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4475 lines
103 KiB
C
4475 lines
103 KiB
C
/*
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* dlls/rsaenh/mpi.c
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* Multi Precision Integer functions
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*
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* Copyright 2004 Michael Jung
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* Based on public domain code by Tom St Denis (tomstdenis@iahu.ca)
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
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*/
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/*
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* This file contains code from the LibTomCrypt cryptographic
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* library written by Tom St Denis (tomstdenis@iahu.ca). LibTomCrypt
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* is in the public domain. The code in this file is tailored to
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* special requirements. Take a look at http://libtomcrypt.org for the
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* original version.
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*/
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#include <stdarg.h>
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#include <windef.h>
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#include <winbase.h>
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#include "tomcrypt.h"
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/* Known optimal configurations
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CPU /Compiler /MUL CUTOFF/SQR CUTOFF
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-------------------------------------------------------------
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Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
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*/
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static const int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
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KARATSUBA_SQR_CUTOFF = 128; /* Min. number of digits before Karatsuba squaring is used. */
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/* trim unused digits */
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static void mp_clamp(mp_int *a);
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/* compare |a| to |b| */
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static int mp_cmp_mag(const mp_int *a, const mp_int *b);
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/* Counts the number of lsbs which are zero before the first zero bit */
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static int mp_cnt_lsb(const mp_int *a);
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/* computes a = B**n mod b without division or multiplication useful for
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* normalizing numbers in a Montgomery system.
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*/
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static int mp_montgomery_calc_normalization(mp_int *a, const mp_int *b);
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/* computes x/R == x (mod N) via Montgomery Reduction */
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static int mp_montgomery_reduce(mp_int *a, const mp_int *m, mp_digit mp);
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/* setups the montgomery reduction */
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static int mp_montgomery_setup(const mp_int *a, mp_digit *mp);
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/* Barrett Reduction, computes a (mod b) with a precomputed value c
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*
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* Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
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* compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
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*/
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static int mp_reduce(mp_int *a, const mp_int *b, const mp_int *c);
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/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
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static int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d);
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/* determines k value for 2k reduction */
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static int mp_reduce_2k_setup(const mp_int *a, mp_digit *d);
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/* used to setup the Barrett reduction for a given modulus b */
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static int mp_reduce_setup(mp_int *a, const mp_int *b);
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/* set to a digit */
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static void mp_set(mp_int *a, mp_digit b);
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/* b = a*a */
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static int mp_sqr(const mp_int *a, mp_int *b);
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/* c = a * a (mod b) */
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static int mp_sqrmod(const mp_int *a, mp_int *b, mp_int *c);
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static void bn_reverse(unsigned char *s, int len);
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static int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
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static int s_mp_exptmod (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y);
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#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
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static int s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs);
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static int s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs);
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static int s_mp_sqr(const mp_int *a, mp_int *b);
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static int s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c);
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static int mp_exptmod_fast(const mp_int *G, const mp_int *X, mp_int *P, mp_int *Y, int mode);
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static int mp_invmod_slow (const mp_int * a, mp_int * b, mp_int * c);
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static int mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c);
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static int mp_karatsuba_sqr(const mp_int *a, mp_int *b);
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/* grow as required */
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static int mp_grow (mp_int * a, int size)
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{
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int i;
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mp_digit *tmp;
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/* if the alloc size is smaller alloc more ram */
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if (a->alloc < size) {
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/* ensure there are always at least MP_PREC digits extra on top */
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size += (MP_PREC * 2) - (size % MP_PREC);
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/* reallocate the array a->dp
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*
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* We store the return in a temporary variable
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* in case the operation failed we don't want
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* to overwrite the dp member of a.
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*/
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tmp = HeapReAlloc(GetProcessHeap(), 0, a->dp, sizeof (mp_digit) * size);
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if (tmp == NULL) {
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/* reallocation failed but "a" is still valid [can be freed] */
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return MP_MEM;
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}
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/* reallocation succeeded so set a->dp */
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a->dp = tmp;
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/* zero excess digits */
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i = a->alloc;
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a->alloc = size;
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for (; i < a->alloc; i++) {
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a->dp[i] = 0;
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}
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}
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return MP_OKAY;
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}
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/* b = a/2 */
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static int mp_div_2(const mp_int * a, mp_int * b)
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{
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int x, res, oldused;
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/* copy */
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if (b->alloc < a->used) {
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if ((res = mp_grow (b, a->used)) != MP_OKAY) {
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return res;
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}
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}
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oldused = b->used;
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b->used = a->used;
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{
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register mp_digit r, rr, *tmpa, *tmpb;
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/* source alias */
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tmpa = a->dp + b->used - 1;
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/* dest alias */
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tmpb = b->dp + b->used - 1;
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/* carry */
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r = 0;
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for (x = b->used - 1; x >= 0; x--) {
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/* get the carry for the next iteration */
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rr = *tmpa & 1;
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/* shift the current digit, add in carry and store */
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*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
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/* forward carry to next iteration */
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r = rr;
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}
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/* zero excess digits */
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tmpb = b->dp + b->used;
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for (x = b->used; x < oldused; x++) {
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*tmpb++ = 0;
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}
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}
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b->sign = a->sign;
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mp_clamp (b);
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return MP_OKAY;
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}
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/* swap the elements of two integers, for cases where you can't simply swap the
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* mp_int pointers around
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*/
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static void
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mp_exch (mp_int * a, mp_int * b)
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{
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mp_int t;
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t = *a;
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*a = *b;
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*b = t;
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}
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/* init a new mp_int */
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static int mp_init (mp_int * a)
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{
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int i;
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/* allocate memory required and clear it */
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a->dp = HeapAlloc(GetProcessHeap(), 0, sizeof (mp_digit) * MP_PREC);
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if (a->dp == NULL) {
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return MP_MEM;
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}
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/* set the digits to zero */
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for (i = 0; i < MP_PREC; i++) {
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a->dp[i] = 0;
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}
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/* set the used to zero, allocated digits to the default precision
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* and sign to positive */
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a->used = 0;
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a->alloc = MP_PREC;
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a->sign = MP_ZPOS;
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return MP_OKAY;
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}
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/* init an mp_init for a given size */
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static int mp_init_size (mp_int * a, int size)
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{
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int x;
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/* pad size so there are always extra digits */
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size += (MP_PREC * 2) - (size % MP_PREC);
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/* alloc mem */
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a->dp = HeapAlloc(GetProcessHeap(), 0, sizeof (mp_digit) * size);
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if (a->dp == NULL) {
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return MP_MEM;
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}
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/* set the members */
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a->used = 0;
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a->alloc = size;
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a->sign = MP_ZPOS;
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/* zero the digits */
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for (x = 0; x < size; x++) {
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a->dp[x] = 0;
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}
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return MP_OKAY;
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}
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/* clear one (frees) */
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static void
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mp_clear (mp_int * a)
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{
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int i;
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/* only do anything if a hasn't been freed previously */
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if (a->dp != NULL) {
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/* first zero the digits */
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for (i = 0; i < a->used; i++) {
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a->dp[i] = 0;
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}
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/* free ram */
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HeapFree(GetProcessHeap(), 0, a->dp);
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/* reset members to make debugging easier */
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a->dp = NULL;
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a->alloc = a->used = 0;
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a->sign = MP_ZPOS;
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}
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}
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/* set to zero */
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static void
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mp_zero (mp_int * a)
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{
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a->sign = MP_ZPOS;
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a->used = 0;
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memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
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}
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/* b = |a|
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*
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* Simple function copies the input and fixes the sign to positive
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*/
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static int
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mp_abs (const mp_int * a, mp_int * b)
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{
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int res;
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/* copy a to b */
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if (a != b) {
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if ((res = mp_copy (a, b)) != MP_OKAY) {
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return res;
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}
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}
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/* force the sign of b to positive */
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b->sign = MP_ZPOS;
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return MP_OKAY;
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}
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/* computes the modular inverse via binary extended euclidean algorithm,
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* that is c = 1/a mod b
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*
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* Based on slow invmod except this is optimized for the case where b is
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* odd as per HAC Note 14.64 on pp. 610
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*/
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static int
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fast_mp_invmod (const mp_int * a, mp_int * b, mp_int * c)
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{
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mp_int x, y, u, v, B, D;
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int res, neg;
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/* 2. [modified] b must be odd */
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if (mp_iseven (b) == 1) {
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return MP_VAL;
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}
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/* init all our temps */
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if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
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return res;
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}
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/* x == modulus, y == value to invert */
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if ((res = mp_copy (b, &x)) != MP_OKAY) {
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goto __ERR;
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}
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/* we need y = |a| */
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if ((res = mp_abs (a, &y)) != MP_OKAY) {
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goto __ERR;
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}
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/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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if ((res = mp_copy (&x, &u)) != MP_OKAY) {
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goto __ERR;
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}
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if ((res = mp_copy (&y, &v)) != MP_OKAY) {
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goto __ERR;
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}
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mp_set (&D, 1);
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top:
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/* 4. while u is even do */
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while (mp_iseven (&u) == 1) {
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/* 4.1 u = u/2 */
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if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
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goto __ERR;
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}
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/* 4.2 if B is odd then */
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if (mp_isodd (&B) == 1) {
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if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
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goto __ERR;
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}
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}
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/* B = B/2 */
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if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
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goto __ERR;
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}
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}
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/* 5. while v is even do */
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while (mp_iseven (&v) == 1) {
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/* 5.1 v = v/2 */
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if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
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goto __ERR;
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}
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/* 5.2 if D is odd then */
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if (mp_isodd (&D) == 1) {
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/* D = (D-x)/2 */
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if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
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goto __ERR;
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}
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}
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/* D = D/2 */
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if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
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goto __ERR;
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}
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}
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/* 6. if u >= v then */
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if (mp_cmp (&u, &v) != MP_LT) {
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/* u = u - v, B = B - D */
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if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
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goto __ERR;
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}
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if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
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goto __ERR;
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}
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} else {
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/* v - v - u, D = D - B */
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if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
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goto __ERR;
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}
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if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
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goto __ERR;
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}
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}
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/* if not zero goto step 4 */
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if (mp_iszero (&u) == 0) {
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goto top;
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}
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/* now a = C, b = D, gcd == g*v */
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/* if v != 1 then there is no inverse */
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if (mp_cmp_d (&v, 1) != MP_EQ) {
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res = MP_VAL;
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goto __ERR;
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}
|
|
|
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/* b is now the inverse */
|
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neg = a->sign;
|
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while (D.sign == MP_NEG) {
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if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
|
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goto __ERR;
|
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}
|
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}
|
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mp_exch (&D, c);
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c->sign = neg;
|
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res = MP_OKAY;
|
|
|
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__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
|
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return res;
|
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}
|
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|
|
/* 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.
|
|
*/
|
|
static int
|
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fast_mp_montgomery_reduce (mp_int * x, const mp_int * n, mp_digit rho)
|
|
{
|
|
int 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 offsetting 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 int 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;
|
|
|
|
/* nox 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;
|
|
}
|
|
|
|
/* 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.
|
|
*
|
|
*/
|
|
static int
|
|
fast_s_mp_mul_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY];
|
|
register mp_word _W;
|
|
|
|
/* 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++) {
|
|
int tx, ty;
|
|
int 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 iterate, essentially it's
|
|
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);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = digs;
|
|
|
|
{
|
|
register mp_digit *tmpc;
|
|
tmpc = c->dp;
|
|
for (ix = 0; ix < digs; 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);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* this is a modified version of fast_s_mul_digs that only produces
|
|
* output digits *above* digs. See the comments for fast_s_mul_digs
|
|
* to see how it works.
|
|
*
|
|
* This is used in the Barrett reduction since for one of the multiplications
|
|
* only the higher digits were needed. This essentially halves the work.
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*/
|
|
static int
|
|
fast_s_mp_mul_high_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY];
|
|
mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + b->used;
|
|
if (c->alloc < pa) {
|
|
if ((res = mp_grow (c, pa)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = a->used + b->used;
|
|
_W = 0;
|
|
for (ix = digs; ix <= pa; ix++) {
|
|
int tx, ty, 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 iterate, essentially it's
|
|
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);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = pa;
|
|
|
|
{
|
|
register mp_digit *tmpc;
|
|
|
|
tmpc = c->dp + digs;
|
|
for (ix = digs; ix <= pa; 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);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* 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.
|
|
*
|
|
*/
|
|
/* the jist of squaring...
|
|
|
|
you do like mult except the offset of the tmpx [one that starts closer to zero]
|
|
can't equal the offset of tmpy. So basically you set up iy like before then you min it with
|
|
(ty-tx) so that it never happens. You double all those you add in the inner loop
|
|
|
|
After that loop you do the squares and add them in.
|
|
|
|
Remove W2 and don't memset W
|
|
|
|
*/
|
|
|
|
static int fast_s_mp_sqr (const mp_int * a, mp_int * b)
|
|
{
|
|
int 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++) {
|
|
int 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 iterate, essentially it's
|
|
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] = _W;
|
|
|
|
/* 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 int, grows it then just sets one bit
|
|
* as required.
|
|
*/
|
|
static int
|
|
mp_2expt (mp_int * a, int b)
|
|
{
|
|
int res;
|
|
|
|
/* zero a as per default */
|
|
mp_zero (a);
|
|
|
|
/* grow a to accommodate 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;
|
|
}
|
|
|
|
/* high level addition (handles signs) */
|
|
int mp_add (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int 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;
|
|
}
|
|
|
|
|
|
/* single digit addition */
|
|
static int
|
|
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
int 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;
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
|
|
void mp_clear_multi(mp_int *mp, ...)
|
|
{
|
|
mp_int* next_mp = mp;
|
|
va_list args;
|
|
va_start(args, mp);
|
|
while (next_mp != NULL) {
|
|
mp_clear(next_mp);
|
|
next_mp = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
}
|
|
|
|
/* compare two ints (signed)*/
|
|
int
|
|
mp_cmp (const mp_int * a, const 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);
|
|
}
|
|
}
|
|
|
|
/* compare a digit */
|
|
int mp_cmp_d(const 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;
|
|
}
|
|
}
|
|
|
|
/* compare maginitude of two ints (unsigned) */
|
|
int mp_cmp_mag (const mp_int * a, const mp_int * b)
|
|
{
|
|
int 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;
|
|
}
|
|
|
|
static const int lnz[16] = {
|
|
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
|
|
};
|
|
|
|
/* Counts the number of lsbs which are zero before the first zero bit */
|
|
int mp_cnt_lsb(const mp_int *a)
|
|
{
|
|
int x;
|
|
mp_digit q, qq;
|
|
|
|
/* easy out */
|
|
if (mp_iszero(a) == 1) {
|
|
return 0;
|
|
}
|
|
|
|
/* scan lower digits until non-zero */
|
|
for (x = 0; x < a->used && a->dp[x] == 0; x++);
|
|
q = a->dp[x];
|
|
x *= DIGIT_BIT;
|
|
|
|
/* now scan this digit until a 1 is found */
|
|
if ((q & 1) == 0) {
|
|
do {
|
|
qq = q & 15;
|
|
x += lnz[qq];
|
|
q >>= 4;
|
|
} while (qq == 0);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* copy, b = a */
|
|
int
|
|
mp_copy (const mp_int * a, mp_int * b)
|
|
{
|
|
int 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 int */
|
|
int
|
|
mp_count_bits (const mp_int * a)
|
|
{
|
|
int 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 > 0) {
|
|
++r;
|
|
q >>= ((mp_digit) 1);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
/* calc a value mod 2**b */
|
|
static int
|
|
mp_mod_2d (const mp_int * a, int b, mp_int * c)
|
|
{
|
|
int x, res;
|
|
|
|
/* if b is <= 0 then zero the int */
|
|
if (b <= 0) {
|
|
mp_zero (c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* if the modulus is larger than the value than return */
|
|
if (b > 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] &= (1 << ((mp_digit)b % DIGIT_BIT)) - 1;
|
|
mp_clamp (c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* shift right a certain amount of digits */
|
|
static void mp_rshd (mp_int * a, int b)
|
|
{
|
|
int 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;
|
|
}
|
|
|
|
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
|
|
static int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_digit D, r, rr;
|
|
int 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 (&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 >= 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;
|
|
}
|
|
|
|
/* shift left a certain amount of digits */
|
|
static int mp_lshd (mp_int * a, int b)
|
|
{
|
|
int x, res;
|
|
|
|
/* if it's 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 other way 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;
|
|
}
|
|
|
|
/* shift left by a certain bit count */
|
|
static int mp_mul_2d (const mp_int * a, int b, mp_int * c)
|
|
{
|
|
mp_digit d;
|
|
int res;
|
|
|
|
/* copy */
|
|
if (a != c) {
|
|
if ((res = mp_copy (a, c)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
if (c->alloc < 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 >= 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 int 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;
|
|
}
|
|
|
|
/* multiply by a digit */
|
|
static int
|
|
mp_mul_d (const mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
mp_digit u, *tmpa, *tmpc;
|
|
mp_word r;
|
|
int 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] */
|
|
*tmpc++ = u;
|
|
|
|
/* 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;
|
|
}
|
|
|
|
/* 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.
|
|
*/
|
|
static int mp_div (const mp_int * a, const mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_int q, x, y, t1, t2;
|
|
int 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 (&q, a->used + 2)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
q.used = a->used + 2;
|
|
|
|
if ((res = mp_init (&t1)) != MP_OKAY) {
|
|
goto __Q;
|
|
}
|
|
|
|
if ((res = mp_init (&t2)) != MP_OKAY) {
|
|
goto __T1;
|
|
}
|
|
|
|
if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
|
|
goto __T2;
|
|
}
|
|
|
|
if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
|
|
goto __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 < DIGIT_BIT-1) {
|
|
norm = (DIGIT_BIT-1) - norm;
|
|
if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
} else {
|
|
norm = 0;
|
|
}
|
|
|
|
/* note hac does 0 based, so if used==5 then it's 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 __Y;
|
|
}
|
|
|
|
while (mp_cmp (&x, &y) != MP_LT) {
|
|
++(q.dp[n - t]);
|
|
if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
|
|
goto __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 __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 __Y;
|
|
}
|
|
|
|
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
|
|
if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
|
|
goto __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 __Y;
|
|
}
|
|
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
|
|
goto __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 (&x, norm, &x, NULL);
|
|
mp_exch (&x, d);
|
|
}
|
|
|
|
res = MP_OKAY;
|
|
|
|
__Y:mp_clear (&y);
|
|
__X:mp_clear (&x);
|
|
__T2:mp_clear (&t2);
|
|
__T1:mp_clear (&t1);
|
|
__Q:mp_clear (&q);
|
|
return res;
|
|
}
|
|
|
|
static BOOL s_is_power_of_two(mp_digit b, int *p)
|
|
{
|
|
int x;
|
|
|
|
for (x = 1; x < DIGIT_BIT; x++) {
|
|
if (b == (((mp_digit)1)<<x)) {
|
|
*p = x;
|
|
return TRUE;
|
|
}
|
|
}
|
|
return FALSE;
|
|
}
|
|
|
|
/* single digit division (based on routine from MPI) */
|
|
static int mp_div_d (const mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
|
|
{
|
|
mp_int q;
|
|
mp_word w;
|
|
mp_digit t;
|
|
int res, ix;
|
|
|
|
/* cannot divide by zero */
|
|
if (b == 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* quick outs */
|
|
if (b == 1 || mp_iszero(a) == 1) {
|
|
if (d != NULL) {
|
|
*d = 0;
|
|
}
|
|
if (c != NULL) {
|
|
return mp_copy(a, c);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* power of two ? */
|
|
if (s_is_power_of_two(b, &ix)) {
|
|
if (d != NULL) {
|
|
*d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
|
|
}
|
|
if (c != NULL) {
|
|
return mp_div_2d(a, ix, c, NULL);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* no easy answer [c'est la vie]. Just division */
|
|
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
q.used = a->used;
|
|
q.sign = a->sign;
|
|
w = 0;
|
|
for (ix = a->used - 1; ix >= 0; ix--) {
|
|
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
|
|
|
|
if (w >= b) {
|
|
t = (mp_digit)(w / b);
|
|
w -= ((mp_word)t) * ((mp_word)b);
|
|
} else {
|
|
t = 0;
|
|
}
|
|
q.dp[ix] = t;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
*d = (mp_digit)w;
|
|
}
|
|
|
|
if (c != NULL) {
|
|
mp_clamp(&q);
|
|
mp_exch(&q, c);
|
|
}
|
|
mp_clear(&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
|
|
*
|
|
* Based on algorithm from the paper
|
|
*
|
|
* "Generating Efficient Primes for Discrete Log Cryptosystems"
|
|
* Chae Hoon Lim, Pil Loong Lee,
|
|
* POSTECH Information Research Laboratories
|
|
*
|
|
* The modulus must be of a special format [see manual]
|
|
*
|
|
* Has been modified to use algorithm 7.10 from the LTM book instead
|
|
*
|
|
* Input x must be in the range 0 <= x <= (n-1)**2
|
|
*/
|
|
static int
|
|
mp_dr_reduce (mp_int * x, const mp_int * n, mp_digit k)
|
|
{
|
|
int err, i, m;
|
|
mp_word r;
|
|
mp_digit mu, *tmpx1, *tmpx2;
|
|
|
|
/* m = digits in modulus */
|
|
m = n->used;
|
|
|
|
/* ensure that "x" has at least 2m digits */
|
|
if (x->alloc < m + m) {
|
|
if ((err = mp_grow (x, m + m)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* top of loop, this is where the code resumes if
|
|
* another reduction pass is required.
|
|
*/
|
|
top:
|
|
/* aliases for digits */
|
|
/* alias for lower half of x */
|
|
tmpx1 = x->dp;
|
|
|
|
/* alias for upper half of x, or x/B**m */
|
|
tmpx2 = x->dp + m;
|
|
|
|
/* set carry to zero */
|
|
mu = 0;
|
|
|
|
/* compute (x mod B**m) + k * [x/B**m] inline and inplace */
|
|
for (i = 0; i < m; i++) {
|
|
r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
|
|
*tmpx1++ = (mp_digit)(r & MP_MASK);
|
|
mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
|
|
}
|
|
|
|
/* set final carry */
|
|
*tmpx1++ = mu;
|
|
|
|
/* zero words above m */
|
|
for (i = m + 1; i < x->used; i++) {
|
|
*tmpx1++ = 0;
|
|
}
|
|
|
|
/* clamp, sub and return */
|
|
mp_clamp (x);
|
|
|
|
/* if x >= n then subtract and reduce again
|
|
* Each successive "recursion" makes the input smaller and smaller.
|
|
*/
|
|
if (mp_cmp_mag (x, n) != MP_LT) {
|
|
s_mp_sub(x, n, x);
|
|
goto top;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* sets the value of "d" required for mp_dr_reduce */
|
|
static void mp_dr_setup(const mp_int *a, mp_digit *d)
|
|
{
|
|
/* the casts are required if DIGIT_BIT is one less than
|
|
* the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
|
|
*/
|
|
*d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
|
|
((mp_word)a->dp[0]));
|
|
}
|
|
|
|
/* this is a shell function that calls either the normal or Montgomery
|
|
* exptmod functions. Originally the call to the montgomery code was
|
|
* embedded in the normal function but that wasted a lot of stack space
|
|
* for nothing (since 99% of the time the Montgomery code would be called)
|
|
*/
|
|
int mp_exptmod (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y)
|
|
{
|
|
int dr;
|
|
|
|
/* 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;
|
|
int err;
|
|
|
|
/* first compute 1/G mod P */
|
|
if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
|
|
/* now get |X| */
|
|
if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
/* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
|
err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
dr = 0;
|
|
|
|
/* if the modulus is odd use the fast method */
|
|
if (mp_isodd (P) == 1) {
|
|
return mp_exptmod_fast (G, X, P, Y, dr);
|
|
} else {
|
|
/* otherwise use the generic Barrett reduction technique */
|
|
return s_mp_exptmod (G, X, P, Y);
|
|
}
|
|
}
|
|
|
|
/* 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]
|
|
*/
|
|
|
|
int
|
|
mp_exptmod_fast (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_int M[256], res;
|
|
mp_digit buf, mp;
|
|
int 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.
|
|
*/
|
|
int (*redux)(mp_int*,const 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;
|
|
}
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&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(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear (&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* determine and setup reduction code */
|
|
if (redmode == 0) {
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
|
goto __M;
|
|
}
|
|
|
|
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
|
|
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;
|
|
}
|
|
} else if (redmode == 1) {
|
|
/* setup DR reduction for moduli of the form B**k - b */
|
|
mp_dr_setup(P, &mp);
|
|
redux = mp_dr_reduce;
|
|
} else {
|
|
/* setup DR reduction for moduli of the form 2**k - b */
|
|
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
|
goto __M;
|
|
}
|
|
redux = mp_reduce_2k;
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init (&res)) != MP_OKAY) {
|
|
goto __M;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
if (redmode == 0) {
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
} else {
|
|
mp_set(&res, 1);
|
|
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
|
goto __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 __RES;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
|
|
goto __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 = DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* 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 __RES;
|
|
}
|
|
}
|
|
|
|
/* swap res with Y */
|
|
mp_exch (&res, Y);
|
|
err = MP_OKAY;
|
|
__RES:mp_clear (&res);
|
|
__M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear (&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* Greatest Common Divisor using the binary method */
|
|
int mp_gcd (const mp_int * a, const mp_int * b, mp_int * c)
|
|
{
|
|
mp_int u, v;
|
|
int k, u_lsb, v_lsb, res;
|
|
|
|
/* either zero than gcd is the largest */
|
|
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
|
|
return mp_abs (b, c);
|
|
}
|
|
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
|
|
return mp_abs (a, c);
|
|
}
|
|
|
|
/* optimized. At this point if a == 0 then
|
|
* b must equal zero too
|
|
*/
|
|
if (mp_iszero (a) == 1) {
|
|
mp_zero(c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* get copies of a and b we can modify */
|
|
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
|
|
goto __U;
|
|
}
|
|
|
|
/* must be positive for the remainder of the algorithm */
|
|
u.sign = v.sign = MP_ZPOS;
|
|
|
|
/* B1. Find the common power of two for u and v */
|
|
u_lsb = mp_cnt_lsb(&u);
|
|
v_lsb = mp_cnt_lsb(&v);
|
|
k = MIN(u_lsb, v_lsb);
|
|
|
|
if (k > 0) {
|
|
/* divide the power of two out */
|
|
if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
|
|
if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
}
|
|
|
|
/* divide any remaining factors of two out */
|
|
if (u_lsb != k) {
|
|
if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
}
|
|
|
|
if (v_lsb != k) {
|
|
if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
}
|
|
|
|
while (mp_iszero(&v) == 0) {
|
|
/* make sure v is the largest */
|
|
if (mp_cmp_mag(&u, &v) == MP_GT) {
|
|
/* swap u and v to make sure v is >= u */
|
|
mp_exch(&u, &v);
|
|
}
|
|
|
|
/* subtract smallest from largest */
|
|
if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
|
|
/* Divide out all factors of two */
|
|
if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
}
|
|
|
|
/* multiply by 2**k which we divided out at the beginning */
|
|
if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
|
|
goto __V;
|
|
}
|
|
c->sign = MP_ZPOS;
|
|
res = MP_OKAY;
|
|
__V:mp_clear (&u);
|
|
__U:mp_clear (&v);
|
|
return res;
|
|
}
|
|
|
|
/* get the lower 32-bits of an mp_int */
|
|
unsigned long mp_get_int(const mp_int * a)
|
|
{
|
|
int i;
|
|
unsigned long res;
|
|
|
|
if (a->used == 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* get number of digits of the lsb we have to read */
|
|
i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
|
|
|
|
/* get most significant digit of result */
|
|
res = DIGIT(a,i);
|
|
|
|
while (--i >= 0) {
|
|
res = (res << DIGIT_BIT) | DIGIT(a,i);
|
|
}
|
|
|
|
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
|
|
return res & 0xFFFFFFFFUL;
|
|
}
|
|
|
|
/* creates "a" then copies b into it */
|
|
int mp_init_copy (mp_int * a, const mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_init (a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return mp_copy (b, a);
|
|
}
|
|
|
|
int mp_init_multi(mp_int *mp, ...)
|
|
{
|
|
mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
|
|
int n = 0; /* Number of ok inits */
|
|
mp_int* cur_arg = mp;
|
|
va_list args;
|
|
|
|
va_start(args, mp); /* init args to next argument from caller */
|
|
while (cur_arg != NULL) {
|
|
if (mp_init(cur_arg) != MP_OKAY) {
|
|
/* Oops - error! Back-track and mp_clear what we already
|
|
succeeded in init-ing, then return error.
|
|
*/
|
|
va_list clean_args;
|
|
|
|
/* end the current list */
|
|
va_end(args);
|
|
|
|
/* now start cleaning up */
|
|
cur_arg = mp;
|
|
va_start(clean_args, mp);
|
|
while (n--) {
|
|
mp_clear(cur_arg);
|
|
cur_arg = va_arg(clean_args, mp_int*);
|
|
}
|
|
va_end(clean_args);
|
|
res = MP_MEM;
|
|
break;
|
|
}
|
|
n++;
|
|
cur_arg = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
return res; /* Assumed ok, if error flagged above. */
|
|
}
|
|
|
|
/* hac 14.61, pp608 */
|
|
int mp_invmod (const mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
/* 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 (a, b, c);
|
|
}
|
|
|
|
return mp_invmod_slow(a, b, c);
|
|
}
|
|
|
|
/* hac 14.61, pp608 */
|
|
int mp_invmod_slow (const mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x, y, u, v, A, B, C, D;
|
|
int res;
|
|
|
|
/* b cannot be negative */
|
|
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
if ((res = mp_init_multi(&x, &y, &u, &v,
|
|
&A, &B, &C, &D, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* x = a, y = b */
|
|
if ((res = mp_copy (a, &x)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
if ((res = mp_copy (b, &y)) != MP_OKAY) {
|
|
goto __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 __ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
|
goto __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 __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 __ERR;
|
|
}
|
|
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
|
goto __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 __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 __ERR;
|
|
}
|
|
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
|
goto __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 __ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
|
goto __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 __ERR;
|
|
}
|
|
|
|
/* if it's too low */
|
|
while (mp_cmp_d(&C, 0) == MP_LT) {
|
|
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
}
|
|
|
|
/* too big */
|
|
while (mp_cmp_mag(&C, b) != MP_LT) {
|
|
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
|
|
goto __ERR;
|
|
}
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
mp_exch (&C, c);
|
|
res = MP_OKAY;
|
|
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
|
|
return res;
|
|
}
|
|
|
|
/* c = |a| * |b| using Karatsuba Multiplication using
|
|
* three half size multiplications
|
|
*
|
|
* Let B represent the radix [e.g. 2**DIGIT_BIT] and
|
|
* let n represent half of the number of digits in
|
|
* the min(a,b)
|
|
*
|
|
* a = a1 * B**n + a0
|
|
* b = b1 * B**n + b0
|
|
*
|
|
* Then, a * b =>
|
|
a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
|
|
*
|
|
* Note that a1b1 and a0b0 are used twice and only need to be
|
|
* computed once. So in total three half size (half # of
|
|
* digit) multiplications are performed, a0b0, a1b1 and
|
|
* (a1-b1)(a0-b0)
|
|
*
|
|
* Note that a multiplication of half the digits requires
|
|
* 1/4th the number of single precision multiplications so in
|
|
* total after one call 25% of the single precision multiplications
|
|
* are saved. Note also that the call to mp_mul can end up back
|
|
* in this function if the a0, a1, b0, or b1 are above the threshold.
|
|
* This is known as divide-and-conquer and leads to the famous
|
|
* O(N**lg(3)) or O(N**1.584) work which is asymptotically lower than
|
|
* the standard O(N**2) that the baseline/comba methods use.
|
|
* Generally though the overhead of this method doesn't pay off
|
|
* until a certain size (N ~ 80) is reached.
|
|
*/
|
|
int mp_karatsuba_mul (const mp_int * a, const mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
|
|
int B, err;
|
|
|
|
/* default the return code to an error */
|
|
err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = MIN (a->used, b->used);
|
|
|
|
/* now divide in two */
|
|
B = B >> 1;
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size (&x0, B) != MP_OKAY)
|
|
goto ERR;
|
|
if (mp_init_size (&x1, a->used - B) != MP_OKAY)
|
|
goto X0;
|
|
if (mp_init_size (&y0, B) != MP_OKAY)
|
|
goto X1;
|
|
if (mp_init_size (&y1, b->used - B) != MP_OKAY)
|
|
goto Y0;
|
|
|
|
/* init temps */
|
|
if (mp_init_size (&t1, B * 2) != MP_OKAY)
|
|
goto Y1;
|
|
if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
|
|
goto T1;
|
|
if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
|
|
goto X0Y0;
|
|
|
|
/* now shift the digits */
|
|
x0.used = y0.used = B;
|
|
x1.used = a->used - B;
|
|
y1.used = b->used - B;
|
|
|
|
{
|
|
register int x;
|
|
register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
|
|
|
|
/* we copy the digits directly instead of using higher level functions
|
|
* since we also need to shift the digits
|
|
*/
|
|
tmpa = a->dp;
|
|
tmpb = b->dp;
|
|
|
|
tmpx = x0.dp;
|
|
tmpy = y0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
|
|
tmpx = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*tmpx++ = *tmpa++;
|
|
}
|
|
|
|
tmpy = y1.dp;
|
|
for (x = B; x < b->used; x++) {
|
|
*tmpy++ = *tmpb++;
|
|
}
|
|
}
|
|
|
|
/* only need to clamp the lower words since by definition the
|
|
* upper words x1/y1 must have a known number of digits
|
|
*/
|
|
mp_clamp (&x0);
|
|
mp_clamp (&y0);
|
|
|
|
/* now calc the products x0y0 and x1y1 */
|
|
/* after this x0 is no longer required, free temp [x0==t2]! */
|
|
if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
|
|
goto X1Y1; /* x0y0 = x0*y0 */
|
|
if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
|
|
goto X1Y1; /* x1y1 = x1*y1 */
|
|
|
|
/* now calc x1-x0 and y1-y0 */
|
|
if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
|
|
goto X1Y1; /* t1 = x1 - x0 */
|
|
if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
|
|
goto X1Y1; /* t2 = y1 - y0 */
|
|
if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
|
|
goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
|
|
|
|
/* add x0y0 */
|
|
if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
|
|
goto X1Y1; /* t2 = x0y0 + x1y1 */
|
|
if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
|
|
goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
|
|
|
|
/* shift by B */
|
|
if (mp_lshd (&t1, B) != MP_OKAY)
|
|
goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
|
|
if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
|
|
goto X1Y1; /* x1y1 = x1y1 << 2*B */
|
|
|
|
if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
|
|
goto X1Y1; /* t1 = x0y0 + t1 */
|
|
if (mp_add (&t1, &x1y1, c) != MP_OKAY)
|
|
goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
|
|
|
|
/* Algorithm succeeded set the return code to MP_OKAY */
|
|
err = MP_OKAY;
|
|
|
|
X1Y1:mp_clear (&x1y1);
|
|
X0Y0:mp_clear (&x0y0);
|
|
T1:mp_clear (&t1);
|
|
Y1:mp_clear (&y1);
|
|
Y0:mp_clear (&y0);
|
|
X1:mp_clear (&x1);
|
|
X0:mp_clear (&x0);
|
|
ERR:
|
|
return err;
|
|
}
|
|
|
|
/* Karatsuba squaring, computes b = a*a using three
|
|
* half size squarings
|
|
*
|
|
* See comments of karatsuba_mul for details. It
|
|
* is essentially the same algorithm but merely
|
|
* tuned to perform recursive squarings.
|
|
*/
|
|
int mp_karatsuba_sqr (const mp_int * a, mp_int * b)
|
|
{
|
|
mp_int x0, x1, t1, t2, x0x0, x1x1;
|
|
int B, err;
|
|
|
|
err = MP_MEM;
|
|
|
|
/* min # of digits */
|
|
B = a->used;
|
|
|
|
/* now divide in two */
|
|
B = B >> 1;
|
|
|
|
/* init copy all the temps */
|
|
if (mp_init_size (&x0, B) != MP_OKAY)
|
|
goto ERR;
|
|
if (mp_init_size (&x1, a->used - B) != MP_OKAY)
|
|
goto X0;
|
|
|
|
/* init temps */
|
|
if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
|
|
goto X1;
|
|
if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
|
|
goto T1;
|
|
if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
|
|
goto T2;
|
|
if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
|
|
goto X0X0;
|
|
|
|
{
|
|
register int x;
|
|
register mp_digit *dst, *src;
|
|
|
|
src = a->dp;
|
|
|
|
/* now shift the digits */
|
|
dst = x0.dp;
|
|
for (x = 0; x < B; x++) {
|
|
*dst++ = *src++;
|
|
}
|
|
|
|
dst = x1.dp;
|
|
for (x = B; x < a->used; x++) {
|
|
*dst++ = *src++;
|
|
}
|
|
}
|
|
|
|
x0.used = B;
|
|
x1.used = a->used - B;
|
|
|
|
mp_clamp (&x0);
|
|
|
|
/* now calc the products x0*x0 and x1*x1 */
|
|
if (mp_sqr (&x0, &x0x0) != MP_OKAY)
|
|
goto X1X1; /* x0x0 = x0*x0 */
|
|
if (mp_sqr (&x1, &x1x1) != MP_OKAY)
|
|
goto X1X1; /* x1x1 = x1*x1 */
|
|
|
|
/* now calc (x1-x0)**2 */
|
|
if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = x1 - x0 */
|
|
if (mp_sqr (&t1, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
|
|
|
|
/* add x0y0 */
|
|
if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
|
|
goto X1X1; /* t2 = x0x0 + x1x1 */
|
|
if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
|
|
|
|
/* shift by B */
|
|
if (mp_lshd (&t1, B) != MP_OKAY)
|
|
goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
|
|
if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
|
|
goto X1X1; /* x1x1 = x1x1 << 2*B */
|
|
|
|
if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
|
|
goto X1X1; /* t1 = x0x0 + t1 */
|
|
if (mp_add (&t1, &x1x1, b) != MP_OKAY)
|
|
goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
|
|
|
|
err = MP_OKAY;
|
|
|
|
X1X1:mp_clear (&x1x1);
|
|
X0X0:mp_clear (&x0x0);
|
|
T2:mp_clear (&t2);
|
|
T1:mp_clear (&t1);
|
|
X1:mp_clear (&x1);
|
|
X0:mp_clear (&x0);
|
|
ERR:
|
|
return err;
|
|
}
|
|
|
|
/* computes least common multiple as |a*b|/(a, b) */
|
|
int mp_lcm (const mp_int * a, const mp_int * b, mp_int * c)
|
|
{
|
|
int res;
|
|
mp_int t1, t2;
|
|
|
|
|
|
if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* t1 = get the GCD of the two inputs */
|
|
if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
|
|
/* divide the smallest by the GCD */
|
|
if (mp_cmp_mag(a, b) == MP_LT) {
|
|
/* store quotient in t2 so that t2 * b is the LCM */
|
|
if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
res = mp_mul(b, &t2, c);
|
|
} else {
|
|
/* store quotient in t2 so that t2 * a is the LCM */
|
|
if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
|
|
goto __T;
|
|
}
|
|
res = mp_mul(a, &t2, c);
|
|
}
|
|
|
|
/* fix the sign to positive */
|
|
c->sign = MP_ZPOS;
|
|
|
|
__T:
|
|
mp_clear_multi (&t1, &t2, NULL);
|
|
return res;
|
|
}
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
int
|
|
mp_mod (const mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int t;
|
|
int res;
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_div (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;
|
|
}
|
|
|
|
static int
|
|
mp_mod_d (const mp_int * a, mp_digit b, mp_digit * c)
|
|
{
|
|
return mp_div_d(a, b, NULL, c);
|
|
}
|
|
|
|
/* b = a*2 */
|
|
static int mp_mul_2(const mp_int * a, mp_int * b)
|
|
{
|
|
int x, res, oldused;
|
|
|
|
/* grow to accommodate 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;
|
|
}
|
|
|
|
/*
|
|
* shifts with subtractions when the result is greater than b.
|
|
*
|
|
* The method is slightly modified to shift B unconditionally up to just under
|
|
* the leading bit of b. This saves a lot of multiple precision shifting.
|
|
*/
|
|
int mp_montgomery_calc_normalization (mp_int * a, const mp_int * b)
|
|
{
|
|
int 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 < 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;
|
|
}
|
|
|
|
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
|
|
int
|
|
mp_montgomery_reduce (mp_int * x, const mp_int * n, mp_digit rho)
|
|
{
|
|
int 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
|
|
* 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 int 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;
|
|
}
|
|
|
|
/* setups the montgomery reduction stuff */
|
|
int
|
|
mp_montgomery_setup (const 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 *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
|
|
|
/* rho = -1/m mod b */
|
|
*rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* high level multiplication (handles sign) */
|
|
int mp_mul (const mp_int * a, const mp_int * b, mp_int * c)
|
|
{
|
|
int res, neg;
|
|
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
|
|
/* use Karatsuba? */
|
|
if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
|
|
res = mp_karatsuba_mul (a, b, c);
|
|
} else
|
|
{
|
|
/* 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
|
|
*/
|
|
int digs = a->used + b->used + 1;
|
|
|
|
if ((digs < MP_WARRAY) &&
|
|
MIN(a->used, b->used) <=
|
|
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
res = fast_s_mp_mul_digs (a, b, c, digs);
|
|
} else
|
|
res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
|
|
}
|
|
c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
/* d = a * b (mod c) */
|
|
int
|
|
mp_mulmod (const mp_int * a, const mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
int res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
res = mp_mod (&t, c, d);
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
/* table of first PRIME_SIZE primes */
|
|
static const mp_digit __prime_tab[] = {
|
|
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
|
|
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
|
|
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
|
|
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
|
|
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
|
|
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
|
|
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
|
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
|
|
|
|
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
|
|
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
|
|
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
|
|
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
|
|
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
|
|
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
|
|
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
|
|
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
|
|
|
|
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
|
|
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
|
|
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
|
|
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
|
|
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
|
|
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
|
|
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
|
|
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
|
|
|
|
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
|
|
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
|
|
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
|
|
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
|
|
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
|
|
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
|
|
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
|
|
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
|
|
};
|
|
|
|
/* determines if an integers is divisible by one
|
|
* of the first PRIME_SIZE primes or not
|
|
*
|
|
* sets result to 0 if not, 1 if yes
|
|
*/
|
|
static int mp_prime_is_divisible (const mp_int * a, int *result)
|
|
{
|
|
int err, ix;
|
|
mp_digit res;
|
|
|
|
/* default to not */
|
|
*result = MP_NO;
|
|
|
|
for (ix = 0; ix < PRIME_SIZE; ix++) {
|
|
/* what is a mod __prime_tab[ix] */
|
|
if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* is the residue zero? */
|
|
if (res == 0) {
|
|
*result = MP_YES;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* Miller-Rabin test of "a" to the base of "b" as described in
|
|
* HAC pp. 139 Algorithm 4.24
|
|
*
|
|
* Sets result to 0 if definitely composite or 1 if probably prime.
|
|
* Randomly the chance of error is no more than 1/4 and often
|
|
* very much lower.
|
|
*/
|
|
static int mp_prime_miller_rabin (mp_int * a, const mp_int * b, int *result)
|
|
{
|
|
mp_int n1, y, r;
|
|
int s, j, err;
|
|
|
|
/* default */
|
|
*result = MP_NO;
|
|
|
|
/* ensure b > 1 */
|
|
if (mp_cmp_d(b, 1) != MP_GT) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* get n1 = a - 1 */
|
|
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
|
|
goto __N1;
|
|
}
|
|
|
|
/* set 2**s * r = n1 */
|
|
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
|
|
goto __N1;
|
|
}
|
|
|
|
/* count the number of least significant bits
|
|
* which are zero
|
|
*/
|
|
s = mp_cnt_lsb(&r);
|
|
|
|
/* now divide n - 1 by 2**s */
|
|
if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
|
|
goto __R;
|
|
}
|
|
|
|
/* compute y = b**r mod a */
|
|
if ((err = mp_init (&y)) != MP_OKAY) {
|
|
goto __R;
|
|
}
|
|
if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
|
|
/* if y != 1 and y != n1 do */
|
|
if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
|
|
j = 1;
|
|
/* while j <= s-1 and y != n1 */
|
|
while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
|
|
if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
|
|
goto __Y;
|
|
}
|
|
|
|
/* if y == 1 then composite */
|
|
if (mp_cmp_d (&y, 1) == MP_EQ) {
|
|
goto __Y;
|
|
}
|
|
|
|
++j;
|
|
}
|
|
|
|
/* if y != n1 then composite */
|
|
if (mp_cmp (&y, &n1) != MP_EQ) {
|
|
goto __Y;
|
|
}
|
|
}
|
|
|
|
/* probably prime now */
|
|
*result = MP_YES;
|
|
__Y:mp_clear (&y);
|
|
__R:mp_clear (&r);
|
|
__N1:mp_clear (&n1);
|
|
return err;
|
|
}
|
|
|
|
/* performs a variable number of rounds of Miller-Rabin
|
|
*
|
|
* Probability of error after t rounds is no more than
|
|
|
|
*
|
|
* Sets result to 1 if probably prime, 0 otherwise
|
|
*/
|
|
static int mp_prime_is_prime (mp_int * a, int t, int *result)
|
|
{
|
|
mp_int b;
|
|
int ix, err, res;
|
|
|
|
/* default to no */
|
|
*result = MP_NO;
|
|
|
|
/* valid value of t? */
|
|
if (t <= 0 || t > PRIME_SIZE) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* is the input equal to one of the primes in the table? */
|
|
for (ix = 0; ix < PRIME_SIZE; ix++) {
|
|
if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
|
|
*result = 1;
|
|
return MP_OKAY;
|
|
}
|
|
}
|
|
|
|
/* first perform trial division */
|
|
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* return if it was trivially divisible */
|
|
if (res == MP_YES) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* now perform the miller-rabin rounds */
|
|
if ((err = mp_init (&b)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
for (ix = 0; ix < t; ix++) {
|
|
/* set the prime */
|
|
mp_set (&b, __prime_tab[ix]);
|
|
|
|
if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
|
|
goto __B;
|
|
}
|
|
|
|
if (res == MP_NO) {
|
|
goto __B;
|
|
}
|
|
}
|
|
|
|
/* passed the test */
|
|
*result = MP_YES;
|
|
__B:mp_clear (&b);
|
|
return err;
|
|
}
|
|
|
|
static const struct {
|
|
int k, t;
|
|
} sizes[] = {
|
|
{ 128, 28 },
|
|
{ 256, 16 },
|
|
{ 384, 10 },
|
|
{ 512, 7 },
|
|
{ 640, 6 },
|
|
{ 768, 5 },
|
|
{ 896, 4 },
|
|
{ 1024, 4 }
|
|
};
|
|
|
|
/* returns # of RM trials required for a given bit size */
|
|
int mp_prime_rabin_miller_trials(int size)
|
|
{
|
|
int x;
|
|
|
|
for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
|
|
if (sizes[x].k == size) {
|
|
return sizes[x].t;
|
|
} else if (sizes[x].k > size) {
|
|
return (x == 0) ? sizes[0].t : sizes[x - 1].t;
|
|
}
|
|
}
|
|
return sizes[x-1].t + 1;
|
|
}
|
|
|
|
/* makes a truly random prime of a given size (bits),
|
|
*
|
|
* Flags are as follows:
|
|
*
|
|
* LTM_PRIME_BBS - make prime congruent to 3 mod 4
|
|
* LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
|
|
* LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
|
|
* LTM_PRIME_2MSB_ON - make the 2nd highest bit one
|
|
*
|
|
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
|
|
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
|
|
* so it can be NULL
|
|
*
|
|
*/
|
|
|
|
/* This is possibly the mother of all prime generation functions, muahahahahaha! */
|
|
int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
|
|
{
|
|
unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
|
|
int res, err, bsize, maskOR_msb_offset;
|
|
|
|
/* sanity check the input */
|
|
if (size <= 1 || t <= 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
|
|
if (flags & LTM_PRIME_SAFE) {
|
|
flags |= LTM_PRIME_BBS;
|
|
}
|
|
|
|
/* calc the byte size */
|
|
bsize = (size>>3)+((size&7)?1:0);
|
|
|
|
/* we need a buffer of bsize bytes */
|
|
tmp = HeapAlloc(GetProcessHeap(), 0, bsize);
|
|
if (tmp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* calc the maskAND value for the MSbyte*/
|
|
maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
|
|
|
|
/* calc the maskOR_msb */
|
|
maskOR_msb = 0;
|
|
maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
|
|
if (flags & LTM_PRIME_2MSB_ON) {
|
|
maskOR_msb |= 1 << ((size - 2) & 7);
|
|
} else if (flags & LTM_PRIME_2MSB_OFF) {
|
|
maskAND &= ~(1 << ((size - 2) & 7));
|
|
}
|
|
|
|
/* get the maskOR_lsb */
|
|
maskOR_lsb = 0;
|
|
if (flags & LTM_PRIME_BBS) {
|
|
maskOR_lsb |= 3;
|
|
}
|
|
|
|
do {
|
|
/* read the bytes */
|
|
if (cb(tmp, bsize, dat) != bsize) {
|
|
err = MP_VAL;
|
|
goto error;
|
|
}
|
|
|
|
/* work over the MSbyte */
|
|
tmp[0] &= maskAND;
|
|
tmp[0] |= 1 << ((size - 1) & 7);
|
|
|
|
/* mix in the maskORs */
|
|
tmp[maskOR_msb_offset] |= maskOR_msb;
|
|
tmp[bsize-1] |= maskOR_lsb;
|
|
|
|
/* read it in */
|
|
if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
|
|
|
|
/* is it prime? */
|
|
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
|
|
if (res == MP_NO) {
|
|
continue;
|
|
}
|
|
|
|
if (flags & LTM_PRIME_SAFE) {
|
|
/* see if (a-1)/2 is prime */
|
|
if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
|
|
if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
|
|
|
|
/* is it prime? */
|
|
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
|
|
}
|
|
} while (res == MP_NO);
|
|
|
|
if (flags & LTM_PRIME_SAFE) {
|
|
/* restore a to the original value */
|
|
if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
|
|
if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
|
|
}
|
|
|
|
err = MP_OKAY;
|
|
error:
|
|
HeapFree(GetProcessHeap(), 0, tmp);
|
|
return err;
|
|
}
|
|
|
|
/* reads an unsigned char array, assumes the msb is stored first [big endian] */
|
|
int
|
|
mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
|
{
|
|
int 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 int */
|
|
mp_zero (a);
|
|
|
|
/* read the bytes in */
|
|
while (c-- > 0) {
|
|
if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
a->dp[0] |= *b++;
|
|
a->used += 1;
|
|
}
|
|
mp_clamp (a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* reduces x mod m, assumes 0 < x < m**2, mu is
|
|
* precomputed via mp_reduce_setup.
|
|
* From HAC pp.604 Algorithm 14.42
|
|
*/
|
|
int
|
|
mp_reduce (mp_int * x, const mp_int * m, const mp_int * mu)
|
|
{
|
|
mp_int q;
|
|
int res, um = m->used;
|
|
|
|
/* q = x */
|
|
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* q1 = x / b**(k-1) */
|
|
mp_rshd (&q, um - 1);
|
|
|
|
/* according to HAC this optimization is ok */
|
|
if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
|
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else {
|
|
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
/* q3 = q2 / b**(k+1) */
|
|
mp_rshd (&q, um + 1);
|
|
|
|
/* x = x mod b**(k+1), quick (no division) */
|
|
if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* q = q * m mod b**(k+1), quick (no division) */
|
|
if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* x = x - q */
|
|
if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* If x < 0, add b**(k+1) to it */
|
|
if (mp_cmp_d (x, 0) == MP_LT) {
|
|
mp_set (&q, 1);
|
|
if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
|
|
goto CLEANUP;
|
|
if ((res = mp_add (x, &q, x)) != MP_OKAY)
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* Back off if it's too big */
|
|
while (mp_cmp (x, m) != MP_LT) {
|
|
if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
CLEANUP:
|
|
mp_clear (&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
/* reduces a modulo n where n is of the form 2**p - d */
|
|
int
|
|
mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
|
|
{
|
|
mp_int q;
|
|
int p, res;
|
|
|
|
if ((res = mp_init(&q)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (d != 1) {
|
|
/* q = q * d */
|
|
if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (mp_cmp_mag(a, n) != MP_LT) {
|
|
s_mp_sub(a, n, a);
|
|
goto top;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&q);
|
|
return res;
|
|
}
|
|
|
|
/* determines the setup value */
|
|
static int
|
|
mp_reduce_2k_setup(const mp_int *a, mp_digit *d)
|
|
{
|
|
int res, p;
|
|
mp_int tmp;
|
|
|
|
if ((res = mp_init(&tmp)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(a);
|
|
if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
*d = tmp.dp[0];
|
|
mp_clear(&tmp);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* pre-calculate the value required for Barrett reduction
|
|
* For a given modulus "b" it calculates the value required in "a"
|
|
*/
|
|
int mp_reduce_setup (mp_int * a, const mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return mp_div (a, b, a, NULL);
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
|
|
/* set a 32-bit const */
|
|
int mp_set_int (mp_int * a, unsigned long b)
|
|
{
|
|
int x, res;
|
|
|
|
mp_zero (a);
|
|
|
|
/* set four bits at a time */
|
|
for (x = 0; x < 8; x++) {
|
|
/* shift the number up four bits */
|
|
if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* OR in the top four bits of the source */
|
|
a->dp[0] |= (b >> 28) & 15;
|
|
|
|
/* shift the source up to the next four bits */
|
|
b <<= 4;
|
|
|
|
/* ensure that digits are not clamped off */
|
|
a->used += 1;
|
|
}
|
|
mp_clamp (a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* shrink a bignum */
|
|
int mp_shrink (mp_int * a)
|
|
{
|
|
mp_digit *tmp;
|
|
if (a->alloc != a->used && a->used > 0) {
|
|
if ((tmp = HeapReAlloc(GetProcessHeap(), 0, a->dp, sizeof (mp_digit) * a->used)) == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
a->dp = tmp;
|
|
a->alloc = a->used;
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* computes b = a*a */
|
|
int
|
|
mp_sqr (const mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if (a->used >= KARATSUBA_SQR_CUTOFF) {
|
|
res = mp_karatsuba_sqr (a, b);
|
|
} else
|
|
{
|
|
/* 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 (a, b);
|
|
} else
|
|
res = s_mp_sqr (a, b);
|
|
}
|
|
b->sign = MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
/* c = a * a (mod b) */
|
|
int
|
|
mp_sqrmod (const mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_sqr (a, &t)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
res = mp_mod (&t, b, c);
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
/* high level subtraction (handles signs) */
|
|
int
|
|
mp_sub (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
int 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;
|
|
}
|
|
|
|
/* single digit subtraction */
|
|
int
|
|
mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
mp_digit *tmpa, *tmpc, mu;
|
|
int 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;
|
|
}
|
|
|
|
/* store in unsigned [big endian] format */
|
|
int
|
|
mp_to_unsigned_bin (const mp_int * a, unsigned char *b)
|
|
{
|
|
int x, res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
x = 0;
|
|
while (mp_iszero (&t) == 0) {
|
|
b[x++] = (unsigned char) (t.dp[0] & 255);
|
|
if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
}
|
|
bn_reverse (b, x);
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* get the size for an unsigned equivalent */
|
|
int
|
|
mp_unsigned_bin_size (const mp_int * a)
|
|
{
|
|
int size = mp_count_bits (a);
|
|
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
|
|
}
|
|
|
|
/* reverse an array, used for radix code */
|
|
static void
|
|
bn_reverse (unsigned char *s, int len)
|
|
{
|
|
int 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;
|
|
}
|
|
}
|
|
|
|
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
|
|
static int
|
|
s_mp_add (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int *x;
|
|
int 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 int 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;
|
|
}
|
|
|
|
static int s_mp_exptmod (const mp_int * G, const mp_int * X, mp_int * P, mp_int * Y)
|
|
{
|
|
mp_int M[256], res, mu;
|
|
mp_digit buf;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
|
|
/* 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;
|
|
}
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&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(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear (&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* create mu, used for Barrett reduction */
|
|
if ((err = mp_init (&mu)) != MP_OKAY) {
|
|
goto __M;
|
|
}
|
|
if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
* The M table contains powers of the base,
|
|
* e.g. M[x] = G**x mod P
|
|
*
|
|
* The first half of the table is not
|
|
* computed though accept for M[0] and M[1]
|
|
*/
|
|
if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
|
|
/* 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 __MU;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = mp_sqr (&M[1 << (winsize - 1)],
|
|
&M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
}
|
|
|
|
/* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
|
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
|
*/
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init (&res)) != MP_OKAY) {
|
|
goto __MU;
|
|
}
|
|
mp_set (&res, 1);
|
|
|
|
/* 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 */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset the bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (buf >> (mp_digit)(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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
|
|
goto __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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
|
|
goto __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 (&res, &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
|
|
goto __RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
mp_exch (&res, Y);
|
|
err = MP_OKAY;
|
|
__RES:mp_clear (&res);
|
|
__MU:mp_clear (&mu);
|
|
__M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear (&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
/* multiplies |a| * |b| and only computes up to digs digits of result
|
|
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
|
* many digits of output are created.
|
|
*/
|
|
static int
|
|
s_mp_mul_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int 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 (a, b, c, digs);
|
|
}
|
|
|
|
if ((res = mp_init_size (&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;
|
|
}
|
|
|
|
/* multiplies |a| * |b| and does not compute the lower digs digits
|
|
* [meant to get the higher part of the product]
|
|
*/
|
|
static int
|
|
s_mp_mul_high_digs (const mp_int * a, const mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int res, pa, pb, ix, iy;
|
|
mp_digit u;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
/* can we use the fast multiplier? */
|
|
if (((a->used + b->used + 1) < MP_WARRAY)
|
|
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
return fast_s_mp_mul_high_digs (a, b, c, digs);
|
|
}
|
|
|
|
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
t.used = a->used + b->used + 1;
|
|
|
|
pa = a->used;
|
|
pb = b->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* clear the carry */
|
|
u = 0;
|
|
|
|
/* left hand side of A[ix] * B[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias to the address of where the digits will be stored */
|
|
tmpt = &(t.dp[digs]);
|
|
|
|
/* alias for where to read the right hand side from */
|
|
tmpy = b->dp + (digs - ix);
|
|
|
|
for (iy = digs - ix; iy < pb; iy++) {
|
|
/* calculate the double precision result */
|
|
r = ((mp_word)*tmpt) +
|
|
((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
|
((mp_word) u);
|
|
|
|
/* get the lower part */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* carry the carry */
|
|
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
*tmpt = u;
|
|
}
|
|
mp_clamp (&t);
|
|
mp_exch (&t, c);
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
|
static int
|
|
s_mp_sqr (const mp_int * a, mp_int * b)
|
|
{
|
|
mp_int t;
|
|
int res, ix, iy, pa;
|
|
mp_word r;
|
|
mp_digit u, tmpx, *tmpt;
|
|
|
|
pa = a->used;
|
|
if ((res = mp_init_size (&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 != 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;
|
|
}
|
|
|
|
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
|
|
int
|
|
s_mp_sub (const mp_int * a, const mp_int * b, mp_int * c)
|
|
{
|
|
int 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 int 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;
|
|
}
|