+++ /dev/null
-/* tfm.c
- *
- * Copyright (C) 2006-2014 wolfSSL Inc.
- *
- * This file is part of CyaSSL.
- *
- * CyaSSL is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * CyaSSL is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
- */
-
-
-/*
- * Based on public domain TomsFastMath 0.10 by Tom St Denis, tomstdenis@iahu.ca,
- * http://math.libtomcrypt.com
- */
-
-/**
- * Edited by Moisés Guimarães (moisesguimaraesm@gmail.com)
- * to fit CyaSSL's needs.
- */
-
-#ifdef HAVE_CONFIG_H
- #include <config.h>
-#endif
-
-/* in case user set USE_FAST_MATH there */
-#include <cyassl/ctaocrypt/settings.h>
-
-#ifdef USE_FAST_MATH
-
-#include <cyassl/ctaocrypt/tfm.h>
-#include <ctaocrypt/src/asm.c> /* will define asm MACROS or C ones */
-
-
-/* math settings check */
-word32 CheckRunTimeSettings(void)
-{
- return CTC_SETTINGS;
-}
-
-
-/* math settings size check */
-word32 CheckRunTimeFastMath(void)
-{
- return FP_SIZE;
-}
-
-
-/* Functions */
-
-void fp_add(fp_int *a, fp_int *b, fp_int *c)
-{
- int sa, sb;
-
- /* 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;
- s_fp_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 (fp_cmp_mag (a, b) == FP_LT) {
- c->sign = sb;
- s_fp_sub (b, a, c);
- } else {
- c->sign = sa;
- s_fp_sub (a, b, c);
- }
- }
-}
-
-/* unsigned addition */
-void s_fp_add(fp_int *a, fp_int *b, fp_int *c)
-{
- int x, y, oldused;
- register fp_word t;
-
- y = MAX(a->used, b->used);
- oldused = MAX(c->used, FP_SIZE); /* help static analysis w/ max size */
- c->used = y;
-
- t = 0;
- for (x = 0; x < y; x++) {
- t += ((fp_word)a->dp[x]) + ((fp_word)b->dp[x]);
- c->dp[x] = (fp_digit)t;
- t >>= DIGIT_BIT;
- }
- if (t != 0 && x < FP_SIZE) {
- c->dp[c->used++] = (fp_digit)t;
- ++x;
- }
-
- c->used = x;
- for (; x < oldused; x++) {
- c->dp[x] = 0;
- }
- fp_clamp(c);
-}
-
-/* c = a - b */
-void fp_sub(fp_int *a, fp_int *b, fp_int *c)
-{
- int sa, sb;
-
- 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;
- s_fp_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 (fp_cmp_mag (a, b) != FP_LT) {
- /* Copy the sign from the first */
- c->sign = sa;
- /* The first has a larger or equal magnitude */
- s_fp_sub (a, b, c);
- } else {
- /* The result has the *opposite* sign from */
- /* the first number. */
- c->sign = (sa == FP_ZPOS) ? FP_NEG : FP_ZPOS;
- /* The second has a larger magnitude */
- s_fp_sub (b, a, c);
- }
- }
-}
-
-/* unsigned subtraction ||a|| >= ||b|| ALWAYS! */
-void s_fp_sub(fp_int *a, fp_int *b, fp_int *c)
-{
- int x, oldbused, oldused;
- fp_word t;
-
- oldused = c->used;
- oldbused = b->used;
- c->used = a->used;
- t = 0;
- for (x = 0; x < oldbused; x++) {
- t = ((fp_word)a->dp[x]) - (((fp_word)b->dp[x]) + t);
- c->dp[x] = (fp_digit)t;
- t = (t >> DIGIT_BIT)&1;
- }
- for (; x < a->used; x++) {
- t = ((fp_word)a->dp[x]) - t;
- c->dp[x] = (fp_digit)t;
- t = (t >> DIGIT_BIT)&1;
- }
- for (; x < oldused; x++) {
- c->dp[x] = 0;
- }
- fp_clamp(c);
-}
-
-/* c = a * b */
-void fp_mul(fp_int *A, fp_int *B, fp_int *C)
-{
- int y, yy;
-
- y = MAX(A->used, B->used);
- yy = MIN(A->used, B->used);
-
- /* call generic if we're out of range */
- if (y + yy > FP_SIZE) {
- fp_mul_comba(A, B, C);
- return ;
- }
-
- /* pick a comba (unrolled 4/8/16/32 x or rolled) based on the size
- of the largest input. We also want to avoid doing excess mults if the
- inputs are not close to the next power of two. That is, for example,
- if say y=17 then we would do (32-17)^2 = 225 unneeded multiplications
- */
-
-#ifdef TFM_MUL3
- if (y <= 3) {
- fp_mul_comba3(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL4
- if (y == 4) {
- fp_mul_comba4(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL6
- if (y <= 6) {
- fp_mul_comba6(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL7
- if (y == 7) {
- fp_mul_comba7(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL8
- if (y == 8) {
- fp_mul_comba8(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL9
- if (y == 9) {
- fp_mul_comba9(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL12
- if (y <= 12) {
- fp_mul_comba12(A,B,C);
- return;
- }
-#endif
-#ifdef TFM_MUL17
- if (y <= 17) {
- fp_mul_comba17(A,B,C);
- return;
- }
-#endif
-
-#ifdef TFM_SMALL_SET
- if (y <= 16) {
- fp_mul_comba_small(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL20)
- if (y <= 20) {
- fp_mul_comba20(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL24)
- if (yy >= 16 && y <= 24) {
- fp_mul_comba24(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL28)
- if (yy >= 20 && y <= 28) {
- fp_mul_comba28(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL32)
- if (yy >= 24 && y <= 32) {
- fp_mul_comba32(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL48)
- if (yy >= 40 && y <= 48) {
- fp_mul_comba48(A,B,C);
- return;
- }
-#endif
-#if defined(TFM_MUL64)
- if (yy >= 56 && y <= 64) {
- fp_mul_comba64(A,B,C);
- return;
- }
-#endif
- fp_mul_comba(A,B,C);
-}
-
-void fp_mul_2(fp_int * a, fp_int * b)
-{
- int x, oldused;
-
- oldused = b->used;
- b->used = a->used;
-
- {
- register fp_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 >> ((fp_digit)(DIGIT_BIT - 1));
-
- /* now shift up this digit, add in the carry [from the previous] */
- *tmpb++ = ((*tmpa++ << ((fp_digit)1)) | r);
-
- /* copy the carry that would be from the source
- * digit into the next iteration
- */
- r = rr;
- }
-
- /* new leading digit? */
- if (r != 0 && b->used != (FP_SIZE-1)) {
- /* 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;
-}
-
-/* c = a * b */
-void fp_mul_d(fp_int *a, fp_digit b, fp_int *c)
-{
- fp_word w;
- int x, oldused;
-
- oldused = c->used;
- c->used = a->used;
- c->sign = a->sign;
- w = 0;
- for (x = 0; x < a->used; x++) {
- w = ((fp_word)a->dp[x]) * ((fp_word)b) + w;
- c->dp[x] = (fp_digit)w;
- w = w >> DIGIT_BIT;
- }
- if (w != 0 && (a->used != FP_SIZE)) {
- c->dp[c->used++] = (fp_digit) w;
- ++x;
- }
- for (; x < oldused; x++) {
- c->dp[x] = 0;
- }
- fp_clamp(c);
-}
-
-/* c = a * 2**d */
-void fp_mul_2d(fp_int *a, int b, fp_int *c)
-{
- fp_digit carry, carrytmp, shift;
- int x;
-
- /* copy it */
- fp_copy(a, c);
-
- /* handle whole digits */
- if (b >= DIGIT_BIT) {
- fp_lshd(c, b/DIGIT_BIT);
- }
- b %= DIGIT_BIT;
-
- /* shift the digits */
- if (b != 0) {
- carry = 0;
- shift = DIGIT_BIT - b;
- for (x = 0; x < c->used; x++) {
- carrytmp = c->dp[x] >> shift;
- c->dp[x] = (c->dp[x] << b) + carry;
- carry = carrytmp;
- }
- /* store last carry if room */
- if (carry && x < FP_SIZE) {
- c->dp[c->used++] = carry;
- }
- }
- fp_clamp(c);
-}
-
-/* generic PxQ multiplier */
-void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C)
-{
- int ix, iy, iz, tx, ty, pa;
- fp_digit c0, c1, c2, *tmpx, *tmpy;
- fp_int tmp, *dst;
-
- COMBA_START;
- COMBA_CLEAR;
-
- /* get size of output and trim */
- pa = A->used + B->used;
- if (pa >= FP_SIZE) {
- pa = FP_SIZE-1;
- }
-
- if (A == C || B == C) {
- fp_zero(&tmp);
- dst = &tmp;
- } else {
- fp_zero(C);
- dst = C;
- }
-
- for (ix = 0; ix < pa; ix++) {
- /* get offsets into the two bignums */
- ty = MIN(ix, B->used-1);
- tx = ix - ty;
-
- /* setup temp aliases */
- tmpx = A->dp + tx;
- tmpy = B->dp + ty;
-
- /* this is the number of times the loop will iterrate, essentially its
- while (tx++ < a->used && ty-- >= 0) { ... }
- */
- iy = MIN(A->used-tx, ty+1);
-
- /* execute loop */
- COMBA_FORWARD;
- for (iz = 0; iz < iy; ++iz) {
- /* TAO change COMBA_ADD back to MULADD */
- MULADD(*tmpx++, *tmpy--);
- }
-
- /* store term */
- COMBA_STORE(dst->dp[ix]);
- }
- COMBA_FINI;
-
- dst->used = pa;
- dst->sign = A->sign ^ B->sign;
- fp_clamp(dst);
- fp_copy(dst, C);
-}
-
-/* a/b => cb + d == a */
-int fp_div(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
-{
- fp_int q, x, y, t1, t2;
- int n, t, i, norm, neg;
-
- /* is divisor zero ? */
- if (fp_iszero (b) == 1) {
- return FP_VAL;
- }
-
- /* if a < b then q=0, r = a */
- if (fp_cmp_mag (a, b) == FP_LT) {
- if (d != NULL) {
- fp_copy (a, d);
- }
- if (c != NULL) {
- fp_zero (c);
- }
- return FP_OKAY;
- }
-
- fp_init(&q);
- q.used = a->used + 2;
-
- fp_init(&t1);
- fp_init(&t2);
- fp_init_copy(&x, a);
- fp_init_copy(&y, b);
-
- /* fix the sign */
- neg = (a->sign == b->sign) ? FP_ZPOS : FP_NEG;
- x.sign = y.sign = FP_ZPOS;
-
- /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
- norm = fp_count_bits(&y) % DIGIT_BIT;
- if (norm < (int)(DIGIT_BIT-1)) {
- norm = (DIGIT_BIT-1) - norm;
- fp_mul_2d (&x, norm, &x);
- fp_mul_2d (&y, norm, &y);
- } else {
- norm = 0;
- }
-
- /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
- n = x.used - 1;
- t = y.used - 1;
-
- /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
- fp_lshd (&y, n - t); /* y = y*b**{n-t} */
-
- while (fp_cmp (&x, &y) != FP_LT) {
- ++(q.dp[n - t]);
- fp_sub (&x, &y, &x);
- }
-
- /* reset y by shifting it back down */
- fp_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] = (fp_digit) ((((fp_word)1) << DIGIT_BIT) - 1);
- } else {
- fp_word tmp;
- tmp = ((fp_word) x.dp[i]) << ((fp_word) DIGIT_BIT);
- tmp |= ((fp_word) x.dp[i - 1]);
- tmp /= ((fp_word)y.dp[t]);
- q.dp[i - t - 1] = (fp_digit) (tmp);
- }
-
- /* 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);
- do {
- q.dp[i - t - 1] = (q.dp[i - t - 1] - 1);
-
- /* find left hand */
- fp_zero (&t1);
- t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
- t1.dp[1] = y.dp[t];
- t1.used = 2;
- fp_mul_d (&t1, q.dp[i - t - 1], &t1);
-
- /* 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 (fp_cmp_mag(&t1, &t2) == FP_GT);
-
- /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
- fp_mul_d (&y, q.dp[i - t - 1], &t1);
- fp_lshd (&t1, i - t - 1);
- fp_sub (&x, &t1, &x);
-
- /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
- if (x.sign == FP_NEG) {
- fp_copy (&y, &t1);
- fp_lshd (&t1, i - t - 1);
- fp_add (&x, &t1, &x);
- q.dp[i - t - 1] = q.dp[i - t - 1] - 1;
- }
- }
-
- /* 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 ? FP_ZPOS : a->sign;
-
- if (c != NULL) {
- fp_clamp (&q);
- fp_copy (&q, c);
- c->sign = neg;
- }
-
- if (d != NULL) {
- fp_div_2d (&x, norm, &x, NULL);
-
-/* the following is a kludge, essentially we were seeing the right remainder but
- with excess digits that should have been zero
- */
- for (i = b->used; i < x.used; i++) {
- x.dp[i] = 0;
- }
- fp_clamp(&x);
- fp_copy (&x, d);
- }
-
- return FP_OKAY;
-}
-
-/* b = a/2 */
-void fp_div_2(fp_int * a, fp_int * b)
-{
- int x, oldused;
-
- oldused = b->used;
- b->used = a->used;
- {
- register fp_digit r, rr, *tmpa, *tmpb;
-
- /* source alias */
- tmpa = a->dp + b->used - 1;
-
- /* dest alias */
- tmpb = b->dp + b->used - 1;
-
- /* carry */
- r = 0;
- for (x = b->used - 1; x >= 0; x--) {
- /* get the carry for the next iteration */
- rr = *tmpa & 1;
-
- /* shift the current digit, add in carry and store */
- *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-
- /* forward carry to next iteration */
- r = rr;
- }
-
- /* zero excess digits */
- tmpb = b->dp + b->used;
- for (x = b->used; x < oldused; x++) {
- *tmpb++ = 0;
- }
- }
- b->sign = a->sign;
- fp_clamp (b);
-}
-
-/* c = a / 2**b */
-void fp_div_2d(fp_int *a, int b, fp_int *c, fp_int *d)
-{
- int D;
- fp_int t;
-
- /* if the shift count is <= 0 then we do no work */
- if (b <= 0) {
- fp_copy (a, c);
- if (d != NULL) {
- fp_zero (d);
- }
- return;
- }
-
- fp_init(&t);
-
- /* get the remainder */
- if (d != NULL) {
- fp_mod_2d (a, b, &t);
- }
-
- /* copy */
- fp_copy(a, c);
-
- /* shift by as many digits in the bit count */
- if (b >= (int)DIGIT_BIT) {
- fp_rshd (c, b / DIGIT_BIT);
- }
-
- /* shift any bit count < DIGIT_BIT */
- D = (b % DIGIT_BIT);
- if (D != 0) {
- fp_rshb(c, D);
- }
- fp_clamp (c);
- if (d != NULL) {
- fp_copy (&t, d);
- }
-}
-
-/* c = a mod b, 0 <= c < b */
-int fp_mod(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_int t;
- int err;
-
- fp_zero(&t);
- if ((err = fp_div(a, b, NULL, &t)) != FP_OKAY) {
- return err;
- }
- if (t.sign != b->sign) {
- fp_add(&t, b, c);
- } else {
- fp_copy(&t, c);
- }
- return FP_OKAY;
-}
-
-/* c = a mod 2**d */
-void fp_mod_2d(fp_int *a, int b, fp_int *c)
-{
- int x;
-
- /* zero if count less than or equal to zero */
- if (b <= 0) {
- fp_zero(c);
- return;
- }
-
- /* get copy of input */
- fp_copy(a, c);
-
- /* if 2**d is larger than we just return */
- if (b >= (DIGIT_BIT * a->used)) {
- return;
- }
-
- /* 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] &= ~((fp_digit)0) >> (DIGIT_BIT - b);
- fp_clamp (c);
-}
-
-static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
-{
- fp_int x, y, u, v, A, B, C, D;
- int res;
-
- /* b cannot be negative */
- if (b->sign == FP_NEG || fp_iszero(b) == 1) {
- return FP_VAL;
- }
-
- /* init temps */
- fp_init(&x); fp_init(&y);
- fp_init(&u); fp_init(&v);
- fp_init(&A); fp_init(&B);
- fp_init(&C); fp_init(&D);
-
- /* x = a, y = b */
- if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
- return res;
- }
- fp_copy(b, &y);
-
- /* 2. [modified] if x,y are both even then return an error! */
- if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
- return FP_VAL;
- }
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- fp_copy (&x, &u);
- fp_copy (&y, &v);
- fp_set (&A, 1);
- fp_set (&D, 1);
-
-top:
- /* 4. while u is even do */
- while (fp_iseven (&u) == 1) {
- /* 4.1 u = u/2 */
- fp_div_2 (&u, &u);
-
- /* 4.2 if A or B is odd then */
- if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
- /* A = (A+y)/2, B = (B-x)/2 */
- fp_add (&A, &y, &A);
- fp_sub (&B, &x, &B);
- }
- /* A = A/2, B = B/2 */
- fp_div_2 (&A, &A);
- fp_div_2 (&B, &B);
- }
-
- /* 5. while v is even do */
- while (fp_iseven (&v) == 1) {
- /* 5.1 v = v/2 */
- fp_div_2 (&v, &v);
-
- /* 5.2 if C or D is odd then */
- if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
- /* C = (C+y)/2, D = (D-x)/2 */
- fp_add (&C, &y, &C);
- fp_sub (&D, &x, &D);
- }
- /* C = C/2, D = D/2 */
- fp_div_2 (&C, &C);
- fp_div_2 (&D, &D);
- }
-
- /* 6. if u >= v then */
- if (fp_cmp (&u, &v) != FP_LT) {
- /* u = u - v, A = A - C, B = B - D */
- fp_sub (&u, &v, &u);
- fp_sub (&A, &C, &A);
- fp_sub (&B, &D, &B);
- } else {
- /* v - v - u, C = C - A, D = D - B */
- fp_sub (&v, &u, &v);
- fp_sub (&C, &A, &C);
- fp_sub (&D, &B, &D);
- }
-
- /* if not zero goto step 4 */
- if (fp_iszero (&u) == 0)
- goto top;
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (fp_cmp_d (&v, 1) != FP_EQ) {
- return FP_VAL;
- }
-
- /* if its too low */
- while (fp_cmp_d(&C, 0) == FP_LT) {
- fp_add(&C, b, &C);
- }
-
- /* too big */
- while (fp_cmp_mag(&C, b) != FP_LT) {
- fp_sub(&C, b, &C);
- }
-
- /* C is now the inverse */
- fp_copy(&C, c);
- return FP_OKAY;
-}
-
-/* c = 1/a (mod b) for odd b only */
-int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_int x, y, u, v, B, D;
- int neg;
-
- /* 2. [modified] b must be odd */
- if (fp_iseven (b) == FP_YES) {
- return fp_invmod_slow(a,b,c);
- }
-
- /* init all our temps */
- fp_init(&x); fp_init(&y);
- fp_init(&u); fp_init(&v);
- fp_init(&B); fp_init(&D);
-
- /* x == modulus, y == value to invert */
- fp_copy(b, &x);
-
- /* we need y = |a| */
- fp_abs(a, &y);
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- fp_copy(&x, &u);
- fp_copy(&y, &v);
- fp_set (&D, 1);
-
-top:
- /* 4. while u is even do */
- while (fp_iseven (&u) == FP_YES) {
- /* 4.1 u = u/2 */
- fp_div_2 (&u, &u);
-
- /* 4.2 if B is odd then */
- if (fp_isodd (&B) == FP_YES) {
- fp_sub (&B, &x, &B);
- }
- /* B = B/2 */
- fp_div_2 (&B, &B);
- }
-
- /* 5. while v is even do */
- while (fp_iseven (&v) == FP_YES) {
- /* 5.1 v = v/2 */
- fp_div_2 (&v, &v);
-
- /* 5.2 if D is odd then */
- if (fp_isodd (&D) == FP_YES) {
- /* D = (D-x)/2 */
- fp_sub (&D, &x, &D);
- }
- /* D = D/2 */
- fp_div_2 (&D, &D);
- }
-
- /* 6. if u >= v then */
- if (fp_cmp (&u, &v) != FP_LT) {
- /* u = u - v, B = B - D */
- fp_sub (&u, &v, &u);
- fp_sub (&B, &D, &B);
- } else {
- /* v - v - u, D = D - B */
- fp_sub (&v, &u, &v);
- fp_sub (&D, &B, &D);
- }
-
- /* if not zero goto step 4 */
- if (fp_iszero (&u) == FP_NO) {
- goto top;
- }
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (fp_cmp_d (&v, 1) != FP_EQ) {
- return FP_VAL;
- }
-
- /* b is now the inverse */
- neg = a->sign;
- while (D.sign == FP_NEG) {
- fp_add (&D, b, &D);
- }
- fp_copy (&D, c);
- c->sign = neg;
- return FP_OKAY;
-}
-
-/* d = a * b (mod c) */
-int fp_mulmod(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
-{
- fp_int tmp;
- fp_zero(&tmp);
- fp_mul(a, b, &tmp);
- return fp_mod(&tmp, c, d);
-}
-
-#ifdef TFM_TIMING_RESISTANT
-
-/* timing resistant montgomery ladder based exptmod
-
- Based on work by Marc Joye, Sung-Ming Yen, "The Montgomery Powering Ladder", Cryptographic Hardware and Embedded Systems, CHES 2002
-*/
-static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
-{
- fp_int R[2];
- fp_digit buf, mp;
- int err, bitcnt, digidx, y;
-
- /* now setup montgomery */
- if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
- return err;
- }
-
- fp_init(&R[0]);
- fp_init(&R[1]);
-
- /* now we need R mod m */
- fp_montgomery_calc_normalization (&R[0], P);
-
- /* now set R[0][1] to G * R mod m */
- if (fp_cmp_mag(P, G) != FP_GT) {
- /* G > P so we reduce it first */
- fp_mod(G, P, &R[1]);
- } else {
- fp_copy(G, &R[1]);
- }
- fp_mulmod (&R[1], &R[0], P, &R[1]);
-
- /* for j = t-1 downto 0 do
- r_!k = R0*R1; r_k = r_k^2
- */
-
- /* set initial mode and bit cnt */
- bitcnt = 1;
- buf = 0;
- digidx = X->used - 1;
-
- for (;;) {
- /* grab next digit as required */
- if (--bitcnt == 0) {
- /* if digidx == -1 we are out of digits so break */
- if (digidx == -1) {
- break;
- }
- /* read next digit and reset bitcnt */
- buf = X->dp[digidx--];
- bitcnt = (int)DIGIT_BIT;
- }
-
- /* grab the next msb from the exponent */
- y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
- buf <<= (fp_digit)1;
-
- /* do ops */
- fp_mul(&R[0], &R[1], &R[y^1]); fp_montgomery_reduce(&R[y^1], P, mp);
- fp_sqr(&R[y], &R[y]); fp_montgomery_reduce(&R[y], P, mp);
- }
-
- fp_montgomery_reduce(&R[0], P, mp);
- fp_copy(&R[0], Y);
- return FP_OKAY;
-}
-
-#else
-
-/* y = g**x (mod b)
- * Some restrictions... x must be positive and < b
- */
-static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
-{
- fp_int M[64], res;
- fp_digit buf, mp;
- int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
- /* find window size */
- x = fp_count_bits (X);
- if (x <= 21) {
- winsize = 1;
- } else if (x <= 36) {
- winsize = 3;
- } else if (x <= 140) {
- winsize = 4;
- } else if (x <= 450) {
- winsize = 5;
- } else {
- winsize = 6;
- }
-
- /* init M array */
- XMEMSET(M, 0, sizeof(M));
-
- /* now setup montgomery */
- if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
- return err;
- }
-
- /* setup result */
- fp_init(&res);
-
- /* create M table
- *
- * The M table contains powers of the input 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]
- */
-
- /* now we need R mod m */
- fp_montgomery_calc_normalization (&res, P);
-
- /* now set M[1] to G * R mod m */
- if (fp_cmp_mag(P, G) != FP_GT) {
- /* G > P so we reduce it first */
- fp_mod(G, P, &M[1]);
- } else {
- fp_copy(G, &M[1]);
- }
- fp_mulmod (&M[1], &res, P, &M[1]);
-
- /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
- fp_copy (&M[1], &M[1 << (winsize - 1)]);
- for (x = 0; x < (winsize - 1); x++) {
- fp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)]);
- fp_montgomery_reduce (&M[1 << (winsize - 1)], P, mp);
- }
-
- /* create upper table */
- for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
- fp_mul(&M[x - 1], &M[1], &M[x]);
- fp_montgomery_reduce(&M[x], P, mp);
- }
-
- /* set initial mode and bit cnt */
- mode = 0;
- bitcnt = 1;
- buf = 0;
- digidx = X->used - 1;
- bitcpy = 0;
- bitbuf = 0;
-
- for (;;) {
- /* grab next digit as required */
- if (--bitcnt == 0) {
- /* if digidx == -1 we are out of digits so break */
- if (digidx == -1) {
- break;
- }
- /* read next digit and reset bitcnt */
- buf = X->dp[digidx--];
- bitcnt = (int)DIGIT_BIT;
- }
-
- /* grab the next msb from the exponent */
- y = (int)(buf >> (DIGIT_BIT - 1)) & 1;
- buf <<= (fp_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) {
- fp_sqr(&res, &res);
- fp_montgomery_reduce(&res, P, mp);
- 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++) {
- fp_sqr(&res, &res);
- fp_montgomery_reduce(&res, P, mp);
- }
-
- /* then multiply */
- fp_mul(&res, &M[bitbuf], &res);
- fp_montgomery_reduce(&res, P, mp);
-
- /* 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++) {
- fp_sqr(&res, &res);
- fp_montgomery_reduce(&res, P, mp);
-
- /* get next bit of the window */
- bitbuf <<= 1;
- if ((bitbuf & (1 << winsize)) != 0) {
- /* then multiply */
- fp_mul(&res, &M[1], &res);
- fp_montgomery_reduce(&res, P, mp);
- }
- }
- }
-
- /* 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.
- */
- fp_montgomery_reduce(&res, P, mp);
-
- /* swap res with Y */
- fp_copy (&res, Y);
- return FP_OKAY;
-}
-
-#endif
-
-int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
-{
- /* prevent overflows */
- if (P->used > (FP_SIZE/2)) {
- return FP_VAL;
- }
-
- if (X->sign == FP_NEG) {
-#ifndef POSITIVE_EXP_ONLY /* reduce stack if assume no negatives */
- int err;
- fp_int tmp;
-
- /* yes, copy G and invmod it */
- fp_copy(G, &tmp);
- if ((err = fp_invmod(&tmp, P, &tmp)) != FP_OKAY) {
- return err;
- }
- X->sign = FP_ZPOS;
- err = _fp_exptmod(&tmp, X, P, Y);
- if (X != Y) {
- X->sign = FP_NEG;
- }
- return err;
-#else
- return FP_VAL;
-#endif
- }
- else {
- /* Positive exponent so just exptmod */
- return _fp_exptmod(G, X, P, Y);
- }
-}
-
-/* computes a = 2**b */
-void fp_2expt(fp_int *a, int b)
-{
- int z;
-
- /* zero a as per default */
- fp_zero (a);
-
- if (b < 0) {
- return;
- }
-
- z = b / DIGIT_BIT;
- if (z >= FP_SIZE) {
- return;
- }
-
- /* set the used count of where the bit will go */
- a->used = z + 1;
-
- /* put the single bit in its place */
- a->dp[z] = ((fp_digit)1) << (b % DIGIT_BIT);
-}
-
-/* b = a*a */
-void fp_sqr(fp_int *A, fp_int *B)
-{
- int y = A->used;
-
- /* call generic if we're out of range */
- if (y + y > FP_SIZE) {
- fp_sqr_comba(A, B);
- return ;
- }
-
-#if defined(TFM_SQR3)
- if (y <= 3) {
- fp_sqr_comba3(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR4)
- if (y == 4) {
- fp_sqr_comba4(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR6)
- if (y <= 6) {
- fp_sqr_comba6(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR7)
- if (y == 7) {
- fp_sqr_comba7(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR8)
- if (y == 8) {
- fp_sqr_comba8(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR9)
- if (y == 9) {
- fp_sqr_comba9(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR12)
- if (y <= 12) {
- fp_sqr_comba12(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR17)
- if (y <= 17) {
- fp_sqr_comba17(A,B);
- return;
- }
-#endif
-#if defined(TFM_SMALL_SET)
- if (y <= 16) {
- fp_sqr_comba_small(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR20)
- if (y <= 20) {
- fp_sqr_comba20(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR24)
- if (y <= 24) {
- fp_sqr_comba24(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR28)
- if (y <= 28) {
- fp_sqr_comba28(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR32)
- if (y <= 32) {
- fp_sqr_comba32(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR48)
- if (y <= 48) {
- fp_sqr_comba48(A,B);
- return;
- }
-#endif
-#if defined(TFM_SQR64)
- if (y <= 64) {
- fp_sqr_comba64(A,B);
- return;
- }
-#endif
- fp_sqr_comba(A, B);
-}
-
-/* generic comba squarer */
-void fp_sqr_comba(fp_int *A, fp_int *B)
-{
- int pa, ix, iz;
- fp_digit c0, c1, c2;
- fp_int tmp, *dst;
-#ifdef TFM_ISO
- fp_word tt;
-#endif
-
- /* get size of output and trim */
- pa = A->used + A->used;
- if (pa >= FP_SIZE) {
- pa = FP_SIZE-1;
- }
-
- /* number of output digits to produce */
- COMBA_START;
- COMBA_CLEAR;
-
- if (A == B) {
- fp_zero(&tmp);
- dst = &tmp;
- } else {
- fp_zero(B);
- dst = B;
- }
-
- for (ix = 0; ix < pa; ix++) {
- int tx, ty, iy;
- fp_digit *tmpy, *tmpx;
-
- /* get offsets into the two bignums */
- ty = MIN(A->used-1, ix);
- tx = ix - ty;
-
- /* setup temp aliases */
- tmpx = A->dp + tx;
- tmpy = A->dp + ty;
-
- /* this is the number of times the loop will iterrate,
- 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);
-
- /* forward carries */
- COMBA_FORWARD;
-
- /* execute loop */
- for (iz = 0; iz < iy; iz++) {
- SQRADD2(*tmpx++, *tmpy--);
- }
-
- /* even columns have the square term in them */
- if ((ix&1) == 0) {
- /* TAO change COMBA_ADD back to SQRADD */
- SQRADD(A->dp[ix>>1], A->dp[ix>>1]);
- }
-
- /* store it */
- COMBA_STORE(dst->dp[ix]);
- }
-
- COMBA_FINI;
-
- /* setup dest */
- dst->used = pa;
- fp_clamp (dst);
- if (dst != B) {
- fp_copy(dst, B);
- }
-}
-
-int fp_cmp(fp_int *a, fp_int *b)
-{
- if (a->sign == FP_NEG && b->sign == FP_ZPOS) {
- return FP_LT;
- } else if (a->sign == FP_ZPOS && b->sign == FP_NEG) {
- return FP_GT;
- } else {
- /* compare digits */
- if (a->sign == FP_NEG) {
- /* if negative compare opposite direction */
- return fp_cmp_mag(b, a);
- } else {
- return fp_cmp_mag(a, b);
- }
- }
-}
-
-/* compare against a single digit */
-int fp_cmp_d(fp_int *a, fp_digit b)
-{
- /* compare based on sign */
- if ((b && a->used == 0) || a->sign == FP_NEG) {
- return FP_LT;
- }
-
- /* compare based on magnitude */
- if (a->used > 1) {
- return FP_GT;
- }
-
- /* compare the only digit of a to b */
- if (a->dp[0] > b) {
- return FP_GT;
- } else if (a->dp[0] < b) {
- return FP_LT;
- } else {
- return FP_EQ;
- }
-
-}
-
-int fp_cmp_mag(fp_int *a, fp_int *b)
-{
- int x;
-
- if (a->used > b->used) {
- return FP_GT;
- } else if (a->used < b->used) {
- return FP_LT;
- } else {
- for (x = a->used - 1; x >= 0; x--) {
- if (a->dp[x] > b->dp[x]) {
- return FP_GT;
- } else if (a->dp[x] < b->dp[x]) {
- return FP_LT;
- }
- }
- }
- return FP_EQ;
-}
-
-/* setups the montgomery reduction */
-int fp_montgomery_setup(fp_int *a, fp_digit *rho)
-{
- fp_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 = a->dp[0];
-
- if ((b & 1) == 0) {
- return FP_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 */
-#ifdef FP_64BIT
- x *= 2 - b * x; /* here x*a==1 mod 2**64 */
-#endif
-
- /* rho = -1/m mod b */
- *rho = (fp_digit) (((fp_word) 1 << ((fp_word) DIGIT_BIT)) - ((fp_word)x));
-
- return FP_OKAY;
-}
-
-/* computes a = B**n mod b without division or multiplication useful for
- * normalizing numbers in a Montgomery system.
- */
-void fp_montgomery_calc_normalization(fp_int *a, fp_int *b)
-{
- int x, bits;
-
- /* how many bits of last digit does b use */
- bits = fp_count_bits (b) % DIGIT_BIT;
- if (!bits) bits = DIGIT_BIT;
-
- /* compute A = B^(n-1) * 2^(bits-1) */
- if (b->used > 1) {
- fp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1);
- } else {
- fp_set(a, 1);
- bits = 1;
- }
-
- /* now compute C = A * B mod b */
- for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
- fp_mul_2 (a, a);
- if (fp_cmp_mag (a, b) != FP_LT) {
- s_fp_sub (a, b, a);
- }
- }
-}
-
-
-#ifdef TFM_SMALL_MONT_SET
- #include "fp_mont_small.i"
-#endif
-
-/* computes x/R == x (mod N) via Montgomery Reduction */
-void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
-{
- fp_digit c[FP_SIZE], *_c, *tmpm, mu = 0;
- int oldused, x, y, pa;
-
- /* bail if too large */
- if (m->used > (FP_SIZE/2)) {
- (void)mu; /* shut up compiler */
- return;
- }
-
-#ifdef TFM_SMALL_MONT_SET
- if (m->used <= 16) {
- fp_montgomery_reduce_small(a, m, mp);
- return;
- }
-#endif
-
-
- /* now zero the buff */
- XMEMSET(c, 0, sizeof c);
- pa = m->used;
-
- /* copy the input */
- oldused = a->used;
- for (x = 0; x < oldused; x++) {
- c[x] = a->dp[x];
- }
- MONT_START;
-
- for (x = 0; x < pa; x++) {
- fp_digit cy = 0;
- /* get Mu for this round */
- LOOP_START;
- _c = c + x;
- tmpm = m->dp;
- y = 0;
- #if (defined(TFM_SSE2) || defined(TFM_X86_64))
- for (; y < (pa & ~7); y += 8) {
- INNERMUL8;
- _c += 8;
- tmpm += 8;
- }
- #endif
-
- for (; y < pa; y++) {
- INNERMUL;
- ++_c;
- }
- LOOP_END;
- while (cy) {
- PROPCARRY;
- ++_c;
- }
- }
-
- /* now copy out */
- _c = c + pa;
- tmpm = a->dp;
- for (x = 0; x < pa+1; x++) {
- *tmpm++ = *_c++;
- }
-
- for (; x < oldused; x++) {
- *tmpm++ = 0;
- }
-
- MONT_FINI;
-
- a->used = pa+1;
- fp_clamp(a);
-
- /* if A >= m then A = A - m */
- if (fp_cmp_mag (a, m) != FP_LT) {
- s_fp_sub (a, m, a);
- }
-}
-
-void fp_read_unsigned_bin(fp_int *a, unsigned char *b, int c)
-{
- /* zero the int */
- fp_zero (a);
-
- /* If we know the endianness of this architecture, and we're using
- 32-bit fp_digits, we can optimize this */
-#if (defined(LITTLE_ENDIAN_ORDER) || defined(BIG_ENDIAN_ORDER)) && !defined(FP_64BIT)
- /* But not for both simultaneously */
-#if defined(LITTLE_ENDIAN_ORDER) && defined(BIG_ENDIAN_ORDER)
-#error Both LITTLE_ENDIAN_ORDER and BIG_ENDIAN_ORDER defined.
-#endif
- {
- unsigned char *pd = (unsigned char *)a->dp;
-
- if ((unsigned)c > (FP_SIZE * sizeof(fp_digit))) {
- int excess = c - (FP_SIZE * sizeof(fp_digit));
- c -= excess;
- b += excess;
- }
- a->used = (c + sizeof(fp_digit) - 1)/sizeof(fp_digit);
- /* read the bytes in */
-#ifdef BIG_ENDIAN_ORDER
- {
- /* Use Duff's device to unroll the loop. */
- int idx = (c - 1) & ~3;
- switch (c % 4) {
- case 0: do { pd[idx+0] = *b++;
- case 3: pd[idx+1] = *b++;
- case 2: pd[idx+2] = *b++;
- case 1: pd[idx+3] = *b++;
- idx -= 4;
- } while ((c -= 4) > 0);
- }
- }
-#else
- for (c -= 1; c >= 0; c -= 1) {
- pd[c] = *b++;
- }
-#endif
- }
-#else
- /* read the bytes in */
- for (; c > 0; c--) {
- fp_mul_2d (a, 8, a);
- a->dp[0] |= *b++;
- a->used += 1;
- }
-#endif
- fp_clamp (a);
-}
-
-void fp_to_unsigned_bin(fp_int *a, unsigned char *b)
-{
- int x;
- fp_int t;
-
- fp_init_copy(&t, a);
-
- x = 0;
- while (fp_iszero (&t) == FP_NO) {
- b[x++] = (unsigned char) (t.dp[0] & 255);
- fp_div_2d (&t, 8, &t, NULL);
- }
- fp_reverse (b, x);
-}
-
-int fp_unsigned_bin_size(fp_int *a)
-{
- int size = fp_count_bits (a);
- return (size / 8 + ((size & 7) != 0 ? 1 : 0));
-}
-
-void fp_set(fp_int *a, fp_digit b)
-{
- fp_zero(a);
- a->dp[0] = b;
- a->used = a->dp[0] ? 1 : 0;
-}
-
-int fp_count_bits (fp_int * a)
-{
- int r;
- fp_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 > ((fp_digit) 0)) {
- ++r;
- q >>= ((fp_digit) 1);
- }
- return r;
-}
-
-int fp_leading_bit(fp_int *a)
-{
- int bit = 0;
-
- if (a->used != 0) {
- fp_digit q = a->dp[a->used - 1];
- int qSz = sizeof(fp_digit);
-
- while (qSz > 0) {
- if ((unsigned char)q != 0)
- bit = (q & 0x80) != 0;
- q >>= 8;
- qSz--;
- }
- }
-
- return bit;
-}
-
-void fp_lshd(fp_int *a, int x)
-{
- int y;
-
- /* move up and truncate as required */
- y = MIN(a->used + x - 1, (int)(FP_SIZE-1));
-
- /* store new size */
- a->used = y + 1;
-
- /* move digits */
- for (; y >= x; y--) {
- a->dp[y] = a->dp[y-x];
- }
-
- /* zero lower digits */
- for (; y >= 0; y--) {
- a->dp[y] = 0;
- }
-
- /* clamp digits */
- fp_clamp(a);
-}
-
-
-/* right shift by bit count */
-void fp_rshb(fp_int *c, int x)
-{
- register fp_digit *tmpc, mask, shift;
- fp_digit r, rr;
- fp_digit D = x;
-
- /* mask */
- mask = (((fp_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 previous word */
- *tmpc = (*tmpc >> D) | (r << shift);
- --tmpc;
-
- /* set the carry to the carry bits of the current word found above */
- r = rr;
- }
-}
-
-
-void fp_rshd(fp_int *a, int x)
-{
- int y;
-
- /* too many digits just zero and return */
- if (x >= a->used) {
- fp_zero(a);
- return;
- }
-
- /* shift */
- for (y = 0; y < a->used - x; y++) {
- a->dp[y] = a->dp[y+x];
- }
-
- /* zero rest */
- for (; y < a->used; y++) {
- a->dp[y] = 0;
- }
-
- /* decrement count */
- a->used -= x;
- fp_clamp(a);
-}
-
-/* reverse an array, used for radix code */
-void fp_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;
- }
-}
-
-
-/* c = a - b */
-void fp_sub_d(fp_int *a, fp_digit b, fp_int *c)
-{
- fp_int tmp;
- fp_set(&tmp, b);
- fp_sub(a, &tmp, c);
-}
-
-
-/* CyaSSL callers from normal lib */
-
-/* init a new mp_int */
-int mp_init (mp_int * a)
-{
- if (a)
- fp_init(a);
- return MP_OKAY;
-}
-
-/* clear one (frees) */
-void mp_clear (mp_int * a)
-{
- fp_zero(a);
-}
-
-/* handle up to 6 inits */
-int mp_init_multi(mp_int* a, mp_int* b, mp_int* c, mp_int* d, mp_int* e, mp_int* f)
-{
- if (a)
- fp_init(a);
- if (b)
- fp_init(b);
- if (c)
- fp_init(c);
- if (d)
- fp_init(d);
- if (e)
- fp_init(e);
- if (f)
- fp_init(f);
-
- return MP_OKAY;
-}
-
-/* high level addition (handles signs) */
-int mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
- fp_add(a, b, c);
- return MP_OKAY;
-}
-
-/* high level subtraction (handles signs) */
-int mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
- fp_sub(a, b, c);
- return MP_OKAY;
-}
-
-/* high level multiplication (handles sign) */
-int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-{
- fp_mul(a, b, c);
- return MP_OKAY;
-}
-
-/* d = a * b (mod c) */
-int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
- return fp_mulmod(a, b, c, d);
-}
-
-/* c = a mod b, 0 <= c < b */
-int mp_mod (mp_int * a, mp_int * b, mp_int * c)
-{
- return fp_mod (a, b, c);
-}
-
-/* hac 14.61, pp608 */
-int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
- return fp_invmod(a, b, c);
-}
-
-/* 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 alot of stack space
- * for nothing (since 99% of the time the Montgomery code would be called)
- */
-int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-{
- return fp_exptmod(G, X, P, Y);
-}
-
-/* compare two ints (signed)*/
-int mp_cmp (mp_int * a, mp_int * b)
-{
- return fp_cmp(a, b);
-}
-
-/* compare a digit */
-int mp_cmp_d(mp_int * a, mp_digit b)
-{
- return fp_cmp_d(a, b);
-}
-
-/* get the size for an unsigned equivalent */
-int mp_unsigned_bin_size (mp_int * a)
-{
- return fp_unsigned_bin_size(a);
-}
-
-/* store in unsigned [big endian] format */
-int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
-{
- fp_to_unsigned_bin(a,b);
- return MP_OKAY;
-}
-
-/* reads a 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)
-{
- fp_read_unsigned_bin(a, (unsigned char *)b, c);
- return MP_OKAY;
-}
-
-
-int mp_sub_d(fp_int *a, fp_digit b, fp_int *c)
-{
- fp_sub_d(a, b, c);
- return MP_OKAY;
-}
-
-
-/* fast math conversion */
-int mp_copy(fp_int* a, fp_int* b)
-{
- fp_copy(a, b);
- return MP_OKAY;
-}
-
-
-/* fast math conversion */
-int mp_isodd(mp_int* a)
-{
- return fp_isodd(a);
-}
-
-
-/* fast math conversion */
-int mp_iszero(mp_int* a)
-{
- return fp_iszero(a);
-}
-
-
-/* fast math conversion */
-int mp_count_bits (mp_int* a)
-{
- return fp_count_bits(a);
-}
-
-
-int mp_leading_bit (mp_int* a)
-{
- return fp_leading_bit(a);
-}
-
-
-/* fast math conversion */
-void mp_rshb (mp_int* a, int x)
-{
- fp_rshb(a, x);
-}
-
-
-/* fast math wrappers */
-int mp_set_int(fp_int *a, fp_digit b)
-{
- fp_set(a, b);
- return MP_OKAY;
-}
-
-
-#if defined(CYASSL_KEY_GEN) || defined (HAVE_ECC)
-
-/* c = a * a (mod b) */
-int fp_sqrmod(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_int tmp;
- fp_zero(&tmp);
- fp_sqr(a, &tmp);
- return fp_mod(&tmp, b, c);
-}
-
-/* fast math conversion */
-int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c)
-{
- return fp_sqrmod(a, b, c);
-}
-
-/* fast math conversion */
-int mp_montgomery_calc_normalization(mp_int *a, mp_int *b)
-{
- fp_montgomery_calc_normalization(a, b);
- return MP_OKAY;
-}
-
-#endif /* CYASSL_KEYGEN || HAVE_ECC */
-
-
-#ifdef CYASSL_KEY_GEN
-
-void fp_gcd(fp_int *a, fp_int *b, fp_int *c);
-void fp_lcm(fp_int *a, fp_int *b, fp_int *c);
-int fp_isprime(fp_int *a);
-int fp_cnt_lsb(fp_int *a);
-
-int mp_gcd(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_gcd(a, b, c);
- return MP_OKAY;
-}
-
-
-int mp_lcm(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_lcm(a, b, c);
- return MP_OKAY;
-}
-
-
-int mp_prime_is_prime(mp_int* a, int t, int* result)
-{
- (void)t;
- *result = fp_isprime(a);
- return MP_OKAY;
-}
-
-
-
-static int s_is_power_of_two(fp_digit b, int *p)
-{
- int x;
-
- /* fast return if no power of two */
- if ((b==0) || (b & (b-1))) {
- return 0;
- }
-
- for (x = 0; x < DIGIT_BIT; x++) {
- if (b == (((fp_digit)1)<<x)) {
- *p = x;
- return 1;
- }
- }
- return 0;
-}
-
-/* a/b => cb + d == a */
-static int fp_div_d(fp_int *a, fp_digit b, fp_int *c, fp_digit *d)
-{
- fp_int q;
- fp_word w;
- fp_digit t;
- int ix;
-
- /* cannot divide by zero */
- if (b == 0) {
- return FP_VAL;
- }
-
- /* quick outs */
- if (b == 1 || fp_iszero(a) == 1) {
- if (d != NULL) {
- *d = 0;
- }
- if (c != NULL) {
- fp_copy(a, c);
- }
- return FP_OKAY;
- }
-
- /* power of two ? */
- if (s_is_power_of_two(b, &ix) == 1) {
- if (d != NULL) {
- *d = a->dp[0] & ((((fp_digit)1)<<ix) - 1);
- }
- if (c != NULL) {
- fp_div_2d(a, ix, c, NULL);
- }
- return FP_OKAY;
- }
-
- /* no easy answer [c'est la vie]. Just division */
- fp_init(&q);
-
- q.used = a->used;
- q.sign = a->sign;
- w = 0;
- for (ix = a->used - 1; ix >= 0; ix--) {
- w = (w << ((fp_word)DIGIT_BIT)) | ((fp_word)a->dp[ix]);
-
- if (w >= b) {
- t = (fp_digit)(w / b);
- w -= ((fp_word)t) * ((fp_word)b);
- } else {
- t = 0;
- }
- q.dp[ix] = (fp_digit)t;
- }
-
- if (d != NULL) {
- *d = (fp_digit)w;
- }
-
- if (c != NULL) {
- fp_clamp(&q);
- fp_copy(&q, c);
- }
-
- return FP_OKAY;
-}
-
-
-/* c = a mod b, 0 <= c < b */
-static int fp_mod_d(fp_int *a, fp_digit b, fp_digit *c)
-{
- return fp_div_d(a, b, NULL, c);
-}
-
-
-/* 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 void fp_prime_miller_rabin (fp_int * a, fp_int * b, int *result)
-{
- fp_int n1, y, r;
- int s, j;
-
- /* default */
- *result = FP_NO;
-
- /* ensure b > 1 */
- if (fp_cmp_d(b, 1) != FP_GT) {
- return;
- }
-
- /* get n1 = a - 1 */
- fp_init_copy(&n1, a);
- fp_sub_d(&n1, 1, &n1);
-
- /* set 2**s * r = n1 */
- fp_init_copy(&r, &n1);
-
- /* count the number of least significant bits
- * which are zero
- */
- s = fp_cnt_lsb(&r);
-
- /* now divide n - 1 by 2**s */
- fp_div_2d (&r, s, &r, NULL);
-
- /* compute y = b**r mod a */
- fp_init(&y);
- fp_exptmod(b, &r, a, &y);
-
- /* if y != 1 and y != n1 do */
- if (fp_cmp_d (&y, 1) != FP_EQ && fp_cmp (&y, &n1) != FP_EQ) {
- j = 1;
- /* while j <= s-1 and y != n1 */
- while ((j <= (s - 1)) && fp_cmp (&y, &n1) != FP_EQ) {
- fp_sqrmod (&y, a, &y);
-
- /* if y == 1 then composite */
- if (fp_cmp_d (&y, 1) == FP_EQ) {
- return;
- }
- ++j;
- }
-
- /* if y != n1 then composite */
- if (fp_cmp (&y, &n1) != FP_EQ) {
- return;
- }
- }
-
- /* probably prime now */
- *result = FP_YES;
-}
-
-
-/* a few primes */
-static const fp_digit primes[256] = {
- 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
-};
-
-int fp_isprime(fp_int *a)
-{
- fp_int b;
- fp_digit d = 0;
- int r, res;
-
- /* do trial division */
- for (r = 0; r < 256; r++) {
- fp_mod_d(a, primes[r], &d);
- if (d == 0) {
- return FP_NO;
- }
- }
-
- /* now do 8 miller rabins */
- fp_init(&b);
- for (r = 0; r < 8; r++) {
- fp_set(&b, primes[r]);
- fp_prime_miller_rabin(a, &b, &res);
- if (res == FP_NO) {
- return FP_NO;
- }
- }
- return FP_YES;
-}
-
-
-/* c = [a, b] */
-void fp_lcm(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_int t1, t2;
-
- fp_init(&t1);
- fp_init(&t2);
- fp_gcd(a, b, &t1);
- if (fp_cmp_mag(a, b) == FP_GT) {
- fp_div(a, &t1, &t2, NULL);
- fp_mul(b, &t2, c);
- } else {
- fp_div(b, &t1, &t2, NULL);
- fp_mul(a, &t2, c);
- }
-}
-
-
-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 fp_cnt_lsb(fp_int *a)
-{
- int x;
- fp_digit q, qq;
-
- /* easy out */
- if (fp_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;
-}
-
-
-/* c = (a, b) */
-void fp_gcd(fp_int *a, fp_int *b, fp_int *c)
-{
- fp_int u, v, r;
-
- /* either zero than gcd is the largest */
- if (fp_iszero (a) == 1 && fp_iszero (b) == 0) {
- fp_abs (b, c);
- return;
- }
- if (fp_iszero (a) == 0 && fp_iszero (b) == 1) {
- fp_abs (a, c);
- return;
- }
-
- /* optimized. At this point if a == 0 then
- * b must equal zero too
- */
- if (fp_iszero (a) == 1) {
- fp_zero(c);
- return;
- }
-
- /* sort inputs */
- if (fp_cmp_mag(a, b) != FP_LT) {
- fp_init_copy(&u, a);
- fp_init_copy(&v, b);
- } else {
- fp_init_copy(&u, b);
- fp_init_copy(&v, a);
- }
-
- fp_zero(&r);
- while (fp_iszero(&v) == FP_NO) {
- fp_mod(&u, &v, &r);
- fp_copy(&v, &u);
- fp_copy(&r, &v);
- }
- fp_copy(&u, c);
-}
-
-#endif /* CYASSL_KEY_GEN */
-
-
-#if defined(HAVE_ECC) || !defined(NO_PWDBASED)
-/* c = a + b */
-void fp_add_d(fp_int *a, fp_digit b, fp_int *c)
-{
- fp_int tmp;
- fp_set(&tmp, b);
- fp_add(a,&tmp,c);
-}
-
-/* external compatibility */
-int mp_add_d(fp_int *a, fp_digit b, fp_int *c)
-{
- fp_add_d(a, b, c);
- return MP_OKAY;
-}
-
-#endif /* HAVE_ECC || !NO_PWDBASED */
-
-
-#ifdef HAVE_ECC
-
-/* chars used in radix conversions */
-static const char *fp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-
-static int fp_read_radix(fp_int *a, const char *str, int radix)
-{
- int y, neg;
- char ch;
-
- /* make sure the radix is ok */
- if (radix < 2 || radix > 64) {
- return FP_VAL;
- }
-
- /* if the leading digit is a
- * minus set the sign to negative.
- */
- if (*str == '-') {
- ++str;
- neg = FP_NEG;
- } else {
- neg = FP_ZPOS;
- }
-
- /* set the integer to the default of zero */
- fp_zero (a);
-
- /* process each digit of the string */
- while (*str) {
- /* if the radix < 36 the conversion is case insensitive
- * this allows numbers like 1AB and 1ab to represent the same value
- * [e.g. in hex]
- */
- ch = (char) ((radix < 36) ? XTOUPPER(*str) : *str);
- for (y = 0; y < 64; y++) {
- if (ch == fp_s_rmap[y]) {
- break;
- }
- }
-
- /* if the char was found in the map
- * and is less than the given radix add it
- * to the number, otherwise exit the loop.
- */
- if (y < radix) {
- fp_mul_d (a, (fp_digit) radix, a);
- fp_add_d (a, (fp_digit) y, a);
- } else {
- break;
- }
- ++str;
- }
-
- /* set the sign only if a != 0 */
- if (fp_iszero(a) != FP_YES) {
- a->sign = neg;
- }
- return FP_OKAY;
-}
-
-/* fast math conversion */
-int mp_read_radix(mp_int *a, const char *str, int radix)
-{
- return fp_read_radix(a, str, radix);
-}
-
-/* fast math conversion */
-int mp_set(fp_int *a, fp_digit b)
-{
- fp_set(a,b);
- return MP_OKAY;
-}
-
-/* fast math conversion */
-int mp_sqr(fp_int *A, fp_int *B)
-{
- fp_sqr(A, B);
- return MP_OKAY;
-}
-
-/* fast math conversion */
-int mp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
-{
- fp_montgomery_reduce(a, m, mp);
- return MP_OKAY;
-}
-
-
-/* fast math conversion */
-int mp_montgomery_setup(fp_int *a, fp_digit *rho)
-{
- return fp_montgomery_setup(a, rho);
-}
-
-int mp_div_2(fp_int * a, fp_int * b)
-{
- fp_div_2(a, b);
- return MP_OKAY;
-}
-
-
-int mp_init_copy(fp_int * a, fp_int * b)
-{
- fp_init_copy(a, b);
- return MP_OKAY;
-}
-
-
-
-#endif /* HAVE_ECC */
-
-#endif /* USE_FAST_MATH */
projects / freertos / blobdiff