sa = a->sign; - sb = b->sign; - -/* - Handle two cases, not four. - */ - if (sa == sb) { -/* - Both positive or both negative. Add their magnitudes, copy the sign. - */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { -/* - One positive, the other negative. Subtract the one with the greater - magnitude from the one of the lesser magnitude. The result gets the sign of - the one with the greater magnitude. - */ - if (mp_cmp_mag (a, b) == MP_LT) { - c->sign = sb; - res = s_mp_sub (b, a, c); - } else { - c->sign = sa; - res = s_mp_sub (a, b, c); - } - } - return res; -} - -/******************************************************************************/ -/* - Compare a digit. - */ -int32 mp_cmp_d (mp_int * a, mp_digit b) -{ -/* - Compare based on sign - */ - if (a->sign == MP_NEG) { - return MP_LT; - } - -/* - Compare based on magnitude - */ - if (a->used > 1) { - return MP_GT; - } - -/* - Compare the only digit of a to b - */ - if (a->dp[0] > b) { - return MP_GT; - } else if (a->dp[0] < b) { - return MP_LT; - } else { - return MP_EQ; - } -} - -/******************************************************************************/ -/* - b = a/2 - */ -int32 mp_div_2 (mp_int * a, mp_int * b) -{ - int32 x, res, oldused; - -/* - Copy - */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } - - oldused = b->used; - b->used = a->used; - { - register mp_digit r, rr, *tmpa, *tmpb; - -/* - Source alias - */ - tmpa = a->dp + b->used - 1; - -/* - dest alias - */ - tmpb = b->dp + b->used - 1; - -/* - carry - */ - r = 0; - for (x = b->used - 1; x >= 0; x--) { -/* - Get the carry for the next iteration - */ - rr = *tmpa & 1; - -/* - Shift the current digit, add in carry and store - */ - *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); -/* - Forward carry to next iteration - */ - r = rr; - } - -/* - Zero excess digits - */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - mp_clamp (b); - return MP_OKAY; -} - -/******************************************************************************/ -/* - Computes xR**-1 == x (mod N) via Montgomery Reduction - */ -#ifdef USE_SMALL_WORD -int32 mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -{ - int32 ix, res, digs; - mp_digit mu; - -/* Can the fast reduction [comba] method be used? - - Note that unlike in mul you're safely allowed *less* than the available - columns [255 per default] since carries are fixed up in the inner loop. - */ - digs = n->used * 2 + 1; - if ((digs < MP_WARRAY) && - n->used < - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_mp_montgomery_reduce (x, n, rho); - } - -/* - Grow the input as required. - */ - if (x->alloc < digs) { - if ((res = mp_grow (x, digs)) != MP_OKAY) { - return res; - } - } - x->used = digs; - - for (ix = 0; ix < n->used; ix++) { -/* - mu = ai * rho mod b - - The value of rho must be precalculated via mp_montgomery_setup() - such that it equals -1/n0 mod b this allows the following inner - loop to reduce the input one digit at a time - */ - mu = (mp_digit)(((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); - - /* a = a + mu * m * b**i */ - { - register int32 iy; - register mp_digit *tmpn, *tmpx, u; - register mp_word r; - -/* - alias for digits of the modulus - */ - tmpn = n->dp; - -/* - alias for the digits of x [the input] - */ - tmpx = x->dp + ix; - -/* - set the carry to zero - */ - u = 0; - -/* - Multiply and add in place - */ - for (iy = 0; iy < n->used; iy++) { - /* compute product and sum */ - r = ((mp_word)mu) * ((mp_word)*tmpn++) + - ((mp_word) u) + ((mp_word) * tmpx); - - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - - /* fix digit */ - *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); - } - /* At this point the ix'th digit of x should be zero */ - - -/* - propagate carries upwards as required - */ - while (u) { - *tmpx += u; - u = *tmpx >> DIGIT_BIT; - *tmpx++ &= MP_MASK; - } - } - } - -/* - At this point the n.used'th least significant digits of x are all zero - which means we can shift x to the right by n.used digits and the - residue is unchanged. -*/ - /* x = x/b**n.used */ - mp_clamp(x); - mp_rshd (x, n->used); - - /* if x >= n then x = x - n */ - if (mp_cmp_mag (x, n) != MP_LT) { - return s_mp_sub (x, n, x); - } - - return MP_OKAY; -} -#endif /* USE_SMALL_WORD */ - -/******************************************************************************/ -/* - Setups the montgomery reduction stuff. - */ -int32 mp_montgomery_setup (mp_int * n, mp_digit * rho) -{ - mp_digit x, b; - -/* - fast inversion mod 2**k - - Based on the fact that - - XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) - => 2*X*A - X*X*A*A = 1 - => 2*(1) - (1) = 1 -*/ - b = n->dp[0]; - - if ((b & 1) == 0) { - return MP_VAL; - } - - x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ - x = (x * (2 - b * x)) & MP_MASK; /* here x*a==1 mod 2**8 */ -#if !defined(MP_8BIT) - x = (x * (2 - b * x)) & MP_MASK; /* here x*a==1 mod 2**8 */ -#endif /* MP_8BIT */ -#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT)) - x *= 2 - b * x; /* here x*a==1 mod 2**32 */ -#endif -#ifdef MP_64BIT - x *= 2 - b * x; /* here x*a==1 mod 2**64 */ -#endif /* MP_64BIT */ - - /* rho = -1/m mod b */ - *rho = (((mp_word) 1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; - - return MP_OKAY; -} - -/******************************************************************************/ -/* - High level subtraction (handles signs) - */ -int32 mp_sub (mp_int * a, mp_int * b, mp_int * c) -{ - int32 sa, sb, res; - - sa = a->sign; - sb = b->sign; - - if (sa != sb) { -/* - Subtract a negative from a positive, OR subtract a positive from a - negative. In either case, ADD their magnitudes, and use the sign of - the first number. - */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { -/* - Subtract a positive from a positive, OR subtract a negative - from a negative. First, take the difference between their - magnitudes, then... - */ - if (mp_cmp_mag (a, b) != MP_LT) { -/* - Copy the sign from the first - */ - c->sign = sa; - /* The first has a larger or equal magnitude */ - res = s_mp_sub (a, b, c); - } else { -/* - The result has the *opposite* sign from the first number. - */ - c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; -/* - The second has a larger magnitude - */ - res = s_mp_sub (b, a, c); - } - } - return res; -} - -/******************************************************************************/ -/* - calc a value mod 2**b - */ -int32 mp_mod_2d (mp_int * a, int32 b, mp_int * c) -{ - int32 x, res; - -/* - if b is <= 0 then zero the int32 - */ - if (b <= 0) { - mp_zero (c); - return MP_OKAY; - } - -/* - If the modulus is larger than the value than return - */ - if (b >=(int32) (a->used * DIGIT_BIT)) { - res = mp_copy (a, c); - return res; - } - - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } - -/* - Zero digits above the last digit of the modulus - */ - for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) { - c->dp[x] = 0; - } -/* - Clear the digit that is not completely outside/inside the modulus - */ - c->dp[b / DIGIT_BIT] &= - (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); - mp_clamp (c); - return MP_OKAY; -} - -/******************************************************************************/ -/* - Shift right a certain amount of digits. - */ -void mp_rshd (mp_int * a, int32 b) -{ - int32 x; - -/* - If b <= 0 then ignore it - */ - if (b <= 0) { - return; - } - -/* - If b > used then simply zero it and return. -*/ - if (a->used <= b) { - mp_zero (a); - return; - } - - { - register mp_digit *bottom, *top; - -/* - Shift the digits down - */ - /* bottom */ - bottom = a->dp; - - /* top [offset into digits] */ - top = a->dp + b; - -/* - This is implemented as a sliding window where the window is b-digits long - and digits from the top of the window are copied to the bottom. - - e.g. - - b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> - /\ | ----> - \-------------------/ ----> - */ - for (x = 0; x < (a->used - b); x++) { - *bottom++ = *top++; - } - -/* - Zero the top digits - */ - for (; x < a->used; x++) { - *bottom++ = 0; - } - } - -/* - Remove excess digits - */ - a->used -= b; -} - -/******************************************************************************/ -/* - Low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 - */ -int32 s_mp_sub (mp_int * a, mp_int * b, mp_int * c) -{ - int32 olduse, res, min, max; - -/* - Find sizes - */ - min = b->used; - max = a->used; - -/* - init result - */ - if (c->alloc < max) { - if ((res = mp_grow (c, max)) != MP_OKAY) { - return res; - } - } - olduse = c->used; - c->used = max; - - { - register mp_digit u, *tmpa, *tmpb, *tmpc; - register int32 i; - -/* - alias for digit pointers - */ - tmpa = a->dp; - tmpb = b->dp; - tmpc = c->dp; - -/* - set carry to zero - */ - u = 0; - for (i = 0; i < min; i++) { - /* T[i] = A[i] - B[i] - U */ - *tmpc = *tmpa++ - *tmpb++ - u; - -/* - U = carry bit of T[i] - Note this saves performing an AND operation since if a carry does occur it - will propagate all the way to the MSB. As a result a single shift - is enough to get the carry - */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); - - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } - -/* - Now copy higher words if any, e.g. if A has more digits than B - */ - for (; i < max; i++) { - /* T[i] = A[i] - U */ - *tmpc = *tmpa++ - u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); - - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } - -/* - Clear digits above used (since we may not have grown result above) - */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } - - mp_clamp (c); - return MP_OKAY; -} -/******************************************************************************/ -/* - integer signed division. - - c*b + d == a [e.g. a/b, c=quotient, d=remainder] - HAC pp.598 Algorithm 14.20 - - Note that the description in HAC is horribly incomplete. For example, - it doesn't consider the case where digits are removed from 'x' in the inner - loop. It also doesn't consider the case that y has fewer than three - digits, etc.. - - The overall algorithm is as described as 14.20 from HAC but fixed to - treat these cases. - */ -#ifdef MP_DIV_SMALL -int32 mp_div(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, mp_int * d) -{ - mp_int ta, tb, tq, q; - int32 res, n, n2; - -/* - is divisor zero ? - */ - if (mp_iszero (b) == 1) { - return MP_VAL; - } - -/* - if a < b then q=0, r = a - */ - if (mp_cmp_mag (a, b) == MP_LT) { - if (d != NULL) { - res = mp_copy (a, d); - } else { - res = MP_OKAY; - } - if (c != NULL) { - mp_zero (c); - } - return res; - } - -/* - init our temps - */ - if ((res = _mp_init_multi(pool, &ta, &tb, &tq, &q, NULL, NULL, NULL, NULL) != MP_OKAY)) { - return res; - } - -/* - tq = 2^n, tb == b*2^n - */ - mp_set(&tq, 1); - n = mp_count_bits(a) - mp_count_bits(b); - if (((res = mp_abs(a, &ta)) != MP_OKAY) || - ((res = mp_abs(b, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { - goto __ERR; - } -/* old - if (((res = mp_copy(a, &ta)) != MP_OKAY) || - ((res = mp_copy(b, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || - ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { - goto LBL_ERR; - } -*/ - while (n-- >= 0) { - if (mp_cmp(&tb, &ta) != MP_GT) { - if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || - ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { - goto LBL_ERR; - } - } - if (((res = mp_div_2d(pool, &tb, 1, &tb, NULL)) != MP_OKAY) || - ((res = mp_div_2d(pool, &tq, 1, &tq, NULL)) != MP_OKAY)) { - goto LBL_ERR; - } - } - -/* - now q == quotient and ta == remainder - */ - n = a->sign; - n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); - if (c != NULL) { - mp_exch(c, &q); - c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; - } - if (d != NULL) { - mp_exch(d, &ta); - d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; - } -LBL_ERR: - _mp_clear_multi(&ta, &tb, &tq, &q, NULL, NULL, NULL, NULL); - return res; -} -#else /* MP_DIV_SMALL */ - -int32 mp_div(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, mp_int * d) -{ - mp_int q, x, y, t1, t2; - int32 res, n, t, i, norm, neg; - -/* - is divisor zero ? - */ - if (mp_iszero(b) == 1) { - return MP_VAL; - } - -/* - if a < b then q=0, r = a - */ - if (mp_cmp_mag(a, b) == MP_LT) { - if (d != NULL) { - res = mp_copy(a, d); - } else { - res = MP_OKAY; - } - if (c != NULL) { - mp_zero(c); - } - return res; - } - - if ((res = mp_init_size(pool, &q, a->used + 2)) != MP_OKAY) { - return res; - } - q.used = a->used + 2; - - if ((res = mp_init(pool, &t1)) != MP_OKAY) { - goto LBL_Q; - } - - if ((res = mp_init(pool, &t2)) != MP_OKAY) { - goto LBL_T1; - } - - if ((res = mp_init_copy(pool, &x, a)) != MP_OKAY) { - goto LBL_T2; - } - - if ((res = mp_init_copy(pool, &y, b)) != MP_OKAY) { - goto LBL_X; - } - -/* - fix the sign - */ - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - x.sign = y.sign = MP_ZPOS; - -/* - normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] - */ - norm = mp_count_bits(&y) % DIGIT_BIT; - if (norm < (int32)(DIGIT_BIT-1)) { - norm = (DIGIT_BIT-1) - norm; - if ((res = mp_mul_2d(&x, norm, &x)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_mul_2d(&y, norm, &y)) != MP_OKAY) { - goto LBL_Y; - } - } else { - norm = 0; - } - -/* - note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 - */ - n = x.used - 1; - t = y.used - 1; - -/* - while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } - */ - if ((res = mp_lshd(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ - goto LBL_Y; - } - - while (mp_cmp(&x, &y) != MP_LT) { - ++(q.dp[n - t]); - if ((res = mp_sub(&x, &y, &x)) != MP_OKAY) { - goto LBL_Y; - } - } - -/* - reset y by shifting it back down - */ - mp_rshd(&y, n - t); - -/* - step 3. for i from n down to (t + 1) - */ - for (i = n; i >= (t + 1); i--) { - if (i > x.used) { - continue; - } - -/* - step 3.1 if xi == yt then set q{i-t-1} to b-1, - otherwise set q{i-t-1} to (xi*b + x{i-1})/yt - */ - if (x.dp[i] == y.dp[t]) { - q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); - } else { - mp_word tmp; - tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); - tmp |= ((mp_word) x.dp[i - 1]); - tmp /= ((mp_word) y.dp[t]); - if (tmp > (mp_word) MP_MASK) { - tmp = MP_MASK; - } - q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); - } - -/* - while (q{i-t-1} * (yt * b + y{t-1})) > - xi * b**2 + xi-1 * b + xi-2 - - do q{i-t-1} -= 1; - */ - q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; - do { - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; - -/* - find left hand - */ - mp_zero (&t1); - t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; - t1.dp[1] = y.dp[t]; - t1.used = 2; - if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; - } - -/* - find right hand - */ - t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; - t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; - t2.dp[2] = x.dp[i]; - t2.used = 3; - } while (mp_cmp_mag(&t1, &t2) == MP_GT); - -/* - step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} - */ - if ((res = mp_mul_d(&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_lshd(&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_sub(&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; - } - -/* - if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } - */ - if (x.sign == MP_NEG) { - if ((res = mp_copy(&y, &t1)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; - } - - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; - } - } - -/* - now q is the quotient and x is the remainder - [which we have to normalize] - */ - -/* - get sign before writing to c - */ - x.sign = x.used == 0 ? MP_ZPOS : a->sign; - - if (c != NULL) { - mp_clamp(&q); - mp_exch(&q, c); - c->sign = neg; - } - - if (d != NULL) { - mp_div_2d(pool, &x, norm, &x, NULL); - mp_exch(&x, d); - } - - res = MP_OKAY; - -LBL_Y:mp_clear (&y); -LBL_X:mp_clear (&x); -LBL_T2:mp_clear (&t2); -LBL_T1:mp_clear (&t1); -LBL_Q:mp_clear (&q); - return res; -} -#endif /* MP_DIV_SMALL */ - -/******************************************************************************/ -/* - multiplies |a| * |b| and only computes upto digs digits of result - HAC pp. 595, Algorithm 14.12 Modified so you can control how many digits - of output are created. - */ -#ifdef USE_SMALL_WORD -int32 s_mp_mul_digs(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, int32 digs) -{ - mp_int t; - int32 res, pa, pb, ix, iy; - mp_digit u; - mp_word r; - mp_digit tmpx, *tmpt, *tmpy; - -/* - Can we use the fast multiplier? - */ - if (((digs) < MP_WARRAY) && - MIN (a->used, b->used) < - (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_s_mp_mul_digs (pool, a, b, c, digs); - } - - if ((res = mp_init_size(pool, &t, digs)) != MP_OKAY) { - return res; - } - t.used = digs; - -/* - Compute the digits of the product directly - */ - pa = a->used; - for (ix = 0; ix < pa; ix++) { - /* set the carry to zero */ - u = 0; - -/* - Limit ourselves to making digs digits of output. -*/ - pb = MIN (b->used, digs - ix); - -/* - Setup some aliases. Copy of the digit from a used - within the nested loop - */ - tmpx = a->dp[ix]; - -/* - An alias for the destination shifted ix places - */ - tmpt = t.dp + ix; - -/* - An alias for the digits of b - */ - tmpy = b->dp; - -/* - Compute the columns of the output and propagate the carry - */ - for (iy = 0; iy < pb; iy++) { - /* compute the column as a mp_word */ - r = ((mp_word)*tmpt) + - ((mp_word)tmpx) * ((mp_word)*tmpy++) + - ((mp_word) u); - - /* the new column is the lower part of the result */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* get the carry word from the result */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } -/* - Set carry if it is placed below digs - */ - if (ix + iy < digs) { - *tmpt = u; - } - } - - mp_clamp (&t); - mp_exch (&t, c); - - mp_clear (&t); - return MP_OKAY; -} -#endif /* USE_SMALL_WORD */ - -/******************************************************************************/ -/* - Fast (comba) multiplier - - This is the fast column-array [comba] multiplier. It is designed to - compute the columns of the product first then handle the carries afterwards. - This has the effect of making the nested loops that compute the columns - very simple and schedulable on super-scalar processors. - - This has been modified to produce a variable number of digits of output so - if say only a half-product is required you don't have to compute the upper - half (a feature required for fast Barrett reduction). - - Based on Algorithm 14.12 on pp.595 of HAC. -*/ - -int32 fast_s_mp_mul_digs(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, - int32 digs) -{ - int32 olduse, res, pa, ix, iz, neg; - mp_digit W[MP_WARRAY]; - register mp_word _W; - - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - -/* - grow the destination as required - */ - if (c->alloc < digs) { - if ((res = mp_grow(c, digs)) != MP_OKAY) { - return res; - } - } - -/* - number of output digits to produce - */ - pa = MIN(digs, a->used + b->used); - -/* - clear the carry - */ - _W = 0; - for (ix = 0; ix < pa; ix++) { - int32 tx, ty; - int32 iy; - mp_digit *tmpx, *tmpy; - -/* - get offsets into the two bignums - */ - ty = MIN(b->used-1, ix); - tx = ix - ty; - -/* - setup temp aliases - */ - tmpx = a->dp + tx; - tmpy = b->dp + ty; - -/* - this is the number of times the loop will iterrate, essentially its - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - -/* - execute loop - */ - for (iz = 0; iz < iy; ++iz) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - -/* - store term - */ - W[ix] = (mp_digit)(_W & MP_MASK); - -/* - make next carry - */ - _W = _W >> ((mp_word)DIGIT_BIT); - } - -/* - store final carry - */ - W[ix] = (mp_digit)(_W & MP_MASK); - -/* - setup dest - */ - olduse = c->used; - c->used = pa; - - { - register mp_digit *tmpc; - tmpc = c->dp; - for (ix = 0; ix < pa+1; ix++) { -/* - now extract the previous digit [below the carry] - */ - *tmpc++ = W[ix]; - } - -/* - clear unused digits [that existed in the old copy of c] - */ - for (; ix < olduse; ix++) { - *tmpc++ = 0; - } - } - mp_clamp (c); - c->sign = (c->used > 0) ? neg : MP_ZPOS; - return MP_OKAY; -} - -/******************************************************************************/ -/* - b = a*2 - */ -int32 mp_mul_2 (mp_int * a, mp_int * b) -{ - int32 x, res, oldused; - -/* - grow to accomodate result - */ - if (b->alloc < a->used + 1) { - if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) { - return res; - } - } - - oldused = b->used; - b->used = a->used; - - { - register mp_digit r, rr, *tmpa, *tmpb; - - /* alias for source */ - tmpa = a->dp; - - /* alias for dest */ - tmpb = b->dp; - - /* carry */ - r = 0; - for (x = 0; x < a->used; x++) { - -/* - get what will be the *next* carry bit from the MSB of the - current digit - */ - rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1)); - -/* - now shift up this digit, add in the carry [from the previous] - */ - *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK; - -/* copy the carry that would be from the source digit into the next - iteration - */ - r = rr; - } - -/* - new leading digit? - */ - if (r != 0) { -/* - add a MSB which is always 1 at this point - */ - *tmpb = 1; - ++(b->used); - } - -/* - now zero any excess digits on the destination that we didn't write to - */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - return MP_OKAY; -} - -/******************************************************************************/ -/* - multiply by a digit - */ -int32 mp_mul_d(mp_int * a, mp_digit b, mp_int * c) -{ - mp_digit u, *tmpa, *tmpc; - mp_word r; - int32 ix, res, olduse; - -/* - make sure c is big enough to hold a*b - */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) { - return res; - } - } - -/* - get the original destinations used count - */ - olduse = c->used; - -/* - set the sign - */ - c->sign = a->sign; - -/* - alias for a->dp [source] - */ - tmpa = a->dp; - -/* - alias for c->dp [dest] - */ - tmpc = c->dp; - - /* zero carry */ - u = 0; - - /* compute columns */ - for (ix = 0; ix < a->used; ix++) { -/* - compute product and carry sum for this term - */ - r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b); - -/* - mask off higher bits to get a single digit - */ - *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK)); - -/* - send carry into next iteration - */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } - -/* - store final carry [if any] and increment ix offset - */ - *tmpc++ = u; - ++ix; - -/* - now zero digits above the top - */ - while (ix++ < olduse) { - *tmpc++ = 0; - } - - /* set used count */ - c->used = a->used + 1; - mp_clamp(c); - - return MP_OKAY; -} - -/******************************************************************************/ -/* - low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 - */ -#ifdef USE_SMALL_WORD -int32 s_mp_sqr (psPool_t *pool, mp_int * a, mp_int * b) -{ - mp_int t; - int32 res, ix, iy, pa; - mp_word r; - mp_digit u, tmpx, *tmpt; - - pa = a->used; - if ((res = mp_init_size(pool, &t, 2*pa + 1)) != MP_OKAY) { - return res; - } - -/* - default used is maximum possible size - */ - t.used = 2*pa + 1; - - for (ix = 0; ix < pa; ix++) { -/* - first calculate the digit at 2*ix - calculate double precision result - */ - r = ((mp_word) t.dp[2*ix]) + - ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); - -/* - store lower part in result - */ - t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); - -/* - get the carry - */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - -/* - left hand side of A[ix] * A[iy] - */ - tmpx = a->dp[ix]; - -/* - alias for where to store the results - */ - tmpt = t.dp + (2*ix + 1); - - for (iy = ix + 1; iy < pa; iy++) { -/* - first calculate the product - */ - r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); - -/* - now calculate the double precision result, note we use addition - instead of *2 since it's easier to optimize - */ - r = ((mp_word) *tmpt) + r + r + ((mp_word) u); - -/* - store lower part - */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - /* propagate upwards */ - while (u != ((mp_digit) 0)) { - r = ((mp_word) *tmpt) + ((mp_word) u); - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - } - - mp_clamp (&t); - mp_exch (&t, b); - mp_clear (&t); - return MP_OKAY; -} -#endif /* USE_SMALL_WORD */ - -/******************************************************************************/ -/* - fast squaring - - This is the comba method where the columns of the product are computed - first then the carries are computed. This has the effect of making a very - simple inner loop that is executed the most - - W2 represents the outer products and W the inner. - - A further optimizations is made because the inner products are of the - form "A * B * 2". The *2 part does not need to be computed until the end - which is good because 64-bit shifts are slow! - - Based on Algorithm 14.16 on pp.597 of HAC. - - This is the 1.0 version, but no SSE stuff -*/ -int32 fast_s_mp_sqr(psPool_t *pool, mp_int * a, mp_int * b) -{ - int32 olduse, res, pa, ix, iz; - mp_digit W[MP_WARRAY], *tmpx; - mp_word W1; - -/* - grow the destination as required - */ - pa = a->used + a->used; - if (b->alloc < pa) { - if ((res = mp_grow(b, pa)) != MP_OKAY) { - return res; - } - } - -/* - number of output digits to produce - */ - W1 = 0; - for (ix = 0; ix < pa; ix++) { - int32 tx, ty, iy; - mp_word _W; - mp_digit *tmpy; - -/* - clear counter - */ - _W = 0; - -/* - get offsets into the two bignums - */ - ty = MIN(a->used-1, ix); - tx = ix - ty; - -/* - setup temp aliases - */ - tmpx = a->dp + tx; - tmpy = a->dp + ty; - -/* - this is the number of times the loop will iterrate, essentially - while (tx++ < a->used && ty-- >= 0) { ... } -*/ - iy = MIN(a->used-tx, ty+1); - -/* - now for squaring tx can never equal ty - we halve the distance since they approach at a rate of 2x - and we have to round because odd cases need to be executed -*/ - iy = MIN(iy, (ty-tx+1)>>1); - -/* - execute loop - */ - for (iz = 0; iz < iy; iz++) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - -/* - double the inner product and add carry - */ - _W = _W + _W + W1; - -/* - even columns have the square term in them - */ - if ((ix&1) == 0) { - _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); - } - -/* - store it - */ - W[ix] = (mp_digit)(_W & MP_MASK); - -/* - make next carry - */ - W1 = _W >> ((mp_word)DIGIT_BIT); - } - -/* - setup dest - */ - olduse = b->used; - b->used = a->used+a->used; - - { - mp_digit *tmpb; - tmpb = b->dp; - for (ix = 0; ix < pa; ix++) { - *tmpb++ = W[ix] & MP_MASK; - } - -/* - clear unused digits [that existed in the old copy of c] - */ - for (; ix < olduse; ix++) { - *tmpb++ = 0; - } - } - mp_clamp(b); - return MP_OKAY; -} - -/******************************************************************************/ -/* - computes a = 2**b - - Simple algorithm which zeroes the int32, grows it then just sets one bit - as required. - */ -int32 mp_2expt (mp_int * a, int32 b) -{ - int32 res; - -/* - zero a as per default - */ - mp_zero (a); - -/* - grow a to accomodate the single bit - */ - if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } - -/* - set the used count of where the bit will go - */ - a->used = b / DIGIT_BIT + 1; - -/* - put the single bit in its place - */ - a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); - - return MP_OKAY; -} - -/******************************************************************************/ -/* - init an mp_init for a given size - */ -int32 mp_init_size(psPool_t *pool, mp_int * a, int32 size) -{ - int x; -/* - pad size so there are always extra digits - */ - size += (MP_PREC * 2) - (size % MP_PREC); - -/* - alloc mem - */ - a->dp = OPT_CAST(mp_digit) psMalloc(pool, sizeof (mp_digit) * size); - if (a->dp == NULL) { - return MP_MEM; - } - a->used = 0; - a->alloc = size; - a->sign = MP_ZPOS; - -/* - zero the digits - */ - for (x = 0; x < size; x++) { - a->dp[x] = 0; - } - return MP_OKAY; -} - -/******************************************************************************/ -/* - low level addition, based on HAC pp.594, Algorithm 14.7 - */ -int32 s_mp_add (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int *x; - int32 olduse, res, min, max; - -/* - find sizes, we let |a| <= |b| which means we have to sort them. "x" will - point to the input with the most digits - */ - if (a->used > b->used) { - min = b->used; - max = a->used; - x = a; - } else { - min = a->used; - max = b->used; - x = b; - } - - /* init result */ - if (c->alloc < max + 1) { - if ((res = mp_grow (c, max + 1)) != MP_OKAY) { - return res; - } - } - -/* - get old used digit count and set new one - */ - olduse = c->used; - c->used = max + 1; - - { - register mp_digit u, *tmpa, *tmpb, *tmpc; - register int32 i; - - /* alias for digit pointers */ - - /* first input */ - tmpa = a->dp; - - /* second input */ - tmpb = b->dp; - - /* destination */ - tmpc = c->dp; - - /* zero the carry */ - u = 0; - for (i = 0; i < min; i++) { -/* - Compute the sum at one digit, T[i] = A[i] + B[i] + U - */ - *tmpc = *tmpa++ + *tmpb++ + u; - -/* - U = carry bit of T[i] - */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - -/* - take away carry bit from T[i] - */ - *tmpc++ &= MP_MASK; - } - -/* - now copy higher words if any, that is in A+B if A or B has more digits add - those in - */ - if (min != max) { - for (; i < max; i++) { - /* T[i] = X[i] + U */ - *tmpc = x->dp[i] + u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - - /* take away carry bit from T[i] */ - *tmpc++ &= MP_MASK; - } - } - - /* add carry */ - *tmpc++ = u; - -/* - clear digits above oldused - */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } - - mp_clamp (c); - return MP_OKAY; -} - -/******************************************************************************/ -/* - FUTURE - this is only needed by the SSH code, SLOW or not, because RSA - exponents are always odd. -*/ -int32 mp_invmodSSH(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, A, B, C, D; - int32 res; - -/* - b cannot be negative - */ - if (b->sign == MP_NEG || mp_iszero(b) == 1) { - return MP_VAL; - } - -/* - if the modulus is odd we can use a faster routine instead - */ - if (mp_isodd (b) == 1) { - return fast_mp_invmod(pool, a, b, c); - } - -/* - init temps - */ - if ((res = _mp_init_multi(pool, &x, &y, &u, &v, - &A, &B, &C, &D)) != MP_OKAY) { - return res; - } - - /* x = a, y = b */ - if ((res = mp_copy(a, &x)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy(b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - -/* - 2. [modified] if x,y are both even then return an error! - */ - if (mp_iseven(&x) == 1 && mp_iseven (&y) == 1) { - res = MP_VAL; - goto LBL_ERR; - } - -/* - 3. u=x, v=y, A=1, B=0, C=0,D=1 - */ - if ((res = mp_copy(&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy(&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set (&A, 1); - mp_set (&D, 1); - -top: -/* - 4. while u is even do - */ - while (mp_iseven(&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2(&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if A or B is odd then */ - if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { - /* A = (A+y)/2, B = (B-x)/2 */ - if ((res = mp_add(&A, &y, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* A = A/2, B = B/2 */ - if ((res = mp_div_2(&A, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2(&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - 5. while v is even do - */ - while (mp_iseven(&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2(&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if C or D is odd then */ - if (mp_isodd(&C) == 1 || mp_isodd (&D) == 1) { - /* C = (C+y)/2, D = (D-x)/2 */ - if ((res = mp_add(&C, &y, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* C = C/2, D = D/2 */ - if ((res = mp_div_2(&C, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2(&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - 6. if u >= v then - */ - if (mp_cmp(&u, &v) != MP_LT) { - /* u = u - v, A = A - C, B = B - D */ - if ((res = mp_sub(&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&A, &C, &A)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, C = C - A, D = D - B */ - if ((res = mp_sub(&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&C, &A, &C)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - if not zero goto step 4 - */ - if (mp_iszero(&u) == 0) - goto top; - -/* - now a = C, b = D, gcd == g*v - */ - -/* - if v != 1 then there is no inverse - */ - if (mp_cmp_d(&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - -/* - if its too low - */ - while (mp_cmp_d(&C, 0) == MP_LT) { - if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - too big - */ - while (mp_cmp_mag(&C, b) != MP_LT) { - if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - C is now the inverse - */ - mp_exch(&C, c); - res = MP_OKAY; -LBL_ERR:_mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D); - return res; -} - -/******************************************************************************/ - -/* - * Computes the modular inverse via binary extended euclidean algorithm, - * that is c = 1/a mod b - * - * Based on slow invmod except this is optimized for the case where b is - * odd as per HAC Note 14.64 on pp. 610 - */ -int32 fast_mp_invmod(psPool_t *pool, mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, B, D; - int32 res, neg; - -/* - 2. [modified] b must be odd - */ - if (mp_iseven (b) == 1) { - return MP_VAL; - } - -/* - init all our temps - */ - if ((res = _mp_init_multi(pool, &x, &y, &u, &v, &B, &D, NULL, NULL)) != MP_OKAY) { - return res; - } - -/* - x == modulus, y == value to invert - */ - if ((res = mp_copy(b, &x)) != MP_OKAY) { - goto LBL_ERR; - } - -/* - we need y = |a| - */ - if ((res = mp_mod(pool, a, b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - -/* - 3. u=x, v=y, A=1, B=0, C=0,D=1 - */ - if ((res = mp_copy(&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy(&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set(&D, 1); - -top: -/* - 4. while u is even do -*/ - while (mp_iseven(&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2(&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if B is odd then */ - if (mp_isodd(&B) == 1) { - if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* B = B/2 */ - if ((res = mp_div_2(&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - 5. while v is even do - */ - while (mp_iseven(&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2(&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if D is odd then */ - if (mp_isodd(&D) == 1) { - /* D = (D-x)/2 */ - if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* D = D/2 */ - if ((res = mp_div_2(&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - 6. if u >= v then - */ - if (mp_cmp(&u, &v) != MP_LT) { - /* u = u - v, B = B - D */ - if ((res = mp_sub(&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, D = D - B */ - if ((res = mp_sub(&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub(&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - -/* - if not zero goto step 4 - */ - if (mp_iszero(&u) == 0) { - goto top; - } - -/* - now a = C, b = D, gcd == g*v - */ - -/* - if v != 1 then there is no inverse - */ - if (mp_cmp_d(&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - -/* - b is now the inverse - */ - neg = a->sign; - while (D.sign == MP_NEG) { - if ((res = mp_add(&D, b, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - mp_exch(&D, c); - c->sign = neg; - res = MP_OKAY; - -LBL_ERR:_mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL, NULL); - return res; -} - -/******************************************************************************/ -/* - d = a + b (mod c) - */ -int32 mp_addmod (psPool_t *pool, mp_int * a, mp_int * b, mp_int * c, mp_int * d) -{ - int32 res; - mp_int t; - - if ((res = mp_init(pool, &t)) != MP_OKAY) { - return res; - } - - if ((res = mp_add (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (pool, &t, c, d); - mp_clear (&t); - return res; -} - -/******************************************************************************/ -/* - shrink a bignum - */ -int32 mp_shrink (mp_int * a) -{ - mp_digit *tmp; - - if (a->alloc != a->used && a->used > 0) { - if ((tmp = psRealloc(a->dp, sizeof (mp_digit) * a->used)) == NULL) { - return MP_MEM; - } - a->dp = tmp; - a->alloc = a->used; - } - return MP_OKAY; -} - -/* single digit subtraction */ -int32 mp_sub_d (mp_int * a, mp_digit b, mp_int * c) -{ - mp_digit *tmpa, *tmpc, mu; - int32 res, ix, oldused; - - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } - - /* if a is negative just do an unsigned - * addition [with fudged signs] - */ - if (a->sign == MP_NEG) { - a->sign = MP_ZPOS; - res = mp_add_d(a, b, c); - a->sign = c->sign = MP_NEG; - return res; - } - - /* setup regs */ - oldused = c->used; - tmpa = a->dp; - tmpc = c->dp; - - /* if a <= b simply fix the single digit */ - if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) { - if (a->used == 1) { - *tmpc++ = b - *tmpa; - } else { - *tmpc++ = b; - } - ix = 1; - - /* negative/1digit */ - c->sign = MP_NEG; - c->used = 1; - } else { - /* positive/size */ - c->sign = MP_ZPOS; - c->used = a->used; - - /* subtract first digit */ - *tmpc = *tmpa++ - b; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; - - /* handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ - mu; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; - } - } - - /* zero excess digits */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - return MP_OKAY; -} - -/* single digit addition */ -int32 mp_add_d (mp_int * a, mp_digit b, mp_int * c) -{ - int32 res, ix, oldused; - mp_digit *tmpa, *tmpc, mu; - - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } - - /* if a is negative and |a| >= b, call c = |a| - b */ - if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) { - /* temporarily fix sign of a */ - a->sign = MP_ZPOS; - - /* c = |a| - b */ - res = mp_sub_d(a, b, c); - - /* fix sign */ - a->sign = c->sign = MP_NEG; - return res; - } - - /* old number of used digits in c */ - oldused = c->used; - - /* sign always positive */ - c->sign = MP_ZPOS; - - /* source alias */ - tmpa = a->dp; - - /* destination alias */ - tmpc = c->dp; - - /* if a is positive */ - if (a->sign == MP_ZPOS) { - /* add digit, after this we're propagating the carry */ - *tmpc = *tmpa++ + b; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - - /* now handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ + mu; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - } - /* set final carry */ - ix++; - *tmpc++ = mu; - - /* setup size */ - c->used = a->used + 1; - } else { - /* a was negative and |a| < b */ - c->used = 1; - - /* the result is a single digit */ - if (a->used == 1) { - *tmpc++ = b - a->dp[0]; - } else { - *tmpc++ = b; - } - - /* setup count so the clearing of oldused - * can fall through correctly - */ - ix = 1; - } - - /* now zero to oldused */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - return MP_OKAY; -} - - -/******************************************************************************/ - -#endif /* USE_MPI2 */ |