Ashley Mills
This is a port of cyaSSL 2.7.0.
Dependents: CyaSSL_DTLS_Cellular CyaSSL_DTLS_Ethernet
Diff: ctaocrypt/src/tfm.c
- Revision:
- 0:714293de3836
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ctaocrypt/src/tfm.c Thu Sep 05 10:33:04 2013 +0000
@@ -0,0 +1,2473 @@
+/* tfm.c
+ *
+ * Copyright (C) 2006-2013 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, 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 = c->used;
+ 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)
+{
+ fp_digit D, r, rr;
+ int x;
+ 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 = (fp_digit) (b % DIGIT_BIT);
+ if (D != 0) {
+ register fp_digit *tmpc, mask, shift;
+
+ /* 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 the previous word */
+ *tmpc = (*tmpc >> D) | (r << shift);
+ --tmpc;
+
+ /* set the carry to the carry bits of the current word found above */
+ r = rr;
+ }
+ }
+ 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;
+}
+
+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);
+}
+
+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);
+}
+
+
+/* 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 */
+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 */
