#include "tommath_private.h"
#ifdef BN_CUTOFFS_C
#ifndef MP_FIXED_CUTOFFS
#include "tommath_cutoffs.h"
int KARATSUBA_MUL_CUTOFF = MP_DEFAULT_KARATSUBA_MUL_CUTOFF,
KARATSUBA_SQR_CUTOFF = MP_DEFAULT_KARATSUBA_SQR_CUTOFF,
TOOM_MUL_CUTOFF = MP_DEFAULT_TOOM_MUL_CUTOFF,
TOOM_SQR_CUTOFF = MP_DEFAULT_TOOM_SQR_CUTOFF;
#endif
#endif
#include "tommath_private.h"
#ifdef BN_DEPRECATED_C
#ifdef BN_MP_GET_BIT_C
int mp_get_bit(const mp_int *a, int b)
{
if (b < 0) {
return MP_VAL;
}
return (s_mp_get_bit(a, (unsigned int)b) == MP_YES) ? MP_YES : MP_NO;
}
#endif
#ifdef BN_MP_JACOBI_C
mp_err mp_jacobi(const mp_int *a, const mp_int *n, int *c)
{
if (a->sign == MP_NEG) {
return MP_VAL;
}
if (mp_cmp_d(n, 0uL) != MP_GT) {
return MP_VAL;
}
return mp_kronecker(a, n, c);
}
#endif
#ifdef BN_MP_PRIME_RANDOM_EX_C
mp_err mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat)
{
return s_mp_prime_random_ex(a, t, size, flags, cb, dat);
}
#endif
#ifdef BN_MP_RAND_DIGIT_C
mp_err mp_rand_digit(mp_digit *r)
{
mp_err err = s_mp_rand_source(r, sizeof(mp_digit));
*r &= MP_MASK;
return err;
}
#endif
#ifdef BN_FAST_MP_INVMOD_C
mp_err fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
return s_mp_invmod_fast(a, b, c);
}
#endif
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
mp_err fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
return s_mp_montgomery_reduce_fast(x, n, rho);
}
#endif
#ifdef BN_FAST_S_MP_MUL_DIGS_C
mp_err fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
return s_mp_mul_digs_fast(a, b, c, digs);
}
#endif
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
mp_err fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
return s_mp_mul_high_digs_fast(a, b, c, digs);
}
#endif
#ifdef BN_FAST_S_MP_SQR_C
mp_err fast_s_mp_sqr(const mp_int *a, mp_int *b)
{
return s_mp_sqr_fast(a, b);
}
#endif
#ifdef BN_MP_BALANCE_MUL_C
mp_err mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
return s_mp_balance_mul(a, b, c);
}
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
mp_err mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
{
return s_mp_exptmod_fast(G, X, P, Y, redmode);
}
#endif
#ifdef BN_MP_INVMOD_SLOW_C
mp_err mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
return s_mp_invmod_slow(a, b, c);
}
#endif
#ifdef BN_MP_KARATSUBA_MUL_C
mp_err mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
return s_mp_karatsuba_mul(a, b, c);
}
#endif
#ifdef BN_MP_KARATSUBA_SQR_C
mp_err mp_karatsuba_sqr(const mp_int *a, mp_int *b)
{
return s_mp_karatsuba_sqr(a, b);
}
#endif
#ifdef BN_MP_TOOM_MUL_C
mp_err mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
return s_mp_toom_mul(a, b, c);
}
#endif
#ifdef BN_MP_TOOM_SQR_C
mp_err mp_toom_sqr(const mp_int *a, mp_int *b)
{
return s_mp_toom_sqr(a, b);
}
#endif
#ifdef S_MP_REVERSE_C
void bn_reverse(unsigned char *s, int len)
{
if (len > 0) {
s_mp_reverse(s, (size_t)len);
}
}
#endif
#ifdef BN_MP_TC_AND_C
mp_err mp_tc_and(const mp_int *a, const mp_int *b, mp_int *c)
{
return mp_and(a, b, c);
}
#endif
#ifdef BN_MP_TC_OR_C
mp_err mp_tc_or(const mp_int *a, const mp_int *b, mp_int *c)
{
return mp_or(a, b, c);
}
#endif
#ifdef BN_MP_TC_XOR_C
mp_err mp_tc_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
return mp_xor(a, b, c);
}
#endif
#ifdef BN_MP_TC_DIV_2D_C
mp_err mp_tc_div_2d(const mp_int *a, int b, mp_int *c)
{
return mp_signed_rsh(a, b, c);
}
#endif
#ifdef BN_MP_INIT_SET_INT_C
mp_err mp_init_set_int(mp_int *a, unsigned long b)
{
return mp_init_u32(a, (uint32_t)b);
}
#endif
#ifdef BN_MP_SET_INT_C
mp_err mp_set_int(mp_int *a, unsigned long b)
{
mp_set_u32(a, (uint32_t)b);
return MP_OKAY;
}
#endif
#ifdef BN_MP_SET_LONG_C
mp_err mp_set_long(mp_int *a, unsigned long b)
{
mp_set_u64(a, b);
return MP_OKAY;
}
#endif
#ifdef BN_MP_SET_LONG_LONG_C
mp_err mp_set_long_long(mp_int *a, unsigned long long b)
{
mp_set_u64(a, b);
return MP_OKAY;
}
#endif
#ifdef BN_MP_GET_INT_C
unsigned long mp_get_int(const mp_int *a)
{
return (unsigned long)mp_get_mag_u32(a);
}
#endif
#ifdef BN_MP_GET_LONG_C
unsigned long mp_get_long(const mp_int *a)
{
return (unsigned long)mp_get_mag_ul(a);
}
#endif
#ifdef BN_MP_GET_LONG_LONG_C
unsigned long long mp_get_long_long(const mp_int *a)
{
return mp_get_mag_ull(a);
}
#endif
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
mp_err mp_prime_is_divisible(const mp_int *a, mp_bool *result)
{
return s_mp_prime_is_divisible(a, result);
}
#endif
#ifdef BN_MP_EXPT_D_EX_C
mp_err mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
(void)fast;
if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
return MP_VAL;
}
return mp_expt_u32(a, (uint32_t)b, c);
}
#endif
#ifdef BN_MP_EXPT_D_C
mp_err mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
{
if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
return MP_VAL;
}
return mp_expt_u32(a, (uint32_t)b, c);
}
#endif
#ifdef BN_MP_N_ROOT_EX_C
mp_err mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
(void)fast;
if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
return MP_VAL;
}
return mp_root_u32(a, (uint32_t)b, c);
}
#endif
#ifdef BN_MP_N_ROOT_C
mp_err mp_n_root(const mp_int *a, mp_digit b, mp_int *c)
{
if (b > MP_MIN(MP_DIGIT_MAX, UINT32_MAX)) {
return MP_VAL;
}
return mp_root_u32(a, (uint32_t)b, c);
}
#endif
#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
int mp_unsigned_bin_size(const mp_int *a)
{
return (int)mp_ubin_size(a);
}
#endif
#ifdef BN_MP_READ_UNSIGNED_BIN_C
mp_err mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c)
{
return mp_from_ubin(a, b, (size_t) c);
}
#endif
#ifdef BN_MP_TO_UNSIGNED_BIN_C
mp_err mp_to_unsigned_bin(const mp_int *a, unsigned char *b)
{
return mp_to_ubin(a, b, SIZE_MAX, NULL);
}
#endif
#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
mp_err mp_to_unsigned_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
size_t n = mp_ubin_size(a);
if (*outlen < (unsigned long)n) {
return MP_VAL;
}
*outlen = (unsigned long)n;
return mp_to_ubin(a, b, n, NULL);
}
#endif
#ifdef BN_MP_SIGNED_BIN_SIZE_C
int mp_signed_bin_size(const mp_int *a)
{
return (int)mp_sbin_size(a);
}
#endif
#ifdef BN_MP_READ_SIGNED_BIN_C
mp_err mp_read_signed_bin(mp_int *a, const unsigned char *b, int c)
{
return mp_from_sbin(a, b, (size_t) c);
}
#endif
#ifdef BN_MP_TO_SIGNED_BIN_C
mp_err mp_to_signed_bin(const mp_int *a, unsigned char *b)
{
return mp_to_sbin(a, b, SIZE_MAX, NULL);
}
#endif
#ifdef BN_MP_TO_SIGNED_BIN_N_C
mp_err mp_to_signed_bin_n(const mp_int *a, unsigned char *b, unsigned long *outlen)
{
size_t n = mp_sbin_size(a);
if (*outlen < (unsigned long)n) {
return MP_VAL;
}
*outlen = (unsigned long)n;
return mp_to_sbin(a, b, n, NULL);
}
#endif
#ifdef BN_MP_TORADIX_N_C
mp_err mp_toradix_n(const mp_int *a, char *str, int radix, int maxlen)
{
if (maxlen < 0) {
return MP_VAL;
}
return mp_to_radix(a, str, (size_t)maxlen, NULL, radix);
}
#endif
#ifdef BN_MP_TORADIX_C
mp_err mp_toradix(const mp_int *a, char *str, int radix)
{
return mp_to_radix(a, str, SIZE_MAX, NULL, radix);
}
#endif
#ifdef BN_MP_IMPORT_C
mp_err mp_import(mp_int *rop, size_t count, int order, size_t size, int endian, size_t nails,
const void *op)
{
return mp_unpack(rop, count, order, size, endian, nails, op);
}
#endif
#ifdef BN_MP_EXPORT_C
mp_err mp_export(void *rop, size_t *countp, int order, size_t size,
int endian, size_t nails, const mp_int *op)
{
return mp_pack(rop, SIZE_MAX, countp, order, size, endian, nails, op);
}
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_2EXPT_C
*
* Simple algorithm which zeroes the int, grows it then just sets one bit
* as required.
*/
mp_err mp_2expt(mp_int *a, int b)
{
mp_err err;
mp_zero(a);
if ((err = mp_grow(a, (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) {
return err;
}
a->used = (b / MP_DIGIT_BIT) + 1;
a->dp[b / MP_DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ABS_C
*
* Simple function copies the input and fixes the sign to positive
*/
mp_err mp_abs(const mp_int *a, mp_int *b)
{
mp_err err;
if (a != b) {
if ((err = mp_copy(a, b)) != MP_OKAY) {
return err;
}
}
b->sign = MP_ZPOS;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ADD_C
mp_err mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_sign sa, sb;
mp_err err;
sa = a->sign;
sb = b->sign;
if (sa == sb) {
c->sign = sa;
err = s_mp_add(a, b, c);
} else {
if (mp_cmp_mag(a, b) == MP_LT) {
c->sign = sb;
err = s_mp_sub(b, a, c);
} else {
c->sign = sa;
err = s_mp_sub(a, b, c);
}
}
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ADD_D_C
mp_err mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
{
mp_err err;
int ix, oldused;
mp_digit *tmpa, *tmpc;
if (c->alloc < (a->used + 1)) {
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
return err;
}
}
if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
mp_int a_ = *a;
a_.sign = MP_ZPOS;
err = mp_sub_d(&a_, b, c);
c->sign = MP_NEG;
mp_clamp(c);
return err;
}
oldused = c->used;
tmpa = a->dp;
tmpc = c->dp;
if (a->sign == MP_ZPOS) {
mp_digit mu = b;
for (ix = 0; ix < a->used; ix++) {
*tmpc = *tmpa++ + mu;
mu = *tmpc >> MP_DIGIT_BIT;
*tmpc++ &= MP_MASK;
}
ix++;
*tmpc++ = mu;
c->used = a->used + 1;
} else {
c->used = 1;
if (a->used == 1) {
*tmpc++ = b - a->dp[0];
} else {
*tmpc++ = b;
}
* can fall through correctly
*/
ix = 1;
}
c->sign = MP_ZPOS;
MP_ZERO_DIGITS(tmpc, oldused - ix);
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ADDMOD_C
mp_err mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
mp_err err;
mp_int t;
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
if ((err = mp_add(a, b, &t)) != MP_OKAY) {
goto LBL_ERR;
}
err = mp_mod(&t, c, d);
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_AND_C
mp_err mp_and(const mp_int *a, const mp_int *b, mp_int *c)
{
int used = MP_MAX(a->used, b->used) + 1, i;
mp_err err;
mp_digit ac = 1, bc = 1, cc = 1;
mp_sign csign = ((a->sign == MP_NEG) && (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS;
if (c->alloc < used) {
if ((err = mp_grow(c, used)) != MP_OKAY) {
return err;
}
}
for (i = 0; i < used; i++) {
mp_digit x, y;
if (a->sign == MP_NEG) {
ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK);
x = ac & MP_MASK;
ac >>= MP_DIGIT_BIT;
} else {
x = (i >= a->used) ? 0uL : a->dp[i];
}
if (b->sign == MP_NEG) {
bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK);
y = bc & MP_MASK;
bc >>= MP_DIGIT_BIT;
} else {
y = (i >= b->used) ? 0uL : b->dp[i];
}
c->dp[i] = x & y;
if (csign == MP_NEG) {
cc += ~c->dp[i] & MP_MASK;
c->dp[i] = cc & MP_MASK;
cc >>= MP_DIGIT_BIT;
}
}
c->used = used;
c->sign = csign;
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CLAMP_C
*
* This is used to ensure that leading zero digits are
* trimed and the leading "used" digit will be non-zero
* Typically very fast. Also fixes the sign if there
* are no more leading digits
*/
void mp_clamp(mp_int *a)
{
* zero.
*/
while ((a->used > 0) && (a->dp[a->used - 1] == 0u)) {
--(a->used);
}
if (a->used == 0) {
a->sign = MP_ZPOS;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CLEAR_C
void mp_clear(mp_int *a)
{
if (a->dp != NULL) {
MP_FREE_DIGITS(a->dp, a->alloc);
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = MP_ZPOS;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CLEAR_MULTI_C
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
{
mp_int *next_mp = mp;
va_list args;
va_start(args, mp);
while (next_mp != NULL) {
mp_clear(next_mp);
next_mp = va_arg(args, mp_int *);
}
va_end(args);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CMP_C
mp_ord mp_cmp(const mp_int *a, const mp_int *b)
{
if (a->sign != b->sign) {
if (a->sign == MP_NEG) {
return MP_LT;
} else {
return MP_GT;
}
}
if (a->sign == MP_NEG) {
return mp_cmp_mag(b, a);
} else {
return mp_cmp_mag(a, b);
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CMP_D_C
mp_ord mp_cmp_d(const mp_int *a, mp_digit b)
{
if (a->sign == MP_NEG) {
return MP_LT;
}
if (a->used > 1) {
return MP_GT;
}
if (a->dp[0] > b) {
return MP_GT;
} else if (a->dp[0] < b) {
return MP_LT;
} else {
return MP_EQ;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CMP_MAG_C
mp_ord mp_cmp_mag(const mp_int *a, const mp_int *b)
{
int n;
const mp_digit *tmpa, *tmpb;
if (a->used > b->used) {
return MP_GT;
}
if (a->used < b->used) {
return MP_LT;
}
tmpa = a->dp + (a->used - 1);
tmpb = b->dp + (a->used - 1);
for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
if (*tmpa > *tmpb) {
return MP_GT;
}
if (*tmpa < *tmpb) {
return MP_LT;
}
}
return MP_EQ;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_CNT_LSB_C
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
};
int mp_cnt_lsb(const mp_int *a)
{
int x;
mp_digit q, qq;
if (MP_IS_ZERO(a)) {
return 0;
}
for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {}
q = a->dp[x];
x *= MP_DIGIT_BIT;
if ((q & 1u) == 0u) {
do {
qq = q & 15u;
x += lnz[qq];
q >>= 4;
} while (qq == 0u);
}
return x;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_COMPLEMENT_C
mp_err mp_complement(const mp_int *a, mp_int *b)
{
mp_err err = mp_neg(a, b);
return (err == MP_OKAY) ? mp_sub_d(b, 1uL, b) : err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_COPY_C
mp_err mp_copy(const mp_int *a, mp_int *b)
{
int n;
mp_digit *tmpa, *tmpb;
mp_err err;
if (a == b) {
return MP_OKAY;
}
if (b->alloc < a->used) {
if ((err = mp_grow(b, a->used)) != MP_OKAY) {
return err;
}
}
tmpa = a->dp;
tmpb = b->dp;
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
MP_ZERO_DIGITS(tmpb, b->used - n);
b->used = a->used;
b->sign = a->sign;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_COUNT_BITS_C
int mp_count_bits(const mp_int *a)
{
int r;
mp_digit q;
if (MP_IS_ZERO(a)) {
return 0;
}
r = (a->used - 1) * MP_DIGIT_BIT;
q = a->dp[a->used - 1];
while (q > 0u) {
++r;
q >>= 1u;
}
return r;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DECR_C
mp_err mp_decr(mp_int *a)
{
if (MP_IS_ZERO(a)) {
mp_set(a,1uL);
a->sign = MP_NEG;
return MP_OKAY;
} else if (a->sign == MP_NEG) {
mp_err err;
a->sign = MP_ZPOS;
if ((err = mp_incr(a)) != MP_OKAY) {
return err;
}
if (!MP_IS_ZERO(a)) {
a->sign = MP_NEG;
}
return MP_OKAY;
} else if (a->dp[0] > 1uL) {
a->dp[0]--;
if (a->dp[0] == 0u) {
mp_zero(a);
}
return MP_OKAY;
} else {
return mp_sub_d(a, 1uL,a);
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DIV_C
#ifdef BN_MP_DIV_SMALL
mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
mp_int ta, tb, tq, q;
int n, n2;
mp_err err;
if (MP_IS_ZERO(b)) {
return MP_VAL;
}
if (mp_cmp_mag(a, b) == MP_LT) {
if (d != NULL) {
err = mp_copy(a, d);
} else {
err = MP_OKAY;
}
if (c != NULL) {
mp_zero(c);
}
return err;
}
if ((err = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
return err;
}
mp_set(&tq, 1uL);
n = mp_count_bits(a) - mp_count_bits(b);
if ((err = mp_abs(a, &ta)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_abs(b, &tb)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2d(&tq, n, &tq)) != MP_OKAY) goto LBL_ERR;
while (n-- >= 0) {
if (mp_cmp(&tb, &ta) != MP_GT) {
if ((err = mp_sub(&ta, &tb, &ta)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&q, &tq, &q)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY) goto LBL_ERR;
}
n = a->sign;
n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
if (c != NULL) {
mp_exch(c, &q);
c->sign = MP_IS_ZERO(c) ? MP_ZPOS : n2;
}
if (d != NULL) {
mp_exch(d, &ta);
d->sign = MP_IS_ZERO(d) ? MP_ZPOS : n;
}
LBL_ERR:
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
return err;
}
#else
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
* HAC pp.598 Algorithm 14.20
*
* Note that the description in HAC is horribly
* incomplete. For example, it doesn't consider
* the case where digits are removed from 'x' in
* the inner loop. It also doesn't consider the
* case that y has fewer than three digits, etc..
*
* The overall algorithm is as described as
* 14.20 from HAC but fixed to treat these cases.
*/
mp_err mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
mp_int q, x, y, t1, t2;
int n, t, i, norm;
mp_sign neg;
mp_err err;
if (MP_IS_ZERO(b)) {
return MP_VAL;
}
if (mp_cmp_mag(a, b) == MP_LT) {
if (d != NULL) {
err = mp_copy(a, d);
} else {
err = MP_OKAY;
}
if (c != NULL) {
mp_zero(c);
}
return err;
}
if ((err = mp_init_size(&q, a->used + 2)) != MP_OKAY) {
return err;
}
q.used = a->used + 2;
if ((err = mp_init(&t1)) != MP_OKAY) goto LBL_Q;
if ((err = mp_init(&t2)) != MP_OKAY) goto LBL_T1;
if ((err = mp_init_copy(&x, a)) != MP_OKAY) goto LBL_T2;
if ((err = mp_init_copy(&y, b)) != MP_OKAY) goto LBL_X;
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
x.sign = y.sign = MP_ZPOS;
norm = mp_count_bits(&y) % MP_DIGIT_BIT;
if (norm < (MP_DIGIT_BIT - 1)) {
norm = (MP_DIGIT_BIT - 1) - norm;
if ((err = mp_mul_2d(&x, norm, &x)) != MP_OKAY) goto LBL_Y;
if ((err = mp_mul_2d(&y, norm, &y)) != MP_OKAY) goto LBL_Y;
} else {
norm = 0;
}
n = x.used - 1;
t = y.used - 1;
if ((err = mp_lshd(&y, n - t)) != MP_OKAY) goto LBL_Y;
while (mp_cmp(&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((err = mp_sub(&x, &y, &x)) != MP_OKAY) goto LBL_Y;
}
mp_rshd(&y, n - t);
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)MP_DIGIT_BIT) - (mp_digit)1;
} else {
mp_word tmp;
tmp = (mp_word)x.dp[i] << (mp_word)MP_DIGIT_BIT;
tmp |= (mp_word)x.dp[i - 1];
tmp /= (mp_word)y.dp[t];
if (tmp > (mp_word)MP_MASK) {
tmp = MP_MASK;
}
q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK);
}
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK;
do {
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK;
mp_zero(&t1);
t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((err = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y;
t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2];
t2.dp[1] = x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
if ((err = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) goto LBL_Y;
if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y;
if ((err = mp_sub(&x, &t1, &x)) != MP_OKAY) goto LBL_Y;
if (x.sign == MP_NEG) {
if ((err = mp_copy(&y, &t1)) != MP_OKAY) goto LBL_Y;
if ((err = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) goto LBL_Y;
if ((err = mp_add(&x, &t1, &x)) != MP_OKAY) goto LBL_Y;
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK;
}
}
* [which we have to normalize]
*/
x.sign = (x.used == 0) ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
c->sign = neg;
}
if (d != NULL) {
if ((err = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) goto LBL_Y;
mp_exch(&x, d);
}
err = MP_OKAY;
LBL_Y:
mp_clear(&y);
LBL_X:
mp_clear(&x);
LBL_T2:
mp_clear(&t2);
LBL_T1:
mp_clear(&t1);
LBL_Q:
mp_clear(&q);
return err;
}
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_DIV_2_C
mp_err mp_div_2(const mp_int *a, mp_int *b)
{
int x, oldused;
mp_digit r, rr, *tmpa, *tmpb;
mp_err err;
if (b->alloc < a->used) {
if ((err = mp_grow(b, a->used)) != MP_OKAY) {
return err;
}
}
oldused = b->used;
b->used = a->used;
tmpa = a->dp + b->used - 1;
tmpb = b->dp + b->used - 1;
r = 0;
for (x = b->used - 1; x >= 0; x--) {
rr = *tmpa & 1u;
*tmpb-- = (*tmpa-- >> 1) | (r << (MP_DIGIT_BIT - 1));
r = rr;
}
MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used);
b->sign = a->sign;
mp_clamp(b);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DIV_2D_C
mp_err mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
{
mp_digit D, r, rr;
int x;
mp_err err;
if (b <= 0) {
err = mp_copy(a, c);
if (d != NULL) {
mp_zero(d);
}
return err;
}
if ((err = mp_copy(a, c)) != MP_OKAY) {
return err;
}
if (d != NULL) {
if ((err = mp_mod_2d(a, b, d)) != MP_OKAY) {
return err;
}
}
if (b >= MP_DIGIT_BIT) {
mp_rshd(c, b / MP_DIGIT_BIT);
}
D = (mp_digit)(b % MP_DIGIT_BIT);
if (D != 0u) {
mp_digit *tmpc, mask, shift;
mask = ((mp_digit)1 << D) - 1uL;
shift = (mp_digit)MP_DIGIT_BIT - D;
tmpc = c->dp + (c->used - 1);
r = 0;
for (x = c->used - 1; x >= 0; x--) {
rr = *tmpc & mask;
*tmpc = (*tmpc >> D) | (r << shift);
--tmpc;
r = rr;
}
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DIV_3_C
mp_err mp_div_3(const mp_int *a, mp_int *c, mp_digit *d)
{
mp_int q;
mp_word w, t;
mp_digit b;
mp_err err;
int ix;
b = ((mp_word)1 << (mp_word)MP_DIGIT_BIT) / (mp_word)3;
if ((err = mp_init_size(&q, a->used)) != MP_OKAY) {
return err;
}
q.used = a->used;
q.sign = a->sign;
w = 0;
for (ix = a->used - 1; ix >= 0; ix--) {
w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix];
if (w >= 3u) {
t = (w * (mp_word)b) >> (mp_word)MP_DIGIT_BIT;
w -= t+t+t;
* the optimization is not exact.
*/
while (w >= 3u) {
t += 1u;
w -= 3u;
}
} else {
t = 0;
}
q.dp[ix] = (mp_digit)t;
}
if (d != NULL) {
*d = (mp_digit)w;
}
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DIV_D_C
mp_err mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
{
mp_int q;
mp_word w;
mp_digit t;
mp_err err;
int ix;
if (b == 0u) {
return MP_VAL;
}
if ((b == 1u) || MP_IS_ZERO(a)) {
if (d != NULL) {
*d = 0;
}
if (c != NULL) {
return mp_copy(a, c);
}
return MP_OKAY;
}
if ((b & (b - 1u)) == 0u) {
ix = 1;
while ((ix < MP_DIGIT_BIT) && (b != (((mp_digit)1)<<ix))) {
ix++;
}
if (d != NULL) {
*d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
}
return MP_OKAY;
}
if (MP_HAS(MP_DIV_3) && (b == 3u)) {
return mp_div_3(a, c, d);
}
if ((err = mp_init_size(&q, a->used)) != MP_OKAY) {
return err;
}
q.used = a->used;
q.sign = a->sign;
w = 0;
for (ix = a->used - 1; ix >= 0; ix--) {
w = (w << (mp_word)MP_DIGIT_BIT) | (mp_word)a->dp[ix];
if (w >= b) {
t = (mp_digit)(w / b);
w -= (mp_word)t * (mp_word)b;
} else {
t = 0;
}
q.dp[ix] = t;
}
if (d != NULL) {
*d = (mp_digit)w;
}
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DR_IS_MODULUS_C
mp_bool mp_dr_is_modulus(const mp_int *a)
{
int ix;
if (a->used < 2) {
return MP_NO;
}
* but the first digit must be equal to -1 (mod b).
*/
for (ix = 1; ix < a->used; ix++) {
if (a->dp[ix] != MP_MASK) {
return MP_NO;
}
}
return MP_YES;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DR_REDUCE_C
*
* Based on algorithm from the paper
*
* "Generating Efficient Primes for Discrete Log Cryptosystems"
* Chae Hoon Lim, Pil Joong Lee,
* POSTECH Information Research Laboratories
*
* The modulus must be of a special format [see manual]
*
* Has been modified to use algorithm 7.10 from the LTM book instead
*
* Input x must be in the range 0 <= x <= (n-1)**2
*/
mp_err mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k)
{
mp_err err;
int i, m;
mp_word r;
mp_digit mu, *tmpx1, *tmpx2;
m = n->used;
if (x->alloc < (m + m)) {
if ((err = mp_grow(x, m + m)) != MP_OKAY) {
return err;
}
}
* another reduction pass is required.
*/
top:
tmpx1 = x->dp;
tmpx2 = x->dp + m;
mu = 0;
for (i = 0; i < m; i++) {
r = ((mp_word)*tmpx2++ * (mp_word)k) + *tmpx1 + mu;
*tmpx1++ = (mp_digit)(r & MP_MASK);
mu = (mp_digit)(r >> ((mp_word)MP_DIGIT_BIT));
}
*tmpx1++ = mu;
MP_ZERO_DIGITS(tmpx1, (x->used - m) - 1);
mp_clamp(x);
* Each successive "recursion" makes the input smaller and smaller.
*/
if (mp_cmp_mag(x, n) != MP_LT) {
if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
return err;
}
goto top;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_DR_SETUP_C
void mp_dr_setup(const mp_int *a, mp_digit *d)
{
* the number of bits in a mp_digit [e.g. MP_DIGIT_BIT==31]
*/
*d = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - (mp_word)a->dp[0]);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ERROR_TO_STRING_C
const char *mp_error_to_string(mp_err code)
{
switch (code) {
case MP_OKAY:
return "Successful";
case MP_ERR:
return "Unknown error";
case MP_MEM:
return "Out of heap";
case MP_VAL:
return "Value out of range";
case MP_ITER:
return "Max. iterations reached";
case MP_BUF:
return "Buffer overflow";
default:
return "Invalid error code";
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_EXCH_C
* mp_int pointers around
*/
void mp_exch(mp_int *a, mp_int *b)
{
mp_int t;
t = *a;
*a = *b;
*b = t;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_EXPT_U32_C
mp_err mp_expt_u32(const mp_int *a, uint32_t b, mp_int *c)
{
mp_err err;
mp_int g;
if ((err = mp_init_copy(&g, a)) != MP_OKAY) {
return err;
}
mp_set(c, 1uL);
while (b > 0u) {
if ((b & 1u) != 0u) {
if ((err = mp_mul(c, &g, c)) != MP_OKAY) {
goto LBL_ERR;
}
}
if (b > 1u) {
if ((err = mp_sqr(&g, &g)) != MP_OKAY) {
goto LBL_ERR;
}
}
b >>= 1;
}
err = MP_OKAY;
LBL_ERR:
mp_clear(&g);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_EXPTMOD_C
* 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)
*/
mp_err mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y)
{
int dr;
if (P->sign == MP_NEG) {
return MP_VAL;
}
if (X->sign == MP_NEG) {
mp_int tmpG, tmpX;
mp_err err;
if (!MP_HAS(MP_INVMOD)) {
return MP_VAL;
}
if ((err = mp_init_multi(&tmpG, &tmpX, NULL)) != MP_OKAY) {
return err;
}
if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
goto LBL_ERR;
}
err = mp_exptmod(&tmpG, &tmpX, P, Y);
LBL_ERR:
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
}
if (MP_HAS(MP_REDUCE_IS_2K_L) && MP_HAS(MP_REDUCE_2K_L) && MP_HAS(S_MP_EXPTMOD) &&
(mp_reduce_is_2k_l(P) == MP_YES)) {
return s_mp_exptmod(G, X, P, Y, 1);
}
dr = (MP_HAS(MP_DR_IS_MODULUS) && (mp_dr_is_modulus(P) == MP_YES)) ? 1 : 0;
if (MP_HAS(MP_REDUCE_IS_2K) && (dr == 0)) {
dr = (mp_reduce_is_2k(P) == MP_YES) ? 2 : 0;
}
if (MP_HAS(S_MP_EXPTMOD_FAST) && (MP_IS_ODD(P) || (dr != 0))) {
return s_mp_exptmod_fast(G, X, P, Y, dr);
} else if (MP_HAS(S_MP_EXPTMOD)) {
return s_mp_exptmod(G, X, P, Y, 0);
} else {
return MP_VAL;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_EXTEUCLID_C
a*u1 + b*u2 = u3
*/
mp_err mp_exteuclid(const mp_int *a, const mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
{
mp_int u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp;
mp_err err;
if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
return err;
}
mp_set(&u1, 1uL);
if ((err = mp_copy(a, &u3)) != MP_OKAY) goto LBL_ERR;
mp_set(&v2, 1uL);
if ((err = mp_copy(b, &v3)) != MP_OKAY) goto LBL_ERR;
while (!MP_IS_ZERO(&v3)) {
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) goto LBL_ERR;
}
if (u3.sign == MP_NEG) {
if ((err = mp_neg(&u1, &u1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_neg(&u2, &u2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_neg(&u3, &u3)) != MP_OKAY) goto LBL_ERR;
}
if (U1 != NULL) {
mp_exch(U1, &u1);
}
if (U2 != NULL) {
mp_exch(U2, &u2);
}
if (U3 != NULL) {
mp_exch(U3, &u3);
}
err = MP_OKAY;
LBL_ERR:
mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_FREAD_C
#ifndef MP_NO_FILE
mp_err mp_fread(mp_int *a, int radix, FILE *stream)
{
mp_err err;
mp_sign neg;
int ch = fgetc(stream);
if (ch == (int)'-') {
neg = MP_NEG;
ch = fgetc(stream);
} else {
neg = MP_ZPOS;
}
if (ch == EOF) {
return MP_ERR;
}
mp_zero(a);
do {
int y;
unsigned pos = (unsigned)(ch - (int)'(');
if (mp_s_rmap_reverse_sz < pos) {
break;
}
y = (int)mp_s_rmap_reverse[pos];
if ((y == 0xff) || (y >= radix)) {
break;
}
if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) {
return err;
}
} while ((ch = fgetc(stream)) != EOF);
if (a->used != 0) {
a->sign = neg;
}
return MP_OKAY;
}
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_FROM_SBIN_C
mp_err mp_from_sbin(mp_int *a, const unsigned char *buf, size_t size)
{
mp_err err;
if ((err = mp_from_ubin(a, buf + 1, size - 1u)) != MP_OKAY) {
return err;
}
if (buf[0] == (unsigned char)0) {
a->sign = MP_ZPOS;
} else {
a->sign = MP_NEG;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_FROM_UBIN_C
mp_err mp_from_ubin(mp_int *a, const unsigned char *buf, size_t size)
{
mp_err err;
if (a->alloc < 2) {
if ((err = mp_grow(a, 2)) != MP_OKAY) {
return err;
}
}
mp_zero(a);
while (size-- > 0u) {
if ((err = mp_mul_2d(a, 8, a)) != MP_OKAY) {
return err;
}
#ifndef MP_8BIT
a->dp[0] |= *buf++;
a->used += 1;
#else
a->dp[0] = (*buf & MP_MASK);
a->dp[1] |= ((*buf++ >> 7) & 1u);
a->used += 2;
#endif
}
mp_clamp(a);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_FWRITE_C
#ifndef MP_NO_FILE
mp_err mp_fwrite(const mp_int *a, int radix, FILE *stream)
{
char *buf;
mp_err err;
int len;
size_t written;
if (MP_HAS(MP_RADIX_SIZE_OVERESTIMATE)) {
} else {
if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
return err;
}
}
buf = (char *) MP_MALLOC((size_t)len);
if (buf == NULL) {
return MP_MEM;
}
if ((err = mp_to_radix(a, buf, (size_t)len, &written, radix)) != MP_OKAY) {
goto LBL_ERR;
}
if (fwrite(buf, written, 1uL, stream) != 1uL) {
err = MP_ERR;
goto LBL_ERR;
}
err = MP_OKAY;
LBL_ERR:
MP_FREE_BUFFER(buf, (size_t)len);
return err;
}
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_GCD_C
mp_err mp_gcd(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int u, v;
int k, u_lsb, v_lsb;
mp_err err;
if (MP_IS_ZERO(a)) {
return mp_abs(b, c);
}
if (MP_IS_ZERO(b)) {
return mp_abs(a, c);
}
if ((err = mp_init_copy(&u, a)) != MP_OKAY) {
return err;
}
if ((err = mp_init_copy(&v, b)) != MP_OKAY) {
goto LBL_U;
}
u.sign = v.sign = MP_ZPOS;
u_lsb = mp_cnt_lsb(&u);
v_lsb = mp_cnt_lsb(&v);
k = MP_MIN(u_lsb, v_lsb);
if (k > 0) {
if ((err = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
goto LBL_V;
}
if ((err = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
if (u_lsb != k) {
if ((err = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
if (v_lsb != k) {
if ((err = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
while (!MP_IS_ZERO(&v)) {
if (mp_cmp_mag(&u, &v) == MP_GT) {
mp_exch(&u, &v);
}
if ((err = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
goto LBL_V;
}
if ((err = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
if ((err = mp_mul_2d(&u, k, c)) != MP_OKAY) {
goto LBL_V;
}
c->sign = MP_ZPOS;
err = MP_OKAY;
LBL_V:
mp_clear(&u);
LBL_U:
mp_clear(&v);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_DOUBLE_C
double mp_get_double(const mp_int *a)
{
int i;
double d = 0.0, fac = 1.0;
for (i = 0; i < MP_DIGIT_BIT; ++i) {
fac *= 2.0;
}
for (i = a->used; i --> 0;) {
d = (d * fac) + (double)a->dp[i];
}
return (a->sign == MP_NEG) ? -d : d;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_I32_C
MP_GET_SIGNED(mp_get_i32, mp_get_mag_u32, int32_t, uint32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_I64_C
MP_GET_SIGNED(mp_get_i64, mp_get_mag_u64, int64_t, uint64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_L_C
MP_GET_SIGNED(mp_get_l, mp_get_mag_ul, long, unsigned long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_LL_C
MP_GET_SIGNED(mp_get_ll, mp_get_mag_ull, long long, unsigned long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_MAG_U32_C
MP_GET_MAG(mp_get_mag_u32, uint32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_MAG_U64_C
MP_GET_MAG(mp_get_mag_u64, uint64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_MAG_UL_C
MP_GET_MAG(mp_get_mag_ul, unsigned long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GET_MAG_ULL_C
MP_GET_MAG(mp_get_mag_ull, unsigned long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_GROW_C
mp_err mp_grow(mp_int *a, int size)
{
int i;
mp_digit *tmp;
if (a->alloc < size) {
*
* We store the return in a temporary variable
* in case the operation failed we don't want
* to overwrite the dp member of a.
*/
tmp = (mp_digit *) MP_REALLOC(a->dp,
(size_t)a->alloc * sizeof(mp_digit),
(size_t)size * sizeof(mp_digit));
if (tmp == NULL) {
return MP_MEM;
}
a->dp = tmp;
i = a->alloc;
a->alloc = size;
MP_ZERO_DIGITS(a->dp + i, a->alloc - i);
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INCR_C
mp_err mp_incr(mp_int *a)
{
if (MP_IS_ZERO(a)) {
mp_set(a,1uL);
return MP_OKAY;
} else if (a->sign == MP_NEG) {
mp_err err;
a->sign = MP_ZPOS;
if ((err = mp_decr(a)) != MP_OKAY) {
return err;
}
if (!MP_IS_ZERO(a)) {
a->sign = MP_NEG;
}
return MP_OKAY;
} else if (a->dp[0] < MP_DIGIT_MAX) {
a->dp[0]++;
return MP_OKAY;
} else {
return mp_add_d(a, 1uL,a);
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_C
mp_err mp_init(mp_int *a)
{
a->dp = (mp_digit *) MP_CALLOC((size_t)MP_PREC, sizeof(mp_digit));
if (a->dp == NULL) {
return MP_MEM;
}
* and sign to positive */
a->used = 0;
a->alloc = MP_PREC;
a->sign = MP_ZPOS;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_COPY_C
mp_err mp_init_copy(mp_int *a, const mp_int *b)
{
mp_err err;
if ((err = mp_init_size(a, b->used)) != MP_OKAY) {
return err;
}
if ((err = mp_copy(b, a)) != MP_OKAY) {
mp_clear(a);
}
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_I32_C
MP_INIT_INT(mp_init_i32, mp_set_i32, int32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_I64_C
MP_INIT_INT(mp_init_i64, mp_set_i64, int64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_L_C
MP_INIT_INT(mp_init_l, mp_set_l, long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_LL_C
MP_INIT_INT(mp_init_ll, mp_set_ll, long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_MULTI_C
#include <stdarg.h>
mp_err mp_init_multi(mp_int *mp, ...)
{
mp_err err = MP_OKAY;
int n = 0;
mp_int *cur_arg = mp;
va_list args;
va_start(args, mp);
while (cur_arg != NULL) {
if (mp_init(cur_arg) != MP_OKAY) {
succeeded in init-ing, then return error.
*/
va_list clean_args;
cur_arg = mp;
va_start(clean_args, mp);
while (n-- != 0) {
mp_clear(cur_arg);
cur_arg = va_arg(clean_args, mp_int *);
}
va_end(clean_args);
err = MP_MEM;
break;
}
n++;
cur_arg = va_arg(args, mp_int *);
}
va_end(args);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_SET_C
mp_err mp_init_set(mp_int *a, mp_digit b)
{
mp_err err;
if ((err = mp_init(a)) != MP_OKAY) {
return err;
}
mp_set(a, b);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_SIZE_C
mp_err mp_init_size(mp_int *a, int size)
{
size = MP_MAX(MP_MIN_PREC, size);
a->dp = (mp_digit *) MP_CALLOC((size_t)size, sizeof(mp_digit));
if (a->dp == NULL) {
return MP_MEM;
}
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_U32_C
MP_INIT_INT(mp_init_u32, mp_set_u32, uint32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_U64_C
MP_INIT_INT(mp_init_u64, mp_set_u64, uint64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_UL_C
MP_INIT_INT(mp_init_ul, mp_set_ul, unsigned long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INIT_ULL_C
MP_INIT_INT(mp_init_ull, mp_set_ull, unsigned long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_INVMOD_C
mp_err mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) {
return MP_VAL;
}
if (MP_HAS(S_MP_INVMOD_FAST) && MP_IS_ODD(b)) {
return s_mp_invmod_fast(a, b, c);
}
return MP_HAS(S_MP_INVMOD_SLOW)
? s_mp_invmod_slow(a, b, c)
: MP_VAL;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_IS_SQUARE_C
static const char rem_128[128] = {
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
};
static const char rem_105[105] = {
0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
};
mp_err mp_is_square(const mp_int *arg, mp_bool *ret)
{
mp_err err;
mp_digit c;
mp_int t;
unsigned long r;
*ret = MP_NO;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
if (MP_IS_ZERO(arg)) {
return MP_OKAY;
}
if (rem_128[127u & arg->dp[0]] == (char)1) {
return MP_OKAY;
}
if ((err = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) {
return err;
}
if (rem_105[c] == (char)1) {
return MP_OKAY;
}
if ((err = mp_init_u32(&t, 11u*13u*17u*19u*23u*29u*31u)) != MP_OKAY) {
return err;
}
if ((err = mp_mod(arg, &t, &t)) != MP_OKAY) {
goto LBL_ERR;
}
r = mp_get_u32(&t);
* free "t" so the easiest way is to goto LBL_ERR. We know that err
* is already equal to MP_OKAY from the mp_mod call
*/
if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_ERR;
if ((err = mp_sqrt(arg, &t)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_sqr(&t, &t)) != MP_OKAY) {
goto LBL_ERR;
}
*ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO;
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ISEVEN_C
mp_bool mp_iseven(const mp_int *a)
{
return MP_IS_EVEN(a) ? MP_YES : MP_NO;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ISODD_C
mp_bool mp_isodd(const mp_int *a)
{
return MP_IS_ODD(a) ? MP_YES : MP_NO;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_KRONECKER_C
Kronecker symbol (a|p)
Straightforward implementation of algorithm 1.4.10 in
Henri Cohen: "A Course in Computational Algebraic Number Theory"
@book{cohen2013course,
title={A course in computational algebraic number theory},
author={Cohen, Henri},
volume={138},
year={2013},
publisher={Springer Science \& Business Media}
}
*/
mp_err mp_kronecker(const mp_int *a, const mp_int *p, int *c)
{
mp_int a1, p1, r;
mp_err err;
int v, k;
static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
if (MP_IS_ZERO(p)) {
if ((a->used == 1) && (a->dp[0] == 1u)) {
*c = 1;
} else {
*c = 0;
}
return MP_OKAY;
}
if (MP_IS_EVEN(a) && MP_IS_EVEN(p)) {
*c = 0;
return MP_OKAY;
}
if ((err = mp_init_copy(&a1, a)) != MP_OKAY) {
return err;
}
if ((err = mp_init_copy(&p1, p)) != MP_OKAY) {
goto LBL_KRON_0;
}
v = mp_cnt_lsb(&p1);
if ((err = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
goto LBL_KRON_1;
}
if ((v & 1) == 0) {
k = 1;
} else {
k = table[a->dp[0] & 7u];
}
if (p1.sign == MP_NEG) {
p1.sign = MP_ZPOS;
if (a1.sign == MP_NEG) {
k = -k;
}
}
if ((err = mp_init(&r)) != MP_OKAY) {
goto LBL_KRON_1;
}
for (;;) {
if (MP_IS_ZERO(&a1)) {
if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
*c = k;
goto LBL_KRON;
} else {
*c = 0;
goto LBL_KRON;
}
}
v = mp_cnt_lsb(&a1);
if ((err = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
goto LBL_KRON;
}
if ((v & 1) == 1) {
k = k * table[p1.dp[0] & 7u];
}
if (a1.sign == MP_NEG) {
* Compute k = (-1)^((a1)*(p1-1)/4) * k
* a1.dp[0] + 1 cannot overflow because the MSB
* of the type mp_digit is not set by definition
*/
if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
k = -k;
}
} else {
if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
k = -k;
}
}
if ((err = mp_copy(&a1, &r)) != MP_OKAY) {
goto LBL_KRON;
}
r.sign = MP_ZPOS;
if ((err = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
goto LBL_KRON;
}
if ((err = mp_copy(&r, &p1)) != MP_OKAY) {
goto LBL_KRON;
}
}
LBL_KRON:
mp_clear(&r);
LBL_KRON_1:
mp_clear(&p1);
LBL_KRON_0:
mp_clear(&a1);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_LCM_C
mp_err mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_err err;
mp_int t1, t2;
if ((err = mp_init_multi(&t1, &t2, NULL)) != MP_OKAY) {
return err;
}
if ((err = mp_gcd(a, b, &t1)) != MP_OKAY) {
goto LBL_T;
}
if (mp_cmp_mag(a, b) == MP_LT) {
if ((err = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
goto LBL_T;
}
err = mp_mul(b, &t2, c);
} else {
if ((err = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
goto LBL_T;
}
err = mp_mul(a, &t2, c);
}
c->sign = MP_ZPOS;
LBL_T:
mp_clear_multi(&t1, &t2, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_LOG_U32_C
static mp_word s_pow(mp_word base, mp_word exponent)
{
mp_word result = 1uLL;
while (exponent != 0u) {
if ((exponent & 1u) == 1u) {
result *= base;
}
exponent >>= 1;
base *= base;
}
return result;
}
static mp_digit s_digit_ilogb(mp_digit base, mp_digit n)
{
mp_word bracket_low = 1uLL, bracket_mid, bracket_high, N;
mp_digit ret, high = 1uL, low = 0uL, mid;
if (n < base) {
return 0uL;
}
if (n == base) {
return 1uL;
}
bracket_high = (mp_word) base ;
N = (mp_word) n;
while (bracket_high < N) {
low = high;
bracket_low = bracket_high;
high <<= 1;
bracket_high *= bracket_high;
}
while (((mp_digit)(high - low)) > 1uL) {
mid = (low + high) >> 1;
bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low));
if (N < bracket_mid) {
high = mid ;
bracket_high = bracket_mid ;
}
if (N > bracket_mid) {
low = mid ;
bracket_low = bracket_mid ;
}
if (N == bracket_mid) {
return (mp_digit) mid;
}
}
if (bracket_high == N) {
ret = high;
} else {
ret = low;
}
return ret;
}
as is the output of mp_bitcount.
With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only!
*/
mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c)
{
mp_err err;
mp_ord cmp;
uint32_t high, low, mid;
mp_int bracket_low, bracket_high, bracket_mid, t, bi_base;
err = MP_OKAY;
if (a->sign == MP_NEG) {
return MP_VAL;
}
if (MP_IS_ZERO(a)) {
return MP_VAL;
}
if (base < 2u) {
return MP_VAL;
}
if ((base & (base - 1u)) == 0u) {
int y, bit_count;
for (y=0; (y < 7) && ((base & 1u) == 0u); y++) {
base >>= 1;
}
bit_count = mp_count_bits(a) - 1;
*c = (uint32_t)(bit_count/y);
return MP_OKAY;
}
if (a->used == 1) {
*c = (uint32_t)s_digit_ilogb(base, a->dp[0]);
return err;
}
cmp = mp_cmp_d(a, base);
if ((cmp == MP_LT) || (cmp == MP_EQ)) {
*c = cmp == MP_EQ;
return err;
}
if ((err =
mp_init_multi(&bracket_low, &bracket_high,
&bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) {
return err;
}
low = 0u;
mp_set(&bracket_low, 1uL);
high = 1u;
mp_set(&bracket_high, base);
A kind of Giant-step/baby-step algorithm.
Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/
The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped
for small n.
*/
while (mp_cmp(&bracket_high, a) == MP_LT) {
low = high;
if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) {
goto LBL_ERR;
}
high <<= 1;
if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_set(&bi_base, base);
while ((high - low) > 1u) {
mid = (high + low) >> 1;
if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) {
goto LBL_ERR;
}
cmp = mp_cmp(a, &bracket_mid);
if (cmp == MP_LT) {
high = mid;
mp_exch(&bracket_mid, &bracket_high);
}
if (cmp == MP_GT) {
low = mid;
mp_exch(&bracket_mid, &bracket_low);
}
if (cmp == MP_EQ) {
*c = mid;
goto LBL_END;
}
}
*c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low;
LBL_END:
LBL_ERR:
mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid,
&t, &bi_base, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_LSHD_C
mp_err mp_lshd(mp_int *a, int b)
{
int x;
mp_err err;
mp_digit *top, *bottom;
if (b <= 0) {
return MP_OKAY;
}
if (MP_IS_ZERO(a)) {
return MP_OKAY;
}
if (a->alloc < (a->used + b)) {
if ((err = mp_grow(a, a->used + b)) != MP_OKAY) {
return err;
}
}
a->used += b;
top = a->dp + a->used - 1;
bottom = (a->dp + a->used - 1) - b;
* except the window goes the otherway around. Copying from
* the bottom to the top. see bn_mp_rshd.c for more info.
*/
for (x = a->used - 1; x >= b; x--) {
*top-- = *bottom--;
}
MP_ZERO_DIGITS(a->dp, b);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MOD_C
mp_err mp_mod(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int t;
mp_err err;
if ((err = mp_init_size(&t, b->used)) != MP_OKAY) {
return err;
}
if ((err = mp_div(a, b, NULL, &t)) != MP_OKAY) {
goto LBL_ERR;
}
if (MP_IS_ZERO(&t) || (t.sign == b->sign)) {
err = MP_OKAY;
mp_exch(&t, c);
} else {
err = mp_add(b, &t, c);
}
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MOD_2D_C
mp_err mp_mod_2d(const mp_int *a, int b, mp_int *c)
{
int x;
mp_err err;
if (b <= 0) {
mp_zero(c);
return MP_OKAY;
}
if (b >= (a->used * MP_DIGIT_BIT)) {
return mp_copy(a, c);
}
if ((err = mp_copy(a, c)) != MP_OKAY) {
return err;
}
x = (b / MP_DIGIT_BIT) + (((b % MP_DIGIT_BIT) == 0) ? 0 : 1);
MP_ZERO_DIGITS(c->dp + x, c->used - x);
c->dp[b / MP_DIGIT_BIT] &=
((mp_digit)1 << (mp_digit)(b % MP_DIGIT_BIT)) - (mp_digit)1;
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MOD_D_C
mp_err mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
{
return mp_div_d(a, b, NULL, c);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
mp_err mp_montgomery_calc_normalization(mp_int *a, const mp_int *b)
{
int x, bits;
mp_err err;
bits = mp_count_bits(b) % MP_DIGIT_BIT;
if (b->used > 1) {
if ((err = mp_2expt(a, ((b->used - 1) * MP_DIGIT_BIT) + bits - 1)) != MP_OKAY) {
return err;
}
} else {
mp_set(a, 1uL);
bits = 1;
}
for (x = bits - 1; x < (int)MP_DIGIT_BIT; x++) {
if ((err = mp_mul_2(a, a)) != MP_OKAY) {
return err;
}
if (mp_cmp_mag(a, b) != MP_LT) {
if ((err = s_mp_sub(a, b, a)) != MP_OKAY) {
return err;
}
}
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_REDUCE_C
mp_err mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, digs;
mp_err err;
mp_digit mu;
*
* Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
digs = (n->used * 2) + 1;
if ((digs < MP_WARRAY) &&
(x->used <= MP_WARRAY) &&
(n->used < MP_MAXFAST)) {
return s_mp_montgomery_reduce_fast(x, n, rho);
}
if (x->alloc < digs) {
if ((err = mp_grow(x, digs)) != MP_OKAY) {
return err;
}
}
x->used = digs;
for (ix = 0; ix < n->used; ix++) {
*
* The value of rho must be precalculated via
* montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
*/
mu = (mp_digit)(((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
{
int iy;
mp_digit *tmpn, *tmpx, u;
mp_word r;
tmpn = n->dp;
tmpx = x->dp + ix;
u = 0;
for (iy = 0; iy < n->used; iy++) {
r = ((mp_word)mu * (mp_word)*tmpn++) +
(mp_word)u + (mp_word)*tmpx;
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
*tmpx++ = (mp_digit)(r & (mp_word)MP_MASK);
}
while (u != 0u) {
*tmpx += u;
u = *tmpx >> MP_DIGIT_BIT;
*tmpx++ &= MP_MASK;
}
}
}
* significant digits of x are all zero
* which means we can shift x to the
* right by n.used digits and the
* residue is unchanged.
*/
mp_clamp(x);
mp_rshd(x, n->used);
if (mp_cmp_mag(x, n) != MP_LT) {
return s_mp_sub(x, n, x);
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_SETUP_C
mp_err mp_montgomery_setup(const mp_int *n, mp_digit *rho)
{
mp_digit x, b;
*
* Based on the fact that
*
* XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
* => 2*X*A - X*X*A*A = 1
* => 2*(1) - (1) = 1
*/
b = n->dp[0];
if ((b & 1u) == 0u) {
return MP_VAL;
}
x = (((b + 2u) & 4u) << 1) + b;
x *= 2u - (b * x);
#if !defined(MP_8BIT)
x *= 2u - (b * x);
#endif
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
x *= 2u - (b * x);
#endif
#ifdef MP_64BIT
x *= 2u - (b * x);
#endif
*rho = (mp_digit)(((mp_word)1 << (mp_word)MP_DIGIT_BIT) - x) & MP_MASK;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MUL_C
mp_err mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_err err;
int min_len = MP_MIN(a->used, b->used),
max_len = MP_MAX(a->used, b->used),
digs = a->used + b->used + 1;
mp_sign neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
if (MP_HAS(S_MP_BALANCE_MUL) &&
* The bigger one needs to be at least about one MP_KARATSUBA_MUL_CUTOFF bigger
* to make some sense, but it depends on architecture, OS, position of the
* stars... so YMMV.
* Using it to cut the input into slices small enough for fast_s_mp_mul_digs
* was actually slower on the author's machine, but YMMV.
*/
(min_len >= MP_KARATSUBA_MUL_CUTOFF) &&
((max_len / 2) >= MP_KARATSUBA_MUL_CUTOFF) &&
(max_len >= (2 * min_len))) {
err = s_mp_balance_mul(a,b,c);
} else if (MP_HAS(S_MP_TOOM_MUL) &&
(min_len >= MP_TOOM_MUL_CUTOFF)) {
err = s_mp_toom_mul(a, b, c);
} else if (MP_HAS(S_MP_KARATSUBA_MUL) &&
(min_len >= MP_KARATSUBA_MUL_CUTOFF)) {
err = s_mp_karatsuba_mul(a, b, c);
} else if (MP_HAS(S_MP_MUL_DIGS_FAST) &&
*
* The fast multiplier can be used if the output will
* have less than MP_WARRAY digits and the number of
* digits won't affect carry propagation
*/
(digs < MP_WARRAY) &&
(min_len <= MP_MAXFAST)) {
err = s_mp_mul_digs_fast(a, b, c, digs);
} else if (MP_HAS(S_MP_MUL_DIGS)) {
err = s_mp_mul_digs(a, b, c, digs);
} else {
err = MP_VAL;
}
c->sign = (c->used > 0) ? neg : MP_ZPOS;
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MUL_2_C
mp_err mp_mul_2(const mp_int *a, mp_int *b)
{
int x, oldused;
mp_err err;
if (b->alloc < (a->used + 1)) {
if ((err = mp_grow(b, a->used + 1)) != MP_OKAY) {
return err;
}
}
oldused = b->used;
b->used = a->used;
{
mp_digit r, rr, *tmpa, *tmpb;
tmpa = a->dp;
tmpb = b->dp;
r = 0;
for (x = 0; x < a->used; x++) {
* MSB of the current digit
*/
rr = *tmpa >> (mp_digit)(MP_DIGIT_BIT - 1);
*tmpb++ = ((*tmpa++ << 1uL) | r) & MP_MASK;
* digit into the next iteration
*/
r = rr;
}
if (r != 0u) {
*tmpb = 1;
++(b->used);
}
* that we didn't write to
*/
MP_ZERO_DIGITS(b->dp + b->used, oldused - b->used);
}
b->sign = a->sign;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MUL_2D_C
mp_err mp_mul_2d(const mp_int *a, int b, mp_int *c)
{
mp_digit d;
mp_err err;
if (a != c) {
if ((err = mp_copy(a, c)) != MP_OKAY) {
return err;
}
}
if (c->alloc < (c->used + (b / MP_DIGIT_BIT) + 1)) {
if ((err = mp_grow(c, c->used + (b / MP_DIGIT_BIT) + 1)) != MP_OKAY) {
return err;
}
}
if (b >= MP_DIGIT_BIT) {
if ((err = mp_lshd(c, b / MP_DIGIT_BIT)) != MP_OKAY) {
return err;
}
}
d = (mp_digit)(b % MP_DIGIT_BIT);
if (d != 0u) {
mp_digit *tmpc, shift, mask, r, rr;
int x;
mask = ((mp_digit)1 << d) - (mp_digit)1;
shift = (mp_digit)MP_DIGIT_BIT - d;
tmpc = c->dp;
r = 0;
for (x = 0; x < c->used; x++) {
rr = (*tmpc >> shift) & mask;
*tmpc = ((*tmpc << d) | r) & MP_MASK;
++tmpc;
r = rr;
}
if (r != 0u) {
c->dp[(c->used)++] = r;
}
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MUL_D_C
mp_err mp_mul_d(const mp_int *a, mp_digit b, mp_int *c)
{
mp_digit u, *tmpa, *tmpc;
mp_word r;
mp_err err;
int ix, olduse;
if (c->alloc < (a->used + 1)) {
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
return err;
}
}
olduse = c->used;
c->sign = a->sign;
tmpa = a->dp;
tmpc = c->dp;
u = 0;
for (ix = 0; ix < a->used; ix++) {
r = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b);
*tmpc++ = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
}
*tmpc++ = u;
++ix;
MP_ZERO_DIGITS(tmpc, olduse - ix);
c->used = a->used + 1;
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_MULMOD_C
mp_err mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
mp_err err;
mp_int t;
if ((err = mp_init_size(&t, c->used)) != MP_OKAY) {
return err;
}
if ((err = mp_mul(a, b, &t)) != MP_OKAY) {
goto LBL_ERR;
}
err = mp_mod(&t, c, d);
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_NEG_C
mp_err mp_neg(const mp_int *a, mp_int *b)
{
mp_err err;
if (a != b) {
if ((err = mp_copy(a, b)) != MP_OKAY) {
return err;
}
}
if (!MP_IS_ZERO(b)) {
b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
} else {
b->sign = MP_ZPOS;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_OR_C
mp_err mp_or(const mp_int *a, const mp_int *b, mp_int *c)
{
int used = MP_MAX(a->used, b->used) + 1, i;
mp_err err;
mp_digit ac = 1, bc = 1, cc = 1;
mp_sign csign = ((a->sign == MP_NEG) || (b->sign == MP_NEG)) ? MP_NEG : MP_ZPOS;
if (c->alloc < used) {
if ((err = mp_grow(c, used)) != MP_OKAY) {
return err;
}
}
for (i = 0; i < used; i++) {
mp_digit x, y;
if (a->sign == MP_NEG) {
ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK);
x = ac & MP_MASK;
ac >>= MP_DIGIT_BIT;
} else {
x = (i >= a->used) ? 0uL : a->dp[i];
}
if (b->sign == MP_NEG) {
bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK);
y = bc & MP_MASK;
bc >>= MP_DIGIT_BIT;
} else {
y = (i >= b->used) ? 0uL : b->dp[i];
}
c->dp[i] = x | y;
if (csign == MP_NEG) {
cc += ~c->dp[i] & MP_MASK;
c->dp[i] = cc & MP_MASK;
cc >>= MP_DIGIT_BIT;
}
}
c->used = used;
c->sign = csign;
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PACK_C
* see http://gmplib.org/manual/Integer-Import-and-Export.html
*/
mp_err mp_pack(void *rop, size_t maxcount, size_t *written, mp_order order, size_t size,
mp_endian endian, size_t nails, const mp_int *op)
{
mp_err err;
size_t odd_nails, nail_bytes, i, j, count;
unsigned char odd_nail_mask;
mp_int t;
count = mp_pack_count(op, nails, size);
if (count > maxcount) {
return MP_BUF;
}
if ((err = mp_init_copy(&t, op)) != MP_OKAY) {
return err;
}
if (endian == MP_NATIVE_ENDIAN) {
MP_GET_ENDIANNESS(endian);
}
odd_nails = (nails % 8u);
odd_nail_mask = 0xff;
for (i = 0u; i < odd_nails; ++i) {
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
}
nail_bytes = nails / 8u;
for (i = 0u; i < count; ++i) {
for (j = 0u; j < size; ++j) {
unsigned char *byte = (unsigned char *)rop +
(((order == MP_LSB_FIRST) ? i : ((count - 1u) - i)) * size) +
((endian == MP_LITTLE_ENDIAN) ? j : ((size - 1u) - j));
if (j >= (size - nail_bytes)) {
*byte = 0;
continue;
}
*byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL));
if ((err = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) {
goto LBL_ERR;
}
}
}
if (written != NULL) {
*written = count;
}
err = MP_OKAY;
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PACK_COUNT_C
size_t mp_pack_count(const mp_int *a, size_t nails, size_t size)
{
size_t bits = (size_t)mp_count_bits(a);
return ((bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u));
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_FERMAT_C
*
* If "a" were prime then b**a == b (mod a) since the order of
* the multiplicative sub-group would be phi(a) = a-1. That means
* it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
*
* Sets result to 1 if the congruence holds, or zero otherwise.
*/
mp_err mp_prime_fermat(const mp_int *a, const mp_int *b, mp_bool *result)
{
mp_int t;
mp_err err;
*result = MP_NO;
if (mp_cmp_d(b, 1uL) != MP_GT) {
return MP_VAL;
}
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
if ((err = mp_exptmod(b, a, a, &t)) != MP_OKAY) {
goto LBL_T;
}
if (mp_cmp(&t, b) == MP_EQ) {
*result = MP_YES;
}
err = MP_OKAY;
LBL_T:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
*/
#ifndef LTM_USE_ONLY_MR
#ifdef MP_8BIT
* floor of positive solution of
* (2^16)-1 = (a+4)*(2*a+5)
* TODO: Both values are smaller than N^(1/4), would have to use a bigint
* for a instead but any a biger than about 120 are already so rare that
* it is possible to ignore them and still get enough pseudoprimes.
* But it is still a restriction of the set of available pseudoprimes
* which makes this implementation less secure if used stand-alone.
*/
#define LTM_FROBENIUS_UNDERWOOD_A 177
#else
#define LTM_FROBENIUS_UNDERWOOD_A 32764
#endif
mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result)
{
mp_int T1z, T2z, Np1z, sz, tz;
int a, ap2, length, i, j;
mp_err err;
*result = MP_NO;
if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
return err;
}
for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
(a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
continue;
}
mp_set_u32(&T1z, (uint32_t)a);
if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR;
if (j == -1) {
break;
}
if (j == 0) {
goto LBL_FU_ERR;
}
}
if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
err = MP_ITER;
goto LBL_FU_ERR;
}
mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5)));
if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR;
ap2 = a + 2;
if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR;
mp_set(&sz, 1uL);
mp_set(&tz, 2uL);
length = mp_count_bits(&Np1z);
for (i = length - 2; i >= 0; i--) {
* temp = (sz*(a*sz+2*tz))%N;
* tz = ((tz-sz)*(tz+sz))%N;
* sz = temp;
*/
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
if (a != 0) {
if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
}
if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR;
if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) {
* temp = (a+2) * sz + tz
* tz = 2 * tz - sz
* sz = temp
*/
if (a == 0) {
if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
} else {
if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
}
if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR;
mp_exch(&sz, &T1z);
}
}
mp_set_u32(&T1z, (uint32_t)((2 * a) + 5));
if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
*result = MP_YES;
}
LBL_FU_ERR:
mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
return err;
}
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_IS_PRIME_C
static unsigned int s_floor_ilog2(int value)
{
unsigned int r = 0;
while ((value >>= 1) != 0) {
r++;
}
return r;
}
mp_err mp_prime_is_prime(const mp_int *a, int t, mp_bool *result)
{
mp_int b;
int ix, p_max = 0, size_a, len;
mp_bool res;
mp_err err;
unsigned int fips_rand, mask;
*result = MP_NO;
if (a->used == 1) {
if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
*result = MP_NO;
return MP_OKAY;
}
if (a->dp[0] == 2u) {
*result = MP_YES;
return MP_OKAY;
}
}
if (MP_IS_EVEN(a)) {
return MP_OKAY;
}
if ((err = mp_is_square(a, &res)) != MP_OKAY) {
return err;
}
if (res != MP_NO) {
return MP_OKAY;
}
for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
if (mp_cmp_d(a, s_mp_prime_tab[ix]) == MP_EQ) {
*result = MP_YES;
return MP_OKAY;
}
}
#ifdef MP_8BIT
if ((a->used == 1) && (PRIVATE_MP_PRIME_TAB_SIZE >= 31)) {
return MP_OKAY;
}
#endif
if ((err = s_mp_prime_is_divisible(a, &res)) != MP_OKAY) {
return err;
}
if (res == MP_YES) {
return MP_OKAY;
}
Run the Miller-Rabin test with base 2 for the BPSW test.
*/
if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
return err;
}
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
Rumours have it that Mathematica does a second M-R test with base 3.
Other rumours have it that their strong L-S test is slightly different.
It does not hurt, though, beside a bit of extra runtime.
*/
b.dp[0]++;
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
* Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
* slow so if speed is an issue, define LTM_USE_ONLY_MR to use M-R tests with
* bases 2, 3 and t random bases.
*/
#ifndef LTM_USE_ONLY_MR
if (t >= 0) {
* Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
* MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
* integers but the necesssary analysis is on the todo-list).
*/
#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
err = mp_prime_frobenius_underwood(a, &res);
if ((err != MP_OKAY) && (err != MP_ITER)) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#else
if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#endif
}
#endif
if (t == 0) {
t = 1;
}
Only recommended if the input range is known to be < 3317044064679887385961981
It uses the bases necessary for a deterministic M-R test if the input is
smaller than 3317044064679887385961981
The caller has to check the size.
TODO: can be made a bit finer grained but comparing is not free.
*/
if (t < 0) {
Sorenson, Jonathan; Webster, Jonathan (2015).
"Strong Pseudoprimes to Twelve Prime Bases".
*/
if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
goto LBL_B;
}
if (mp_cmp(a, &b) == MP_LT) {
p_max = 12;
} else {
if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
goto LBL_B;
}
if (mp_cmp(a, &b) == MP_LT) {
p_max = 13;
} else {
err = MP_VAL;
goto LBL_B;
}
}
for (ix = 2; ix < p_max; ix++) {
mp_set(&b, s_mp_prime_tab[ix]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
}
}
Do "t" M-R tests with random bases between 3 and "a".
See Fips 186.4 p. 126ff
*/
else if (t > 0) {
* The mp_digit's have a defined bit-size but the size of the
* array a.dp is a simple 'int' and this library can not assume full
* compliance to the current C-standard (ISO/IEC 9899:2011) because
* it gets used for small embeded processors, too. Some of those MCUs
* have compilers that one cannot call standard compliant by any means.
* Hence the ugly type-fiddling in the following code.
*/
size_a = mp_count_bits(a);
mask = (1u << s_floor_ilog2(size_a)) - 1u;
Assuming the General Rieman hypothesis (never thought to write that in a
comment) the upper bound can be lowered to 2*(log a)^2.
E. Bach, "Explicit bounds for primality testing and related problems,"
Math. Comp. 55 (1990), 355-380.
size_a = (size_a/10) * 7;
len = 2 * (size_a * size_a);
E.g.: a number of size 2^2048 would be reduced to the upper limit
floor(2048/10)*7 = 1428
2 * 1428^2 = 4078368
(would have been ~4030331.9962 with floats and natural log instead)
That number is smaller than 2^28, the default bit-size of mp_digit.
*/
How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
The function mp_rand() goes to some length to use a cryptographically
good PRNG. That also means that the chance to always get the same base
in the loop is non-zero, although very low.
If the BPSW test and/or the addtional Frobenious test have been
performed instead of just the Miller-Rabin test with the bases 2 and 3,
a single extra test should suffice, so such a very unlikely event
will not do much harm.
To preemptivly answer the dangling question: no, a witness does not
need to be prime.
*/
for (ix = 0; ix < t; ix++) {
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
* Reduce digit before casting because mp_digit might be bigger than
* an unsigned int and "mask" on the other side is most probably not.
*/
fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
#ifdef MP_8BIT
* One 8-bit digit is too small, so concatenate two if the size of
* unsigned int allows for it.
*/
if ((MP_SIZEOF_BITS(unsigned int)/2) >= MP_SIZEOF_BITS(mp_digit)) {
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
fips_rand <<= MP_SIZEOF_BITS(mp_digit);
fips_rand |= (unsigned int) b.dp[0];
fips_rand &= mask;
}
#endif
if (fips_rand > (unsigned int)(INT_MAX - MP_DIGIT_BIT)) {
len = INT_MAX / MP_DIGIT_BIT;
} else {
len = (((int)fips_rand + MP_DIGIT_BIT) / MP_DIGIT_BIT);
}
if (len < 0) {
ix--;
continue;
}
* As mentioned above, one 8-bit digit is too small and
* although it can only happen in the unlikely case that
* an "unsigned int" is smaller than 16 bit a simple test
* is cheap and the correction even cheaper.
*/
#ifdef MP_8BIT
if (len == 1) {
len++;
}
#endif
if ((err = mp_rand(&b, len)) != MP_OKAY) {
goto LBL_B;
}
* That number might got too big and the witness has to be
* smaller than "a"
*/
len = mp_count_bits(&b);
if (len >= size_a) {
len = (len - size_a) + 1;
if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
goto LBL_B;
}
}
if (mp_cmp_d(&b, 3uL) != MP_GT) {
ix--;
continue;
}
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
}
}
*result = MP_YES;
LBL_B:
mp_clear(&b);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_MILLER_RABIN_C
* 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.
*/
mp_err mp_prime_miller_rabin(const mp_int *a, const mp_int *b, mp_bool *result)
{
mp_int n1, y, r;
mp_err err;
int s, j;
*result = MP_NO;
if (mp_cmp_d(b, 1uL) != MP_GT) {
return MP_VAL;
}
if ((err = mp_init_copy(&n1, a)) != MP_OKAY) {
return err;
}
if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) {
goto LBL_N1;
}
if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) {
goto LBL_N1;
}
* which are zero
*/
s = mp_cnt_lsb(&r);
if ((err = mp_div_2d(&r, s, &r, NULL)) != MP_OKAY) {
goto LBL_R;
}
if ((err = mp_init(&y)) != MP_OKAY) {
goto LBL_R;
}
if ((err = mp_exptmod(b, &r, a, &y)) != MP_OKAY) {
goto LBL_Y;
}
if ((mp_cmp_d(&y, 1uL) != MP_EQ) && (mp_cmp(&y, &n1) != MP_EQ)) {
j = 1;
while ((j <= (s - 1)) && (mp_cmp(&y, &n1) != MP_EQ)) {
if ((err = mp_sqrmod(&y, a, &y)) != MP_OKAY) {
goto LBL_Y;
}
if (mp_cmp_d(&y, 1uL) == MP_EQ) {
goto LBL_Y;
}
++j;
}
if (mp_cmp(&y, &n1) != MP_EQ) {
goto LBL_Y;
}
}
*result = MP_YES;
LBL_Y:
mp_clear(&y);
LBL_R:
mp_clear(&r);
LBL_N1:
mp_clear(&n1);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_NEXT_PRIME_C
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
mp_err mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
int x, y;
mp_ord cmp;
mp_err err;
mp_bool res = MP_NO;
mp_digit res_tab[PRIVATE_MP_PRIME_TAB_SIZE], step, kstep;
mp_int b;
a->sign = MP_ZPOS;
if (mp_cmp_d(a, s_mp_prime_tab[PRIVATE_MP_PRIME_TAB_SIZE-1]) == MP_LT) {
for (x = 0; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
cmp = mp_cmp_d(a, s_mp_prime_tab[x]);
if (cmp == MP_EQ) {
continue;
}
if (cmp != MP_GT) {
if ((bbs_style == 1) && ((s_mp_prime_tab[x] & 3u) != 3u)) {
continue;
} else {
mp_set(a, s_mp_prime_tab[x]);
return MP_OKAY;
}
}
}
}
if (bbs_style == 1) {
kstep = 4;
} else {
kstep = 2;
}
if (bbs_style == 1) {
if ((a->dp[0] & 3u) != 3u) {
if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
return err;
}
}
} else {
if (MP_IS_EVEN(a)) {
if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
return err;
}
}
}
for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) {
return err;
}
}
if ((err = mp_init(&b)) != MP_OKAY) {
return err;
}
for (;;) {
step = 0;
do {
y = 0;
step += kstep;
for (x = 1; x < PRIVATE_MP_PRIME_TAB_SIZE; x++) {
res_tab[x] += kstep;
if (res_tab[x] >= s_mp_prime_tab[x]) {
res_tab[x] -= s_mp_prime_tab[x];
}
if (res_tab[x] == 0u) {
y = 1;
}
}
} while ((y == 1) && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep)));
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
goto LBL_ERR;
}
if ((y == 1) && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) {
continue;
}
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto LBL_ERR;
}
if (res == MP_YES) {
break;
}
}
err = MP_OKAY;
LBL_ERR:
mp_clear(&b);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
static const struct {
int k, t;
} sizes[] = {
{ 80, -1 },
{ 81, 37 },
{ 96, 32 },
{ 128, 40 },
{ 160, 35 },
{ 256, 27 },
{ 384, 16 },
{ 512, 18 },
{ 768, 11 },
{ 896, 10 },
{ 1024, 12 },
{ 1536, 8 },
{ 2048, 6 },
{ 3072, 4 },
{ 4096, 5 },
{ 5120, 4 },
{ 6144, 4 },
{ 8192, 3 },
{ 9216, 3 },
{ 10240, 2 }
};
int mp_prime_rabin_miller_trials(int size)
{
int x;
for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
if (sizes[x].k == size) {
return sizes[x].t;
} else if (sizes[x].k > size) {
return (x == 0) ? sizes[0].t : sizes[x - 1].t;
}
}
return sizes[x-1].t;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_RAND_C
*
* Flags are as follows:
*
* MP_PRIME_BBS - make prime congruent to 3 mod 4
* MP_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies MP_PRIME_BBS)
* MP_PRIME_2MSB_ON - make the 2nd highest bit one
*
* You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
* have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
* so it can be NULL
*
*/
mp_err s_mp_prime_random_ex(mp_int *a, int t, int size, int flags, private_mp_prime_callback cb, void *dat)
{
unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
int bsize, maskOR_msb_offset;
mp_bool res;
mp_err err;
if ((size <= 1) || (t <= 0)) {
return MP_VAL;
}
if ((flags & MP_PRIME_SAFE) != 0) {
flags |= MP_PRIME_BBS;
}
bsize = (size>>3) + ((size&7)?1:0);
tmp = (unsigned char *) MP_MALLOC((size_t)bsize);
if (tmp == NULL) {
return MP_MEM;
}
maskAND = ((size&7) == 0) ? 0xFFu : (unsigned char)(0xFFu >> (8 - (size & 7)));
maskOR_msb = 0;
maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
if ((flags & MP_PRIME_2MSB_ON) != 0) {
maskOR_msb |= (unsigned char)(0x80 >> ((9 - size) & 7));
}
maskOR_lsb = 1u;
if ((flags & MP_PRIME_BBS) != 0) {
maskOR_lsb |= 3u;
}
do {
if (cb(tmp, bsize, dat) != bsize) {
err = MP_VAL;
goto error;
}
tmp[0] &= maskAND;
tmp[0] |= (unsigned char)(1 << ((size - 1) & 7));
tmp[maskOR_msb_offset] |= maskOR_msb;
tmp[bsize-1] |= maskOR_lsb;
if ((err = mp_from_ubin(a, tmp, (size_t)bsize)) != MP_OKAY) {
goto error;
}
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto error;
}
if (res == MP_NO) {
continue;
}
if ((flags & MP_PRIME_SAFE) != 0) {
if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
goto error;
}
if ((err = mp_div_2(a, a)) != MP_OKAY) {
goto error;
}
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto error;
}
}
} while (res == MP_NO);
if ((flags & MP_PRIME_SAFE) != 0) {
if ((err = mp_mul_2(a, a)) != MP_OKAY) {
goto error;
}
if ((err = mp_add_d(a, 1uL, a)) != MP_OKAY) {
goto error;
}
}
err = MP_OKAY;
error:
MP_FREE_BUFFER(tmp, (size_t)bsize);
return err;
}
static int s_mp_rand_cb(unsigned char *dst, int len, void *dat)
{
(void)dat;
if (len <= 0) {
return len;
}
if (s_mp_rand_source(dst, (size_t)len) != MP_OKAY) {
return 0;
}
return len;
}
mp_err mp_prime_rand(mp_int *a, int t, int size, int flags)
{
return s_mp_prime_random_ex(a, t, size, flags, s_mp_rand_cb, NULL);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_C
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
*/
#ifndef LTM_USE_ONLY_MR
* 8-bit is just too small. You can try the Frobenius test
* but that frobenius test can fail, too, for the same reason.
*/
#ifndef MP_8BIT
* multiply bigint a with int d and put the result in c
* Like mp_mul_d() but with a signed long as the small input
*/
static mp_err s_mp_mul_si(const mp_int *a, int32_t d, mp_int *c)
{
mp_int t;
mp_err err;
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
* mp_digit might be smaller than a long, which excludes
* the use of mp_mul_d() here.
*/
mp_set_i32(&t, d);
err = mp_mul(a, &t, c);
mp_clear(&t);
return err;
}
Strong Lucas-Selfridge test.
returns MP_YES if it is a strong L-S prime, MP_NO if it is composite
Code ported from Thomas Ray Nicely's implementation of the BPSW test
at http://www.trnicely.net/misc/bpsw.html
Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
Released into the public domain by the author, who disclaims any legal
liability arising from its use
The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
Additional comments marked "CZ" (without the quotes) are by the code-portist.
(If that name sounds familiar, he is the guy who found the fdiv bug in the
Pentium (P5x, I think) Intel processor)
*/
mp_err mp_prime_strong_lucas_selfridge(const mp_int *a, mp_bool *result)
{
mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
mp_err err;
mp_bool oddness;
*result = MP_NO;
Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
indicates that, if N is not a perfect square, D will "nearly
always" be "small." Just in case, an overflow trap for D is
included.
*/
if ((err = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
NULL)) != MP_OKAY) {
return err;
}
D = 5;
sign = 1;
for (;;) {
Ds = sign * D;
sign = -sign;
mp_set_u32(&Dz, (uint32_t)D);
if ((err = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) goto LBL_LS_ERR;
Jacobi(D,N) is technically undefined (but often returned
as zero). */
if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
goto LBL_LS_ERR;
}
if (Ds < 0) {
Dz.sign = MP_NEG;
}
if ((err = mp_kronecker(&Dz, a, &J)) != MP_OKAY) goto LBL_LS_ERR;
if (J == -1) {
break;
}
D += 2;
if (D > (INT_MAX - 2)) {
err = MP_VAL;
goto LBL_LS_ERR;
}
}
P = 1;
Q = (1 - Ds) / 4;
(b) D is square-free or not a perfect square, are included by
some authors; e.g., "Prime numbers and computer methods for
factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
p. 130. For this particular application of Lucas sequences,
these conditions were found to be immaterial. */
odd positive integer d and positive integer s for which
N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
The strong Lucas-Selfridge test then returns N as a strong
Lucas probable prime (slprp) if any of the following
conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
(all equalities mod N). Thus d is the highest index of U that
must be computed (since V_2m is independent of U), compared
to U_{N+1} for the standard Lucas-Selfridge test; and no
index of V beyond (N+1)/2 is required, just as in the
standard Lucas-Selfridge test. However, the quantity Q^d must
be computed for use (if necessary) in the latter stages of
the test. The result is that the strong Lucas-Selfridge test
has a running time only slightly greater (order of 10 %) than
that of the standard Lucas-Selfridge test, while producing
only (roughly) 30 % as many pseudoprimes (and every strong
Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
the evidence indicates that the strong Lucas-Selfridge test is
more effective than the standard Lucas-Selfridge test, and a
Baillie-PSW test based on the strong Lucas-Selfridge test
should be more reliable. */
if ((err = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) goto LBL_LS_ERR;
s = mp_cnt_lsb(&Np1);
* This should round towards zero because
* Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
* and mp_div_2d() is equivalent. Additionally:
* dividing an even number by two does not produce
* any leftovers.
*/
if ((err = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) goto LBL_LS_ERR;
values U and V are initialized to U_1 and V_1 (if the target
index were even, U and V would be initialized instead to U_0=0
and V_0=2). The values of U_2m and V_2m are also initialized to
U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
(1, 2, 3, ...) of t are on (the zero bit having been accounted
for in the initialization of U and V), these values are then
combined with the previous totals for U and V, using the
composition formulas for addition of indices. */
mp_set(&Uz, 1uL);
mp_set(&Vz, (mp_digit)P);
mp_set(&U2mz, 1uL);
mp_set(&V2mz, (mp_digit)P);
mp_set_i32(&Qmz, Q);
if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
mp_set_i32(&Qkdz, Q);
Nbits = mp_count_bits(&Dz);
for (u = 1; u < Nbits; u++) {
* the indices denoted as "2m" are actually powers of 2, specifically
* 2^(ul-1) beginning each loop and 2^ul ending each loop.
*
* U_2m = U_m*V_m
* V_2m = V_m*V_m - 2*Q^m
*/
if ((err = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) goto LBL_LS_ERR;
if (s_mp_get_bit(&Dz, (unsigned int)u) == MP_YES) {
*
* U_(m+n) = (U_m*V_n + U_n*V_m)/2
* V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
*
* Be careful with division by 2 (mod N)!
*/
if ((err = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = s_mp_mul_si(&T4z, Ds, &T4z)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
if (MP_IS_ODD(&Uz)) {
if ((err = mp_add(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
}
* This should round towards negative infinity because
* Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
* But mp_div_2() does not do so, it is truncating instead.
*/
oddness = MP_IS_ODD(&Uz) ? MP_YES : MP_NO;
if ((err = mp_div_2(&Uz, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
if ((err = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
}
if ((err = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if (MP_IS_ODD(&Vz)) {
if ((err = mp_add(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
}
oddness = MP_IS_ODD(&Vz) ? MP_YES : MP_NO;
if ((err = mp_div_2(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
if ((err = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
}
if ((err = mp_mod(&Uz, a, &Uz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
}
}
strong Lucas pseudoprime. */
if (MP_IS_ZERO(&Uz) || MP_IS_ZERO(&Vz)) {
*result = MP_YES;
goto LBL_LS_ERR;
}
1995/6) omits the condition V0 on p.142, but includes it on
p. 130. The condition is NECESSARY; otherwise the test will
return false negatives---e.g., the primes 29 and 2000029 will be
returned as composite. */
by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
these are congruent to 0 mod N, then N is a prime or a strong
Lucas pseudoprime. */
if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
for (r = 1; r < s; r++) {
if ((err = mp_sqr(&Vz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&Vz, a, &Vz)) != MP_OKAY) goto LBL_LS_ERR;
if (MP_IS_ZERO(&Vz)) {
*result = MP_YES;
goto LBL_LS_ERR;
}
if (r < (s - 1)) {
if ((err = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) goto LBL_LS_ERR;
if ((err = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) goto LBL_LS_ERR;
}
}
LBL_LS_ERR:
mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
return err;
}
#endif
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_RADIX_SIZE_C
mp_err mp_radix_size(const mp_int *a, int radix, int *size)
{
mp_err err;
int digs;
mp_int t;
mp_digit d;
*size = 0;
if ((radix < 2) || (radix > 64)) {
return MP_VAL;
}
if (MP_IS_ZERO(a)) {
*size = 2;
return MP_OKAY;
}
if (radix == 2) {
*size = (mp_count_bits(a) + ((a->sign == MP_NEG) ? 1 : 0) + 1);
return MP_OKAY;
}
digs = 0;
if (a->sign == MP_NEG) {
++digs;
}
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
return err;
}
t.sign = MP_ZPOS;
while (!MP_IS_ZERO(&t)) {
if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) {
goto LBL_ERR;
}
++digs;
}
*size = digs + 1;
err = MP_OKAY;
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_RADIX_SMAP_C
const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
const uint8_t mp_s_rmap_reverse[] = {
0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f,
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10,
0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a,
0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32,
0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a,
0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff,
};
const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse);
#endif
#include "tommath_private.h"
#ifdef BN_MP_RAND_C
mp_err(*s_mp_rand_source)(void *out, size_t size) = s_mp_rand_platform;
void mp_rand_source(mp_err(*source)(void *out, size_t size))
{
s_mp_rand_source = (source == NULL) ? s_mp_rand_platform : source;
}
mp_err mp_rand(mp_int *a, int digits)
{
int i;
mp_err err;
mp_zero(a);
if (digits <= 0) {
return MP_OKAY;
}
if ((err = mp_grow(a, digits)) != MP_OKAY) {
return err;
}
if ((err = s_mp_rand_source(a->dp, (size_t)digits * sizeof(mp_digit))) != MP_OKAY) {
return err;
}
while ((a->dp[digits - 1] & MP_MASK) == 0u) {
if ((err = s_mp_rand_source(a->dp + digits - 1, sizeof(mp_digit))) != MP_OKAY) {
return err;
}
}
a->used = digits;
for (i = 0; i < digits; ++i) {
a->dp[i] &= MP_MASK;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_READ_RADIX_C
#define MP_TOUPPER(c) ((((c) >= 'a') && ((c) <= 'z')) ? (((c) + 'A') - 'a') : (c))
mp_err mp_read_radix(mp_int *a, const char *str, int radix)
{
mp_err err;
int y;
mp_sign neg;
unsigned pos;
char ch;
mp_zero(a);
if ((radix < 2) || (radix > 64)) {
return MP_VAL;
}
* minus set the sign to negative.
*/
if (*str == '-') {
++str;
neg = MP_NEG;
} else {
neg = MP_ZPOS;
}
mp_zero(a);
while (*str != '\0') {
* this allows numbers like 1AB and 1ab to represent the same value
* [e.g. in hex]
*/
ch = (radix <= 36) ? (char)MP_TOUPPER((int)*str) : *str;
pos = (unsigned)(ch - '(');
if (mp_s_rmap_reverse_sz < pos) {
break;
}
y = (int)mp_s_rmap_reverse[pos];
* and is less than the given radix add it
* to the number, otherwise exit the loop.
*/
if ((y == 0xff) || (y >= radix)) {
break;
}
if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) {
return err;
}
++str;
}
if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) {
mp_zero(a);
return MP_VAL;
}
if (!MP_IS_ZERO(a)) {
a->sign = neg;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_C
* precomputed via mp_reduce_setup.
* From HAC pp.604 Algorithm 14.42
*/
mp_err mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)
{
mp_int q;
mp_err err;
int um = m->used;
if ((err = mp_init_copy(&q, x)) != MP_OKAY) {
return err;
}
mp_rshd(&q, um - 1);
if ((mp_digit)um > ((mp_digit)1 << (MP_DIGIT_BIT - 1))) {
if ((err = mp_mul(&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
} else if (MP_HAS(S_MP_MUL_HIGH_DIGS)) {
if ((err = s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
} else if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)) {
if ((err = s_mp_mul_high_digs_fast(&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
} else {
err = MP_VAL;
goto CLEANUP;
}
mp_rshd(&q, um + 1);
if ((err = mp_mod_2d(x, MP_DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
goto CLEANUP;
}
if ((err = s_mp_mul_digs(&q, m, &q, um + 1)) != MP_OKAY) {
goto CLEANUP;
}
if ((err = mp_sub(x, &q, x)) != MP_OKAY) {
goto CLEANUP;
}
if (mp_cmp_d(x, 0uL) == MP_LT) {
mp_set(&q, 1uL);
if ((err = mp_lshd(&q, um + 1)) != MP_OKAY) {
goto CLEANUP;
}
if ((err = mp_add(x, &q, x)) != MP_OKAY) {
goto CLEANUP;
}
}
while (mp_cmp(x, m) != MP_LT) {
if ((err = s_mp_sub(x, m, x)) != MP_OKAY) {
goto CLEANUP;
}
}
CLEANUP:
mp_clear(&q);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_2K_C
mp_err mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
{
mp_int q;
mp_err err;
int p;
if ((err = mp_init(&q)) != MP_OKAY) {
return err;
}
p = mp_count_bits(n);
top:
if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
if (d != 1u) {
if ((err = mp_mul_d(&q, d, &q)) != MP_OKAY) {
goto LBL_ERR;
}
}
if ((err = s_mp_add(a, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
if ((err = s_mp_sub(a, n, a)) != MP_OKAY) {
goto LBL_ERR;
}
goto top;
}
LBL_ERR:
mp_clear(&q);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_2K_L_C
This differs from reduce_2k since "d" can be larger
than a single digit.
*/
mp_err mp_reduce_2k_l(mp_int *a, const mp_int *n, const mp_int *d)
{
mp_int q;
mp_err err;
int p;
if ((err = mp_init(&q)) != MP_OKAY) {
return err;
}
p = mp_count_bits(n);
top:
if ((err = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_mul(&q, d, &q)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = s_mp_add(a, &q, a)) != MP_OKAY) {
goto LBL_ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
if ((err = s_mp_sub(a, n, a)) != MP_OKAY) {
goto LBL_ERR;
}
goto top;
}
LBL_ERR:
mp_clear(&q);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_2K_SETUP_C
mp_err mp_reduce_2k_setup(const mp_int *a, mp_digit *d)
{
mp_err err;
mp_int tmp;
int p;
if ((err = mp_init(&tmp)) != MP_OKAY) {
return err;
}
p = mp_count_bits(a);
if ((err = mp_2expt(&tmp, p)) != MP_OKAY) {
mp_clear(&tmp);
return err;
}
if ((err = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
mp_clear(&tmp);
return err;
}
*d = tmp.dp[0];
mp_clear(&tmp);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_2K_SETUP_L_C
mp_err mp_reduce_2k_setup_l(const mp_int *a, mp_int *d)
{
mp_err err;
mp_int tmp;
if ((err = mp_init(&tmp)) != MP_OKAY) {
return err;
}
if ((err = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
goto LBL_ERR;
}
LBL_ERR:
mp_clear(&tmp);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_IS_2K_C
mp_bool mp_reduce_is_2k(const mp_int *a)
{
int ix, iy, iw;
mp_digit iz;
if (a->used == 0) {
return MP_NO;
} else if (a->used == 1) {
return MP_YES;
} else if (a->used > 1) {
iy = mp_count_bits(a);
iz = 1;
iw = 1;
for (ix = MP_DIGIT_BIT; ix < iy; ix++) {
if ((a->dp[iw] & iz) == 0u) {
return MP_NO;
}
iz <<= 1;
if (iz > MP_DIGIT_MAX) {
++iw;
iz = 1;
}
}
return MP_YES;
} else {
return MP_YES;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_IS_2K_L_C
mp_bool mp_reduce_is_2k_l(const mp_int *a)
{
int ix, iy;
if (a->used == 0) {
return MP_NO;
} else if (a->used == 1) {
return MP_YES;
} else if (a->used > 1) {
for (iy = ix = 0; ix < a->used; ix++) {
if (a->dp[ix] == MP_DIGIT_MAX) {
++iy;
}
}
return (iy >= (a->used/2)) ? MP_YES : MP_NO;
} else {
return MP_NO;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_SETUP_C
* For a given modulus "b" it calulates the value required in "a"
*/
mp_err mp_reduce_setup(mp_int *a, const mp_int *b)
{
mp_err err;
if ((err = mp_2expt(a, b->used * 2 * MP_DIGIT_BIT)) != MP_OKAY) {
return err;
}
return mp_div(a, b, a, NULL);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ROOT_U32_C
*
* Result found such that (c)**b <= a and (c+1)**b > a
*
* This algorithm uses Newton's approximation
* x[i+1] = x[i] - f(x[i])/f'(x[i])
* which will find the root in log(N) time where
* each step involves a fair bit.
*/
mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c)
{
mp_int t1, t2, t3, a_;
mp_ord cmp;
int ilog2;
mp_err err;
if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
return MP_VAL;
}
if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) {
return err;
}
a_ = *a;
a_.sign = MP_ZPOS;
ilog2 = mp_count_bits(a);
If "b" is larger than INT_MAX it is also larger than
log_2(n) because the bit-length of the "n" is measured
with an int and hence the root is always < 2 (two).
*/
if (b > (uint32_t)(INT_MAX/2)) {
mp_set(c, 1uL);
c->sign = a->sign;
err = MP_OKAY;
goto LBL_ERR;
}
if (ilog2 < (int)b) {
mp_set(c, 1uL);
c->sign = a->sign;
err = MP_OKAY;
goto LBL_ERR;
}
ilog2 = ilog2 / ((int)b);
if (ilog2 == 0) {
mp_set(c, 1uL);
c->sign = a->sign;
err = MP_OKAY;
goto LBL_ERR;
}
ilog2 += 2;
if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR;
do {
if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR;
Number of rounds is at most log_2(root). If it is more it
got stuck, so break out of the loop and do the rest manually.
*/
if (ilog2-- == 0) {
break;
}
} while (mp_cmp(&t1, &t2) != MP_EQ);
for (;;) {
if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
cmp = mp_cmp(&t2, &a_);
if (cmp == MP_EQ) {
err = MP_OKAY;
goto LBL_ERR;
}
if (cmp == MP_LT) {
if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
} else {
break;
}
}
for (;;) {
if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR;
if (mp_cmp(&t2, &a_) == MP_GT) {
if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR;
} else {
break;
}
}
mp_exch(&t1, c);
c->sign = a->sign;
err = MP_OKAY;
LBL_ERR:
mp_clear_multi(&t1, &t2, &t3, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_RSHD_C
void mp_rshd(mp_int *a, int b)
{
int x;
mp_digit *bottom, *top;
if (b <= 0) {
return;
}
if (a->used <= b) {
mp_zero(a);
return;
}
bottom = a->dp;
top = a->dp + b;
* the window is b-digits long and digits from
* the top of the window are copied to the bottom
*
* e.g.
b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
/\ | ---->
\-------------------/ ---->
*/
for (x = 0; x < (a->used - b); x++) {
*bottom++ = *top++;
}
MP_ZERO_DIGITS(bottom, a->used - x);
a->used -= b;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SBIN_SIZE_C
size_t mp_sbin_size(const mp_int *a)
{
return 1u + mp_ubin_size(a);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_C
void mp_set(mp_int *a, mp_digit b)
{
a->dp[0] = b & MP_MASK;
a->sign = MP_ZPOS;
a->used = (a->dp[0] != 0u) ? 1 : 0;
MP_ZERO_DIGITS(a->dp + a->used, a->alloc - a->used);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_DOUBLE_C
#if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559)
mp_err mp_set_double(mp_int *a, double b)
{
uint64_t frac;
int exp;
mp_err err;
union {
double dbl;
uint64_t bits;
} cast;
cast.dbl = b;
exp = (int)((unsigned)(cast.bits >> 52) & 0x7FFu);
frac = (cast.bits & ((1uLL << 52) - 1uLL)) | (1uLL << 52);
if (exp == 0x7FF) {
return MP_VAL;
}
exp -= 1023 + 52;
mp_set_u64(a, frac);
err = (exp < 0) ? mp_div_2d(a, -exp, a, NULL) : mp_mul_2d(a, exp, a);
if (err != MP_OKAY) {
return err;
}
if (((cast.bits >> 63) != 0uLL) && !MP_IS_ZERO(a)) {
a->sign = MP_NEG;
}
return MP_OKAY;
}
#else
# ifdef _MSC_VER
# pragma message("mp_set_double implementation is only available on platforms with IEEE754 floating point format")
# else
# warning "mp_set_double implementation is only available on platforms with IEEE754 floating point format"
# endif
#endif
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_I32_C
MP_SET_SIGNED(mp_set_i32, mp_set_u32, int32_t, uint32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_I64_C
MP_SET_SIGNED(mp_set_i64, mp_set_u64, int64_t, uint64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_L_C
MP_SET_SIGNED(mp_set_l, mp_set_ul, long, unsigned long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_LL_C
MP_SET_SIGNED(mp_set_ll, mp_set_ull, long long, unsigned long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_U32_C
MP_SET_UNSIGNED(mp_set_u32, uint32_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_U64_C
MP_SET_UNSIGNED(mp_set_u64, uint64_t)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_UL_C
MP_SET_UNSIGNED(mp_set_ul, unsigned long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SET_ULL_C
MP_SET_UNSIGNED(mp_set_ull, unsigned long long)
#endif
#include "tommath_private.h"
#ifdef BN_MP_SHRINK_C
mp_err mp_shrink(mp_int *a)
{
mp_digit *tmp;
int alloc = MP_MAX(MP_MIN_PREC, a->used);
if (a->alloc != alloc) {
if ((tmp = (mp_digit *) MP_REALLOC(a->dp,
(size_t)a->alloc * sizeof(mp_digit),
(size_t)alloc * sizeof(mp_digit))) == NULL) {
return MP_MEM;
}
a->dp = tmp;
a->alloc = alloc;
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SIGNED_RSH_C
mp_err mp_signed_rsh(const mp_int *a, int b, mp_int *c)
{
mp_err res;
if (a->sign == MP_ZPOS) {
return mp_div_2d(a, b, c, NULL);
}
res = mp_add_d(a, 1uL, c);
if (res != MP_OKAY) {
return res;
}
res = mp_div_2d(c, b, c, NULL);
return (res == MP_OKAY) ? mp_sub_d(c, 1uL, c) : res;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SQR_C
mp_err mp_sqr(const mp_int *a, mp_int *b)
{
mp_err err;
if (MP_HAS(S_MP_TOOM_SQR) &&
(a->used >= MP_TOOM_SQR_CUTOFF)) {
err = s_mp_toom_sqr(a, b);
} else if (MP_HAS(S_MP_KARATSUBA_SQR) &&
(a->used >= MP_KARATSUBA_SQR_CUTOFF)) {
err = s_mp_karatsuba_sqr(a, b);
} else if (MP_HAS(S_MP_SQR_FAST) &&
(((a->used * 2) + 1) < MP_WARRAY) &&
(a->used < (MP_MAXFAST / 2))) {
err = s_mp_sqr_fast(a, b);
} else if (MP_HAS(S_MP_SQR)) {
err = s_mp_sqr(a, b);
} else {
err = MP_VAL;
}
b->sign = MP_ZPOS;
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SQRMOD_C
mp_err mp_sqrmod(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_err err;
mp_int t;
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
if ((err = mp_sqr(a, &t)) != MP_OKAY) {
goto LBL_ERR;
}
err = mp_mod(&t, b, c);
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SQRT_C
mp_err mp_sqrt(const mp_int *arg, mp_int *ret)
{
mp_err err;
mp_int t1, t2;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
if (MP_IS_ZERO(arg)) {
mp_zero(ret);
return MP_OKAY;
}
if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) {
return err;
}
if ((err = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
mp_rshd(&t1, t1.used/2);
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
do {
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
mp_exch(&t1, ret);
E1:
mp_clear(&t2);
E2:
mp_clear(&t1);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SQRTMOD_PRIME_C
* https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
* https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
*
*/
mp_err mp_sqrtmod_prime(const mp_int *n, const mp_int *prime, mp_int *ret)
{
mp_err err;
int legendre;
mp_int t1, C, Q, S, Z, M, T, R, two;
mp_digit i;
if (mp_cmp_d(n, 0uL) == MP_EQ) {
mp_zero(ret);
return MP_OKAY;
}
if (mp_cmp_d(prime, 2uL) == MP_EQ) return MP_VAL;
if ((err = mp_kronecker(n, prime, &legendre)) != MP_OKAY) return err;
if (legendre == -1) return MP_VAL;
if ((err = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
return err;
}
* compute directly: err = n^(prime+1)/4 mod prime
* Handbook of Applied Cryptography algorithm 3.36
*/
if ((err = mp_mod_d(prime, 4uL, &i)) != MP_OKAY) goto cleanup;
if (i == 3u) {
if ((err = mp_add_d(prime, 1uL, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY) goto cleanup;
err = MP_OKAY;
goto cleanup;
}
if ((err = mp_copy(prime, &Q)) != MP_OKAY) goto cleanup;
if ((err = mp_sub_d(&Q, 1uL, &Q)) != MP_OKAY) goto cleanup;
mp_zero(&S);
while (MP_IS_EVEN(&Q)) {
if ((err = mp_div_2(&Q, &Q)) != MP_OKAY) goto cleanup;
if ((err = mp_add_d(&S, 1uL, &S)) != MP_OKAY) goto cleanup;
}
mp_set_u32(&Z, 2u);
for (;;) {
if ((err = mp_kronecker(&Z, prime, &legendre)) != MP_OKAY) goto cleanup;
if (legendre == -1) break;
if ((err = mp_add_d(&Z, 1uL, &Z)) != MP_OKAY) goto cleanup;
}
if ((err = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY) goto cleanup;
if ((err = mp_add_d(&Q, 1uL, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY) goto cleanup;
if ((err = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY) goto cleanup;
if ((err = mp_copy(&S, &M)) != MP_OKAY) goto cleanup;
mp_set_u32(&two, 2u);
for (;;) {
if ((err = mp_copy(&T, &t1)) != MP_OKAY) goto cleanup;
i = 0;
for (;;) {
if (mp_cmp_d(&t1, 1uL) == MP_EQ) break;
if ((err = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
i++;
}
if (i == 0u) {
if ((err = mp_copy(&R, ret)) != MP_OKAY) goto cleanup;
err = MP_OKAY;
goto cleanup;
}
if ((err = mp_sub_d(&M, i, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY) goto cleanup;
if ((err = mp_sqrmod(&t1, prime, &C)) != MP_OKAY) goto cleanup;
if ((err = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY) goto cleanup;
if ((err = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY) goto cleanup;
mp_set(&M, i);
}
cleanup:
mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SUB_C
mp_err mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_sign sa = a->sign, sb = b->sign;
mp_err err;
if (sa != sb) {
c->sign = sa;
err = s_mp_add(a, b, c);
} else {
if (mp_cmp_mag(a, b) != MP_LT) {
c->sign = sa;
err = s_mp_sub(a, b, c);
} else {
c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
err = s_mp_sub(b, a, c);
}
}
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SUB_D_C
mp_err mp_sub_d(const mp_int *a, mp_digit b, mp_int *c)
{
mp_digit *tmpa, *tmpc;
mp_err err;
int ix, oldused;
if (c->alloc < (a->used + 1)) {
if ((err = mp_grow(c, a->used + 1)) != MP_OKAY) {
return err;
}
}
* addition [with fudged signs]
*/
if (a->sign == MP_NEG) {
mp_int a_ = *a;
a_.sign = MP_ZPOS;
err = mp_add_d(&a_, b, c);
c->sign = MP_NEG;
mp_clamp(c);
return err;
}
oldused = c->used;
tmpa = a->dp;
tmpc = c->dp;
if (((a->used == 1) && (a->dp[0] <= b)) || (a->used == 0)) {
if (a->used == 1) {
*tmpc++ = b - *tmpa;
} else {
*tmpc++ = b;
}
ix = 1;
c->sign = MP_NEG;
c->used = 1;
} else {
mp_digit mu = b;
c->sign = MP_ZPOS;
c->used = a->used;
for (ix = 0; ix < a->used; ix++) {
*tmpc = *tmpa++ - mu;
mu = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u);
*tmpc++ &= MP_MASK;
}
}
MP_ZERO_DIGITS(tmpc, oldused - ix);
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_SUBMOD_C
mp_err mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
mp_err err;
mp_int t;
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
if ((err = mp_sub(a, b, &t)) != MP_OKAY) {
goto LBL_ERR;
}
err = mp_mod(&t, c, d);
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_TO_RADIX_C
*
* Stores upto "size - 1" chars and always a NULL byte, puts the number of characters
* written, including the '\0', in "written".
*/
mp_err mp_to_radix(const mp_int *a, char *str, size_t maxlen, size_t *written, int radix)
{
size_t digs;
mp_err err;
mp_int t;
mp_digit d;
char *_s = str;
if (maxlen < 2u) {
return MP_BUF;
}
if ((radix < 2) || (radix > 64)) {
return MP_VAL;
}
if (MP_IS_ZERO(a)) {
*str++ = '0';
*str = '\0';
if (written != NULL) {
*written = 2u;
}
return MP_OKAY;
}
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
return err;
}
if (t.sign == MP_NEG) {
++_s;
*str++ = '-';
t.sign = MP_ZPOS;
--maxlen;
}
digs = 0u;
while (!MP_IS_ZERO(&t)) {
if (--maxlen < 1u) {
err = MP_BUF;
goto LBL_ERR;
}
if ((err = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) {
goto LBL_ERR;
}
*str++ = mp_s_rmap[d];
++digs;
}
* to the first digit [exluding the sign] of the number
*/
s_mp_reverse((unsigned char *)_s, digs);
*str = '\0';
digs++;
if (written != NULL) {
*written = (a->sign == MP_NEG) ? (digs + 1u): digs;
}
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_TO_SBIN_C
mp_err mp_to_sbin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written)
{
mp_err err;
if (maxlen == 0u) {
return MP_BUF;
}
if ((err = mp_to_ubin(a, buf + 1, maxlen - 1u, written)) != MP_OKAY) {
return err;
}
if (written != NULL) {
(*written)++;
}
buf[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_TO_UBIN_C
mp_err mp_to_ubin(const mp_int *a, unsigned char *buf, size_t maxlen, size_t *written)
{
size_t x, count;
mp_err err;
mp_int t;
count = mp_ubin_size(a);
if (count > maxlen) {
return MP_BUF;
}
if ((err = mp_init_copy(&t, a)) != MP_OKAY) {
return err;
}
for (x = count; x --> 0u;) {
#ifndef MP_8BIT
buf[x] = (unsigned char)(t.dp[0] & 255u);
#else
buf[x] = (unsigned char)(t.dp[0] | ((t.dp[1] & 1u) << 7));
#endif
if ((err = mp_div_2d(&t, 8, &t, NULL)) != MP_OKAY) {
goto LBL_ERR;
}
}
if (written != NULL) {
*written = count;
}
LBL_ERR:
mp_clear(&t);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_UBIN_SIZE_C
size_t mp_ubin_size(const mp_int *a)
{
size_t size = (size_t)mp_count_bits(a);
return (size / 8u) + (((size & 7u) != 0u) ? 1u : 0u);
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_UNPACK_C
* see http://gmplib.org/manual/Integer-Import-and-Export.html
*/
mp_err mp_unpack(mp_int *rop, size_t count, mp_order order, size_t size,
mp_endian endian, size_t nails, const void *op)
{
mp_err err;
size_t odd_nails, nail_bytes, i, j;
unsigned char odd_nail_mask;
mp_zero(rop);
if (endian == MP_NATIVE_ENDIAN) {
MP_GET_ENDIANNESS(endian);
}
odd_nails = (nails % 8u);
odd_nail_mask = 0xff;
for (i = 0; i < odd_nails; ++i) {
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
}
nail_bytes = nails / 8u;
for (i = 0; i < count; ++i) {
for (j = 0; j < (size - nail_bytes); ++j) {
unsigned char byte = *((const unsigned char *)op +
(((order == MP_MSB_FIRST) ? i : ((count - 1u) - i)) * size) +
((endian == MP_BIG_ENDIAN) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes)));
if ((err = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) {
return err;
}
rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte;
rop->used += 1;
}
}
mp_clamp(rop);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_XOR_C
mp_err mp_xor(const mp_int *a, const mp_int *b, mp_int *c)
{
int used = MP_MAX(a->used, b->used) + 1, i;
mp_err err;
mp_digit ac = 1, bc = 1, cc = 1;
mp_sign csign = (a->sign != b->sign) ? MP_NEG : MP_ZPOS;
if (c->alloc < used) {
if ((err = mp_grow(c, used)) != MP_OKAY) {
return err;
}
}
for (i = 0; i < used; i++) {
mp_digit x, y;
if (a->sign == MP_NEG) {
ac += (i >= a->used) ? MP_MASK : (~a->dp[i] & MP_MASK);
x = ac & MP_MASK;
ac >>= MP_DIGIT_BIT;
} else {
x = (i >= a->used) ? 0uL : a->dp[i];
}
if (b->sign == MP_NEG) {
bc += (i >= b->used) ? MP_MASK : (~b->dp[i] & MP_MASK);
y = bc & MP_MASK;
bc >>= MP_DIGIT_BIT;
} else {
y = (i >= b->used) ? 0uL : b->dp[i];
}
c->dp[i] = x ^ y;
if (csign == MP_NEG) {
cc += ~c->dp[i] & MP_MASK;
c->dp[i] = cc & MP_MASK;
cc >>= MP_DIGIT_BIT;
}
}
c->used = used;
c->sign = csign;
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_MP_ZERO_C
void mp_zero(mp_int *a)
{
a->sign = MP_ZPOS;
a->used = 0;
MP_ZERO_DIGITS(a->dp, a->alloc);
}
#endif
#include "tommath_private.h"
#ifdef BN_PRIME_TAB_C
const mp_digit ltm_prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
#ifndef MP_8BIT
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
#endif
};
#if defined(__GNUC__) && __GNUC__ >= 4
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
#pragma GCC diagnostic pop
#elif defined(_MSC_VER) && _MSC_VER >= 1500
#pragma warning(push)
#pragma warning(disable: 4996)
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
#pragma warning(pop)
#else
const mp_digit *s_mp_prime_tab = ltm_prime_tab;
#endif
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_ADD_C
mp_err s_mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
const mp_int *x;
mp_err err;
int olduse, min, max;
* them. "x" will point to the input with the most digits
*/
if (a->used > b->used) {
min = b->used;
max = a->used;
x = a;
} else {
min = a->used;
max = b->used;
x = b;
}
if (c->alloc < (max + 1)) {
if ((err = mp_grow(c, max + 1)) != MP_OKAY) {
return err;
}
}
olduse = c->used;
c->used = max + 1;
{
mp_digit u, *tmpa, *tmpb, *tmpc;
int i;
tmpa = a->dp;
tmpb = b->dp;
tmpc = c->dp;
u = 0;
for (i = 0; i < min; i++) {
*tmpc = *tmpa++ + *tmpb++ + u;
u = *tmpc >> (mp_digit)MP_DIGIT_BIT;
*tmpc++ &= MP_MASK;
}
* if A or B has more digits add those in
*/
if (min != max) {
for (; i < max; i++) {
*tmpc = x->dp[i] + u;
u = *tmpc >> (mp_digit)MP_DIGIT_BIT;
*tmpc++ &= MP_MASK;
}
}
*tmpc++ = u;
MP_ZERO_DIGITS(tmpc, olduse - c->used);
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_BALANCE_MUL_C
mp_err s_mp_balance_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
int count, len_a, len_b, nblocks, i, j, bsize;
mp_int a0, tmp, A, B, r;
mp_err err;
len_a = a->used;
len_b = b->used;
nblocks = MP_MAX(a->used, b->used) / MP_MIN(a->used, b->used);
bsize = MP_MIN(a->used, b->used) ;
if ((err = mp_init_size(&a0, bsize + 2)) != MP_OKAY) {
return err;
}
if ((err = mp_init_multi(&tmp, &r, NULL)) != MP_OKAY) {
mp_clear(&a0);
return err;
}
if (len_a < len_b) {
B = *a;
A = *b;
} else {
A = *a;
B = *b;
}
for (i = 0, j=0; i < nblocks; i++) {
a0.used = 0;
for (count = 0; count < bsize; count++) {
a0.dp[count] = A.dp[ j++ ];
a0.used++;
}
mp_clamp(&a0);
if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) {
goto LBL_ERR;
}
}
if (j < A.used) {
a0.used = 0;
for (count = 0; j < A.used; count++) {
a0.dp[count] = A.dp[ j++ ];
a0.used++;
}
mp_clamp(&a0);
if ((err = mp_mul(&a0, &B, &tmp)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_lshd(&tmp, bsize * i)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_add(&r, &tmp, &r)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_exch(&r,c);
LBL_ERR:
mp_clear_multi(&a0, &tmp, &r,NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_EXPTMOD_C
#ifdef MP_LOW_MEM
# define TAB_SIZE 32
# define MAX_WINSIZE 5
#else
# define TAB_SIZE 256
# define MAX_WINSIZE 0
#endif
mp_err s_mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
{
mp_int M[TAB_SIZE], res, mu;
mp_digit buf;
mp_err err;
int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
mp_err(*redux)(mp_int *x, const mp_int *m, const mp_int *mu);
x = mp_count_bits(X);
if (x <= 7) {
winsize = 2;
} else if (x <= 36) {
winsize = 3;
} else if (x <= 140) {
winsize = 4;
} else if (x <= 450) {
winsize = 5;
} else if (x <= 1303) {
winsize = 6;
} else if (x <= 3529) {
winsize = 7;
} else {
winsize = 8;
}
winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize;
if ((err = mp_init(&M[1])) != MP_OKAY) {
return err;
}
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
if ((err = mp_init(&M[x])) != MP_OKAY) {
for (y = 1<<(winsize-1); y < x; y++) {
mp_clear(&M[y]);
}
mp_clear(&M[1]);
return err;
}
}
if ((err = mp_init(&mu)) != MP_OKAY) goto LBL_M;
if (redmode == 0) {
if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) goto LBL_MU;
redux = mp_reduce;
} else {
if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) goto LBL_MU;
redux = mp_reduce_2k_l;
}
*
* The M table contains powers of the base,
* e.g. M[x] = G**x mod P
*
* The first half of the table is not
* computed though accept for M[0] and M[1]
*/
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_MU;
* M[1] (winsize-1) times
*/
if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU;
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)],
&M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_MU;
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, &mu)) != MP_OKAY) goto LBL_MU;
}
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
*/
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_MU;
if ((err = redux(&M[x], P, &mu)) != MP_OKAY) goto LBL_MU;
}
if ((err = mp_init(&res)) != MP_OKAY) goto LBL_MU;
mp_set(&res, 1uL);
mode = 0;
bitcnt = 1;
buf = 0;
digidx = X->used - 1;
bitcpy = 0;
bitbuf = 0;
for (;;) {
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = X->dp[digidx--];
bitcnt = (int)MP_DIGIT_BIT;
}
y = (buf >> (mp_digit)(MP_DIGIT_BIT - 1)) & 1uL;
buf <<= (mp_digit)1;
* 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 ((mode == 1) && (y == 0)) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
continue;
}
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
if (bitcpy == winsize) {
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
}
if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
bitcpy = 0;
bitbuf = 0;
mode = 1;
}
}
if ((mode == 2) && (bitcpy > 0)) {
for (x = 0; x < bitcpy; x++) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, &mu)) != MP_OKAY) goto LBL_RES;
}
}
}
mp_exch(&res, Y);
err = MP_OKAY;
LBL_RES:
mp_clear(&res);
LBL_MU:
mp_clear(&mu);
LBL_M:
mp_clear(&M[1]);
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear(&M[x]);
}
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_EXPTMOD_FAST_C
*
* Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
* The value of k changes based on the size of the exponent.
*
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
*/
#ifdef MP_LOW_MEM
# define TAB_SIZE 32
# define MAX_WINSIZE 5
#else
# define TAB_SIZE 256
# define MAX_WINSIZE 0
#endif
mp_err s_mp_exptmod_fast(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y, int redmode)
{
mp_int M[TAB_SIZE], res;
mp_digit buf, mp;
int bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
mp_err err;
* one of many reduction algorithms without modding the guts of
* the code with if statements everywhere.
*/
mp_err(*redux)(mp_int *x, const mp_int *n, mp_digit rho);
x = mp_count_bits(X);
if (x <= 7) {
winsize = 2;
} else if (x <= 36) {
winsize = 3;
} else if (x <= 140) {
winsize = 4;
} else if (x <= 450) {
winsize = 5;
} else if (x <= 1303) {
winsize = 6;
} else if (x <= 3529) {
winsize = 7;
} else {
winsize = 8;
}
winsize = MAX_WINSIZE ? MP_MIN(MAX_WINSIZE, winsize) : winsize;
if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
return err;
}
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
for (y = 1<<(winsize-1); y < x; y++) {
mp_clear(&M[y]);
}
mp_clear(&M[1]);
return err;
}
}
if (redmode == 0) {
if (MP_HAS(MP_MONTGOMERY_SETUP)) {
if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) goto LBL_M;
} else {
err = MP_VAL;
goto LBL_M;
}
if (MP_HAS(S_MP_MONTGOMERY_REDUCE_FAST) &&
(((P->used * 2) + 1) < MP_WARRAY) &&
(P->used < MP_MAXFAST)) {
redux = s_mp_montgomery_reduce_fast;
} else if (MP_HAS(MP_MONTGOMERY_REDUCE)) {
redux = mp_montgomery_reduce;
} else {
err = MP_VAL;
goto LBL_M;
}
} else if (redmode == 1) {
if (MP_HAS(MP_DR_SETUP) && MP_HAS(MP_DR_REDUCE)) {
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
} else {
err = MP_VAL;
goto LBL_M;
}
} else if (MP_HAS(MP_REDUCE_2K_SETUP) && MP_HAS(MP_REDUCE_2K)) {
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) goto LBL_M;
redux = mp_reduce_2k;
} else {
err = MP_VAL;
goto LBL_M;
}
if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) goto LBL_M;
*
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
if (MP_HAS(MP_MONTGOMERY_CALC_NORMALIZATION)) {
if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) goto LBL_RES;
if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) goto LBL_RES;
} else {
err = MP_VAL;
goto LBL_RES;
}
} else {
mp_set(&res, 1uL);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) goto LBL_RES;
}
if ((err = mp_copy(&M[1], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES;
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) goto LBL_RES;
if ((err = redux(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) goto LBL_RES;
}
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
if ((err = mp_mul(&M[x - 1], &M[1], &M[x])) != MP_OKAY) goto LBL_RES;
if ((err = redux(&M[x], P, mp)) != MP_OKAY) goto LBL_RES;
}
mode = 0;
bitcnt = 1;
buf = 0;
digidx = X->used - 1;
bitcpy = 0;
bitbuf = 0;
for (;;) {
if (--bitcnt == 0) {
if (digidx == -1) {
break;
}
buf = X->dp[digidx--];
bitcnt = (int)MP_DIGIT_BIT;
}
y = (mp_digit)(buf >> (MP_DIGIT_BIT - 1)) & 1uL;
buf <<= (mp_digit)1;
* 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 ((mode == 1) && (y == 0)) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
continue;
}
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
if (bitcpy == winsize) {
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
}
if ((err = mp_mul(&res, &M[bitbuf], &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
bitcpy = 0;
bitbuf = 0;
mode = 1;
}
}
if ((mode == 2) && (bitcpy > 0)) {
for (x = 0; x < bitcpy; x++) {
if ((err = mp_sqr(&res, &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
if ((err = mp_mul(&res, &M[1], &res)) != MP_OKAY) goto LBL_RES;
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
}
}
}
if (redmode == 0) {
* recall that any value in a Montgomery system is
* actually multiplied by R mod n. So we have
* to reduce one more time to cancel out the factor
* of R.
*/
if ((err = redux(&res, P, mp)) != MP_OKAY) goto LBL_RES;
}
mp_exch(&res, Y);
err = MP_OKAY;
LBL_RES:
mp_clear(&res);
LBL_M:
mp_clear(&M[1]);
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear(&M[x]);
}
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_GET_BIT_C
mp_bool s_mp_get_bit(const mp_int *a, unsigned int b)
{
mp_digit bit;
int limb = (int)(b / MP_DIGIT_BIT);
if (limb >= a->used) {
return MP_NO;
}
bit = (mp_digit)1 << (b % MP_DIGIT_BIT);
return ((a->dp[limb] & bit) != 0u) ? MP_YES : MP_NO;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_INVMOD_FAST_C
* that is c = 1/a mod b
*
* Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
mp_err s_mp_invmod_fast(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x, y, u, v, B, D;
mp_sign neg;
mp_err err;
if (MP_IS_EVEN(b)) {
return MP_VAL;
}
if ((err = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return err;
}
if ((err = mp_copy(b, &x)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mod(a, b, &y)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_ZERO(&x) || MP_IS_ZERO(&y)) {
err = MP_VAL;
goto LBL_ERR;
}
if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR;
mp_set(&D, 1uL);
top:
while (MP_IS_EVEN(&u)) {
if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_ODD(&B)) {
if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR;
}
while (MP_IS_EVEN(&v)) {
if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_ODD(&D)) {
if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR;
}
if (mp_cmp(&u, &v) != MP_LT) {
if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR;
} else {
if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR;
}
if (!MP_IS_ZERO(&u)) {
goto top;
}
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
err = MP_VAL;
goto LBL_ERR;
}
neg = a->sign;
while (D.sign == MP_NEG) {
if ((err = mp_add(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
}
while (mp_cmp_mag(&D, b) != MP_LT) {
if ((err = mp_sub(&D, b, &D)) != MP_OKAY) goto LBL_ERR;
}
mp_exch(&D, c);
c->sign = neg;
err = MP_OKAY;
LBL_ERR:
mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_INVMOD_SLOW_C
mp_err s_mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x, y, u, v, A, B, C, D;
mp_err err;
if ((b->sign == MP_NEG) || MP_IS_ZERO(b)) {
return MP_VAL;
}
if ((err = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
return err;
}
if ((err = mp_mod(a, b, &x)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(b, &y)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_EVEN(&x) && MP_IS_EVEN(&y)) {
err = MP_VAL;
goto LBL_ERR;
}
if ((err = mp_copy(&x, &u)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_copy(&y, &v)) != MP_OKAY) goto LBL_ERR;
mp_set(&A, 1uL);
mp_set(&D, 1uL);
top:
while (MP_IS_EVEN(&u)) {
if ((err = mp_div_2(&u, &u)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_ODD(&A) || MP_IS_ODD(&B)) {
if ((err = mp_add(&A, &y, &A)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&B, &x, &B)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_div_2(&A, &A)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2(&B, &B)) != MP_OKAY) goto LBL_ERR;
}
while (MP_IS_EVEN(&v)) {
if ((err = mp_div_2(&v, &v)) != MP_OKAY) goto LBL_ERR;
if (MP_IS_ODD(&C) || MP_IS_ODD(&D)) {
if ((err = mp_add(&C, &y, &C)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&D, &x, &D)) != MP_OKAY) goto LBL_ERR;
}
if ((err = mp_div_2(&C, &C)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2(&D, &D)) != MP_OKAY) goto LBL_ERR;
}
if (mp_cmp(&u, &v) != MP_LT) {
if ((err = mp_sub(&u, &v, &u)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&A, &C, &A)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&B, &D, &B)) != MP_OKAY) goto LBL_ERR;
} else {
if ((err = mp_sub(&v, &u, &v)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&C, &A, &C)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&D, &B, &D)) != MP_OKAY) goto LBL_ERR;
}
if (!MP_IS_ZERO(&u)) {
goto top;
}
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
err = MP_VAL;
goto LBL_ERR;
}
while (mp_cmp_d(&C, 0uL) == MP_LT) {
if ((err = mp_add(&C, b, &C)) != MP_OKAY) goto LBL_ERR;
}
while (mp_cmp_mag(&C, b) != MP_LT) {
if ((err = mp_sub(&C, b, &C)) != MP_OKAY) goto LBL_ERR;
}
mp_exch(&C, c);
err = MP_OKAY;
LBL_ERR:
mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_KARATSUBA_MUL_C
* three half size multiplications
*
* Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
* let n represent half of the number of digits in
* the min(a,b)
*
* a = a1 * B**n + a0
* b = b1 * B**n + b0
*
* Then, a * b =>
a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
*
* Note that a1b1 and a0b0 are used twice and only need to be
* computed once. So in total three half size (half # of
* digit) multiplications are performed, a0b0, a1b1 and
* (a1+b1)(a0+b0)
*
* Note that a multiplication of half the digits requires
* 1/4th the number of single precision multiplications so in
* total after one call 25% of the single precision multiplications
* are saved. Note also that the call to mp_mul can end up back
* in this function if the a0, a1, b0, or b1 are above the threshold.
* This is known as divide-and-conquer and leads to the famous
* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
* the standard O(N**2) that the baseline/comba methods use.
* Generally though the overhead of this method doesn't pay off
* until a certain size (N ~ 80) is reached.
*/
mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
int B;
mp_err err = MP_MEM;
B = MP_MIN(a->used, b->used);
B = B >> 1;
if (mp_init_size(&x0, B) != MP_OKAY) {
goto LBL_ERR;
}
if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
goto X0;
}
if (mp_init_size(&y0, B) != MP_OKAY) {
goto X1;
}
if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
goto Y0;
}
if (mp_init_size(&t1, B * 2) != MP_OKAY) {
goto Y1;
}
if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
goto T1;
}
if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
goto X0Y0;
}
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
{
int x;
mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
* since we also need to shift the digits
*/
tmpa = a->dp;
tmpb = b->dp;
tmpx = x0.dp;
tmpy = y0.dp;
for (x = 0; x < B; x++) {
*tmpx++ = *tmpa++;
*tmpy++ = *tmpb++;
}
tmpx = x1.dp;
for (x = B; x < a->used; x++) {
*tmpx++ = *tmpa++;
}
tmpy = y1.dp;
for (x = B; x < b->used; x++) {
*tmpy++ = *tmpb++;
}
}
* upper words x1/y1 must have a known number of digits
*/
mp_clamp(&x0);
mp_clamp(&y0);
if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
goto X1Y1;
}
if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
goto X1Y1;
}
if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
goto X1Y1;
}
if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
goto X1Y1;
}
if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
goto X1Y1;
}
if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
goto X1Y1;
}
if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
goto X1Y1;
}
if (mp_lshd(&t1, B) != MP_OKAY) {
goto X1Y1;
}
if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
goto X1Y1;
}
if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
goto X1Y1;
}
if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
goto X1Y1;
}
err = MP_OKAY;
X1Y1:
mp_clear(&x1y1);
X0Y0:
mp_clear(&x0y0);
T1:
mp_clear(&t1);
Y1:
mp_clear(&y1);
Y0:
mp_clear(&y0);
X1:
mp_clear(&x1);
X0:
mp_clear(&x0);
LBL_ERR:
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_KARATSUBA_SQR_C
* half size squarings
*
* See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
mp_err s_mp_karatsuba_sqr(const mp_int *a, mp_int *b)
{
mp_int x0, x1, t1, t2, x0x0, x1x1;
int B;
mp_err err = MP_MEM;
B = a->used;
B = B >> 1;
if (mp_init_size(&x0, B) != MP_OKAY)
goto LBL_ERR;
if (mp_init_size(&x1, a->used - B) != MP_OKAY)
goto X0;
if (mp_init_size(&t1, a->used * 2) != MP_OKAY)
goto X1;
if (mp_init_size(&t2, a->used * 2) != MP_OKAY)
goto T1;
if (mp_init_size(&x0x0, B * 2) != MP_OKAY)
goto T2;
if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY)
goto X0X0;
{
int x;
mp_digit *dst, *src;
src = a->dp;
dst = x0.dp;
for (x = 0; x < B; x++) {
*dst++ = *src++;
}
dst = x1.dp;
for (x = B; x < a->used; x++) {
*dst++ = *src++;
}
}
x0.used = B;
x1.used = a->used - B;
mp_clamp(&x0);
if (mp_sqr(&x0, &x0x0) != MP_OKAY)
goto X1X1;
if (mp_sqr(&x1, &x1x1) != MP_OKAY)
goto X1X1;
if (s_mp_add(&x1, &x0, &t1) != MP_OKAY)
goto X1X1;
if (mp_sqr(&t1, &t1) != MP_OKAY)
goto X1X1;
if (s_mp_add(&x0x0, &x1x1, &t2) != MP_OKAY)
goto X1X1;
if (s_mp_sub(&t1, &t2, &t1) != MP_OKAY)
goto X1X1;
if (mp_lshd(&t1, B) != MP_OKAY)
goto X1X1;
if (mp_lshd(&x1x1, B * 2) != MP_OKAY)
goto X1X1;
if (mp_add(&x0x0, &t1, &t1) != MP_OKAY)
goto X1X1;
if (mp_add(&t1, &x1x1, b) != MP_OKAY)
goto X1X1;
err = MP_OKAY;
X1X1:
mp_clear(&x1x1);
X0X0:
mp_clear(&x0x0);
T2:
mp_clear(&t2);
T1:
mp_clear(&t1);
X1:
mp_clear(&x1);
X0:
mp_clear(&x0);
LBL_ERR:
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_MONTGOMERY_REDUCE_FAST_C
*
* This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
* Based on Algorithm 14.32 on pp.601 of HAC.
*/
mp_err s_mp_montgomery_reduce_fast(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, olduse;
mp_err err;
mp_word W[MP_WARRAY];
if (x->used > MP_WARRAY) {
return MP_VAL;
}
olduse = x->used;
if (x->alloc < (n->used + 1)) {
if ((err = mp_grow(x, n->used + 1)) != MP_OKAY) {
return err;
}
}
* an array of double precision words W[...]
*/
{
mp_word *_W;
mp_digit *tmpx;
_W = W;
tmpx = x->dp;
for (ix = 0; ix < x->used; ix++) {
*_W++ = *tmpx++;
}
if (ix < ((n->used * 2) + 1)) {
MP_ZERO_BUFFER(_W, sizeof(mp_word) * (size_t)(((n->used * 2) + 1) - ix));
}
}
* from the least significant upwards
*/
for (ix = 0; ix < n->used; ix++) {
*
* We avoid a double precision multiplication (which isn't required)
* by casting the value down to a mp_digit. Note this requires
* that W[ix-1] have the carry cleared (see after the inner loop)
*/
mp_digit mu;
mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
*
* This is computed in place and on the fly. The multiplication
* by b**i is handled by offseting which columns the results
* are added to.
*
* Note the comba method normally doesn't handle carries in the
* inner loop In this case we fix the carry from the previous
* column since the Montgomery reduction requires digits of the
* result (so far) [see above] to work. This is
* handled by fixing up one carry after the inner loop. The
* carry fixups are done in order so after these loops the
* first m->used words of W[] have the carries fixed
*/
{
int iy;
mp_digit *tmpn;
mp_word *_W;
tmpn = n->dp;
_W = W + ix;
for (iy = 0; iy < n->used; iy++) {
*_W++ += (mp_word)mu * (mp_word)*tmpn++;
}
}
W[ix + 1] += W[ix] >> (mp_word)MP_DIGIT_BIT;
}
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
mp_digit *tmpx;
mp_word *_W, *_W1;
_W1 = W + ix;
_W = W + ++ix;
for (; ix < ((n->used * 2) + 1); ix++) {
*_W++ += *_W1++ >> (mp_word)MP_DIGIT_BIT;
}
*
* The result is A/b**n but instead of converting from an
* array of mp_word to mp_digit than calling mp_rshd
* we just copy them in the right order
*/
tmpx = x->dp;
_W = W + n->used;
for (ix = 0; ix < (n->used + 1); ix++) {
*tmpx++ = *_W++ & (mp_word)MP_MASK;
}
* m->used+1 we'll have to clear the digits
*/
MP_ZERO_DIGITS(tmpx, olduse - ix);
}
x->used = n->used + 1;
mp_clamp(x);
if (mp_cmp_mag(x, n) != MP_LT) {
return s_mp_sub(x, n, x);
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_MUL_DIGS_C
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
* many digits of output are created.
*/
mp_err s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
mp_int t;
mp_err err;
int pa, pb, ix, iy;
mp_digit u;
mp_word r;
mp_digit tmpx, *tmpt, *tmpy;
if ((digs < MP_WARRAY) &&
(MP_MIN(a->used, b->used) < MP_MAXFAST)) {
return s_mp_mul_digs_fast(a, b, c, digs);
}
if ((err = mp_init_size(&t, digs)) != MP_OKAY) {
return err;
}
t.used = digs;
pa = a->used;
for (ix = 0; ix < pa; ix++) {
u = 0;
pb = MP_MIN(b->used, digs - ix);
tmpx = a->dp[ix];
tmpt = t.dp + ix;
tmpy = b->dp;
for (iy = 0; iy < pb; iy++) {
r = (mp_word)*tmpt +
((mp_word)tmpx * (mp_word)*tmpy++) +
(mp_word)u;
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
}
if ((ix + iy) < digs) {
*tmpt = u;
}
}
mp_clamp(&t);
mp_exch(&t, c);
mp_clear(&t);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_MUL_DIGS_FAST_C
*
* This is the fast column-array [comba] multiplier. It is
* designed to compute the columns of the product first
* then handle the carries afterwards. This has the effect
* of making the nested loops that compute the columns very
* simple and schedulable on super-scalar processors.
*
* This has been modified to produce a variable number of
* digits of output so if say only a half-product is required
* you don't have to compute the upper half (a feature
* required for fast Barrett reduction).
*
* Based on Algorithm 14.12 on pp.595 of HAC.
*
*/
mp_err s_mp_mul_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
int olduse, pa, ix, iz;
mp_err err;
mp_digit W[MP_WARRAY];
mp_word _W;
if (c->alloc < digs) {
if ((err = mp_grow(c, digs)) != MP_OKAY) {
return err;
}
}
pa = MP_MIN(digs, a->used + b->used);
_W = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty;
int iy;
mp_digit *tmpx, *tmpy;
ty = MP_MIN(b->used-1, ix);
tx = ix - ty;
tmpx = a->dp + tx;
tmpy = b->dp + ty;
while (tx++ < a->used && ty-- >= 0) { ... }
*/
iy = MP_MIN(a->used-tx, ty+1);
for (iz = 0; iz < iy; ++iz) {
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
}
W[ix] = (mp_digit)_W & MP_MASK;
_W = _W >> (mp_word)MP_DIGIT_BIT;
}
olduse = c->used;
c->used = pa;
{
mp_digit *tmpc;
tmpc = c->dp;
for (ix = 0; ix < pa; ix++) {
*tmpc++ = W[ix];
}
MP_ZERO_DIGITS(tmpc, olduse - ix);
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
* [meant to get the higher part of the product]
*/
mp_err s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
mp_int t;
int pa, pb, ix, iy;
mp_err err;
mp_digit u;
mp_word r;
mp_digit tmpx, *tmpt, *tmpy;
if (MP_HAS(S_MP_MUL_HIGH_DIGS_FAST)
&& ((a->used + b->used + 1) < MP_WARRAY)
&& (MP_MIN(a->used, b->used) < MP_MAXFAST)) {
return s_mp_mul_high_digs_fast(a, b, c, digs);
}
if ((err = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) {
return err;
}
t.used = a->used + b->used + 1;
pa = a->used;
pb = b->used;
for (ix = 0; ix < pa; ix++) {
u = 0;
tmpx = a->dp[ix];
tmpt = &(t.dp[digs]);
tmpy = b->dp + (digs - ix);
for (iy = digs - ix; iy < pb; iy++) {
r = (mp_word)*tmpt +
((mp_word)tmpx * (mp_word)*tmpy++) +
(mp_word)u;
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
}
*tmpt = u;
}
mp_clamp(&t);
mp_exch(&t, c);
mp_clear(&t);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_MUL_HIGH_DIGS_FAST_C
* output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
* only the higher digits were needed. This essentially halves the work.
*
* Based on Algorithm 14.12 on pp.595 of HAC.
*/
mp_err s_mp_mul_high_digs_fast(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
int olduse, pa, ix, iz;
mp_err err;
mp_digit W[MP_WARRAY];
mp_word _W;
pa = a->used + b->used;
if (c->alloc < pa) {
if ((err = mp_grow(c, pa)) != MP_OKAY) {
return err;
}
}
pa = a->used + b->used;
_W = 0;
for (ix = digs; ix < pa; ix++) {
int tx, ty, iy;
mp_digit *tmpx, *tmpy;
ty = MP_MIN(b->used-1, ix);
tx = ix - ty;
tmpx = a->dp + tx;
tmpy = b->dp + ty;
while (tx++ < a->used && ty-- >= 0) { ... }
*/
iy = MP_MIN(a->used-tx, ty+1);
for (iz = 0; iz < iy; iz++) {
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
}
W[ix] = (mp_digit)_W & MP_MASK;
_W = _W >> (mp_word)MP_DIGIT_BIT;
}
olduse = c->used;
c->used = pa;
{
mp_digit *tmpc;
tmpc = c->dp + digs;
for (ix = digs; ix < pa; ix++) {
*tmpc++ = W[ix];
}
MP_ZERO_DIGITS(tmpc, olduse - ix);
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_PRIME_IS_DIVISIBLE_C
* of the first PRIME_SIZE primes or not
*
* sets result to 0 if not, 1 if yes
*/
mp_err s_mp_prime_is_divisible(const mp_int *a, mp_bool *result)
{
int ix;
mp_err err;
mp_digit res;
*result = MP_NO;
for (ix = 0; ix < PRIVATE_MP_PRIME_TAB_SIZE; ix++) {
if ((err = mp_mod_d(a, s_mp_prime_tab[ix], &res)) != MP_OKAY) {
return err;
}
if (res == 0u) {
*result = MP_YES;
return MP_OKAY;
}
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_RAND_JENKINS_C
typedef struct {
uint64_t a;
uint64_t b;
uint64_t c;
uint64_t d;
} ranctx;
static ranctx jenkins_x;
#define rot(x,k) (((x)<<(k))|((x)>>(64-(k))))
static uint64_t s_rand_jenkins_val(void)
{
uint64_t e = jenkins_x.a - rot(jenkins_x.b, 7);
jenkins_x.a = jenkins_x.b ^ rot(jenkins_x.c, 13);
jenkins_x.b = jenkins_x.c + rot(jenkins_x.d, 37);
jenkins_x.c = jenkins_x.d + e;
jenkins_x.d = e + jenkins_x.a;
return jenkins_x.d;
}
void s_mp_rand_jenkins_init(uint64_t seed)
{
uint64_t i;
jenkins_x.a = 0xf1ea5eedULL;
jenkins_x.b = jenkins_x.c = jenkins_x.d = seed;
for (i = 0uLL; i < 20uLL; ++i) {
(void)s_rand_jenkins_val();
}
}
mp_err s_mp_rand_jenkins(void *p, size_t n)
{
char *q = (char *)p;
while (n > 0u) {
int i;
uint64_t x = s_rand_jenkins_val();
for (i = 0; (i < 8) && (n > 0u); ++i, --n) {
*q++ = (char)(x & 0xFFuLL);
x >>= 8;
}
}
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_RAND_PLATFORM_C
* - *BSD
* - Windows
*/
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
#define BN_S_READ_ARC4RANDOM_C
static mp_err s_read_arc4random(void *p, size_t n)
{
arc4random_buf(p, n);
return MP_OKAY;
}
#endif
#if defined(_WIN32) || defined(_WIN32_WCE)
#define BN_S_READ_WINCSP_C
#ifndef _WIN32_WINNT
#define _WIN32_WINNT 0x0400
#endif
#ifdef _WIN32_WCE
#define UNDER_CE
#define ARM
#endif
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <wincrypt.h>
static mp_err s_read_wincsp(void *p, size_t n)
{
static HCRYPTPROV hProv = 0;
if (hProv == 0) {
HCRYPTPROV h = 0;
if (!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL,
(CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) &&
!CryptAcquireContext(&h, NULL, MS_DEF_PROV, PROV_RSA_FULL,
CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) {
return MP_ERR;
}
hProv = h;
}
return CryptGenRandom(hProv, (DWORD)n, (BYTE *)p) == TRUE ? MP_OKAY : MP_ERR;
}
#endif
#if !defined(BN_S_READ_WINCSP_C) && defined(__linux__) && defined(__GLIBC_PREREQ)
#if __GLIBC_PREREQ(2, 25)
#define BN_S_READ_GETRANDOM_C
#include <sys/random.h>
#include <errno.h>
static mp_err s_read_getrandom(void *p, size_t n)
{
char *q = (char *)p;
while (n > 0u) {
ssize_t ret = getrandom(q, n, 0);
if (ret < 0) {
if (errno == EINTR) {
continue;
}
return MP_ERR;
}
q += ret;
n -= (size_t)ret;
}
return MP_OKAY;
}
#endif
#endif
* In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time.
*/
#if !defined(BN_S_READ_WINCSP_C) && !defined(MP_NO_DEV_URANDOM)
#define BN_S_READ_URANDOM_C
#ifndef MP_DEV_URANDOM
#define MP_DEV_URANDOM "/dev/urandom"
#endif
#include <fcntl.h>
#include <errno.h>
#include <unistd.h>
static mp_err s_read_urandom(void *p, size_t n)
{
int fd;
char *q = (char *)p;
do {
fd = open(MP_DEV_URANDOM, O_RDONLY);
} while ((fd == -1) && (errno == EINTR));
if (fd == -1) return MP_ERR;
while (n > 0u) {
ssize_t ret = read(fd, p, n);
if (ret < 0) {
if (errno == EINTR) {
continue;
}
close(fd);
return MP_ERR;
}
q += ret;
n -= (size_t)ret;
}
close(fd);
return MP_OKAY;
}
#endif
#if defined(MP_PRNG_ENABLE_LTM_RNG)
#define BN_S_READ_LTM_RNG
unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
void (*ltm_rng_callback)(void);
static mp_err s_read_ltm_rng(void *p, size_t n)
{
unsigned long res;
if (ltm_rng == NULL) return MP_ERR;
res = ltm_rng(p, n, ltm_rng_callback);
if (res != n) return MP_ERR;
return MP_OKAY;
}
#endif
mp_err s_read_arc4random(void *p, size_t n);
mp_err s_read_wincsp(void *p, size_t n);
mp_err s_read_getrandom(void *p, size_t n);
mp_err s_read_urandom(void *p, size_t n);
mp_err s_read_ltm_rng(void *p, size_t n);
mp_err s_mp_rand_platform(void *p, size_t n)
{
mp_err err = MP_ERR;
if ((err != MP_OKAY) && MP_HAS(S_READ_ARC4RANDOM)) err = s_read_arc4random(p, n);
if ((err != MP_OKAY) && MP_HAS(S_READ_WINCSP)) err = s_read_wincsp(p, n);
if ((err != MP_OKAY) && MP_HAS(S_READ_GETRANDOM)) err = s_read_getrandom(p, n);
if ((err != MP_OKAY) && MP_HAS(S_READ_URANDOM)) err = s_read_urandom(p, n);
if ((err != MP_OKAY) && MP_HAS(S_READ_LTM_RNG)) err = s_read_ltm_rng(p, n);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_REVERSE_C
void s_mp_reverse(unsigned char *s, size_t len)
{
size_t ix, iy;
unsigned char t;
ix = 0u;
iy = len - 1u;
while (ix < iy) {
t = s[ix];
s[ix] = s[iy];
s[iy] = t;
++ix;
--iy;
}
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_SQR_C
mp_err s_mp_sqr(const mp_int *a, mp_int *b)
{
mp_int t;
int ix, iy, pa;
mp_err err;
mp_word r;
mp_digit u, tmpx, *tmpt;
pa = a->used;
if ((err = mp_init_size(&t, (2 * pa) + 1)) != MP_OKAY) {
return err;
}
t.used = (2 * pa) + 1;
for (ix = 0; ix < pa; ix++) {
r = (mp_word)t.dp[2*ix] +
((mp_word)a->dp[ix] * (mp_word)a->dp[ix]);
t.dp[ix+ix] = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
tmpx = a->dp[ix];
tmpt = t.dp + ((2 * ix) + 1);
for (iy = ix + 1; iy < pa; iy++) {
r = (mp_word)tmpx * (mp_word)a->dp[iy];
* addition instead of *2 since it's easier to optimize
*/
r = (mp_word)*tmpt + r + r + (mp_word)u;
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
}
while (u != 0uL) {
r = (mp_word)*tmpt + (mp_word)u;
*tmpt++ = (mp_digit)(r & (mp_word)MP_MASK);
u = (mp_digit)(r >> (mp_word)MP_DIGIT_BIT);
}
}
mp_clamp(&t);
mp_exch(&t, b);
mp_clear(&t);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_SQR_FAST_C
* you do like mult except the offset of the tmpx [one that
* starts closer to zero] can't equal the offset of tmpy.
* So basically you set up iy like before then you min it with
* (ty-tx) so that it never happens. You double all those
* you add in the inner loop
After that loop you do the squares and add them in.
*/
mp_err s_mp_sqr_fast(const mp_int *a, mp_int *b)
{
int olduse, pa, ix, iz;
mp_digit W[MP_WARRAY], *tmpx;
mp_word W1;
mp_err err;
pa = a->used + a->used;
if (b->alloc < pa) {
if ((err = mp_grow(b, pa)) != MP_OKAY) {
return err;
}
}
W1 = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty, iy;
mp_word _W;
mp_digit *tmpy;
_W = 0;
ty = MP_MIN(a->used-1, ix);
tx = ix - ty;
tmpx = a->dp + tx;
tmpy = a->dp + ty;
while (tx++ < a->used && ty-- >= 0) { ... }
*/
iy = MP_MIN(a->used-tx, ty+1);
* 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 = MP_MIN(iy, ((ty-tx)+1)>>1);
for (iz = 0; iz < iy; iz++) {
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
}
_W = _W + _W + W1;
if (((unsigned)ix & 1u) == 0u) {
_W += (mp_word)a->dp[ix>>1] * (mp_word)a->dp[ix>>1];
}
W[ix] = (mp_digit)_W & MP_MASK;
W1 = _W >> (mp_word)MP_DIGIT_BIT;
}
olduse = b->used;
b->used = a->used+a->used;
{
mp_digit *tmpb;
tmpb = b->dp;
for (ix = 0; ix < pa; ix++) {
*tmpb++ = W[ix] & MP_MASK;
}
MP_ZERO_DIGITS(tmpb, olduse - ix);
}
mp_clamp(b);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_SUB_C
mp_err s_mp_sub(const mp_int *a, const mp_int *b, mp_int *c)
{
int olduse, min, max;
mp_err err;
min = b->used;
max = a->used;
if (c->alloc < max) {
if ((err = mp_grow(c, max)) != MP_OKAY) {
return err;
}
}
olduse = c->used;
c->used = max;
{
mp_digit u, *tmpa, *tmpb, *tmpc;
int i;
tmpa = a->dp;
tmpb = b->dp;
tmpc = c->dp;
u = 0;
for (i = 0; i < min; i++) {
*tmpc = (*tmpa++ - *tmpb++) - u;
* Note this saves performing an AND operation since
* if a carry does occur it will propagate all the way to the
* MSB. As a result a single shift is enough to get the carry
*/
u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u);
*tmpc++ &= MP_MASK;
}
for (; i < max; i++) {
*tmpc = *tmpa++ - u;
u = *tmpc >> (MP_SIZEOF_BITS(mp_digit) - 1u);
*tmpc++ &= MP_MASK;
}
MP_ZERO_DIGITS(tmpc, olduse - c->used);
}
mp_clamp(c);
return MP_OKAY;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_TOOM_MUL_C
*
* Much more complicated than Karatsuba but has a lower
* asymptotic running time of O(N**1.464). This algorithm is
* only particularly useful on VERY large inputs
* (we're talking 1000s of digits here...).
*/
This file contains code from J. Arndt's book "Matters Computational"
and the accompanying FXT-library with permission of the author.
*/
Setup from
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
The interpolation from above needed one temporary variable more
than the interpolation here:
Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
Centro Vito Volterra Universita di Roma Tor Vergata (2006)
*/
mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2;
int B, count;
mp_err err;
if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) {
return err;
}
B = MP_MIN(a->used, b->used) / 3;
if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
for (count = 0; count < B; count++) {
a0.dp[count] = a->dp[count];
a0.used++;
}
mp_clamp(&a0);
if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
for (; count < (2 * B); count++) {
a1.dp[count - B] = a->dp[count];
a1.used++;
}
mp_clamp(&a1);
if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
for (; count < a->used; count++) {
a2.dp[count - (2 * B)] = a->dp[count];
a2.used++;
}
mp_clamp(&a2);
if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0;
for (count = 0; count < B; count++) {
b0.dp[count] = b->dp[count];
b0.used++;
}
mp_clamp(&b0);
if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1;
for (; count < (2 * B); count++) {
b1.dp[count - B] = b->dp[count];
b1.used++;
}
mp_clamp(&b1);
if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2;
for (; count < b->used; count++) {
b2.dp[count - (2 * B)] = b->dp[count];
b2.used++;
}
mp_clamp(&b2);
if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR;
LBL_ERR:
mp_clear(&b2);
LBL_ERRb2:
mp_clear(&b1);
LBL_ERRb1:
mp_clear(&b0);
LBL_ERRb0:
mp_clear(&a2);
LBL_ERRa2:
mp_clear(&a1);
LBL_ERRa1:
mp_clear(&a0);
LBL_ERRa0:
mp_clear_multi(&S1, &S2, &T1, NULL);
return err;
}
#endif
#include "tommath_private.h"
#ifdef BN_S_MP_TOOM_SQR_C
This file contains code from J. Arndt's book "Matters Computational"
and the accompanying FXT-library with permission of the author.
*/
Setup and interpolation from algorithm SQR_3 in
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
*/
mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b)
{
mp_int S0, a0, a1, a2;
mp_digit *tmpa, *tmpc;
int B, count;
mp_err err;
if ((err = mp_init(&S0)) != MP_OKAY) {
return err;
}
B = a->used / 3;
if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
a0.used = B;
if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
a1.used = B;
if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
tmpa = a->dp;
tmpc = a0.dp;
for (count = 0; count < B; count++) {
*tmpc++ = *tmpa++;
}
tmpc = a1.dp;
for (; count < (2 * B); count++) {
*tmpc++ = *tmpa++;
}
tmpc = a2.dp;
for (; count < a->used; count++) {
*tmpc++ = *tmpa++;
a2.used++;
}
mp_clamp(&a0);
mp_clamp(&a1);
mp_clamp(&a2);
if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
LBL_ERR:
mp_clear(&a2);
LBL_ERRa2:
mp_clear(&a1);
LBL_ERRa1:
mp_clear(&a0);
LBL_ERRa0:
mp_clear(&S0);
return err;
}
#endif