static void getg(dropbear_dss_key * key) {
DEF_MP_INT(div);
DEF_MP_INT(h);
DEF_MP_INT(val);
m_mp_init_multi(&div, &h, &val, NULL);
/* get div=(p-1)/q */
if (mp_sub_d(key->p, 1, &val) != MP_OKAY) {
fprintf(stderr, "DSS key generation failed\n");
exit(1);
}
if (mp_div(&val, key->q, &div, NULL) != MP_OKAY) {
fprintf(stderr, "DSS key generation failed\n");
exit(1);
}
/* initialise h=1 */
mp_set(&h, 1);
do {
/* now keep going with g=h^div mod p, until g > 1 */
if (mp_exptmod(&h, &div, key->p, key->g) != MP_OKAY) {
fprintf(stderr, "DSS key generation failed\n");
exit(1);
}
if (mp_add_d(&h, 1, &h) != MP_OKAY) {
fprintf(stderr, "DSS key generation failed\n");
exit(1);
}
} while (mp_cmp_d(key->g, 1) != MP_GT);
mp_clear_multi(&div, &h, &val, NULL);
}
void
bn_set_digit (mp_int *a, int digit)
{
mp_set (a, digit);
}
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
*/
int 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;
int err;
if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
return err;
}
/* initialize, (u1,u2,u3) = (1,0,a) */
mp_set(&u1, 1uL);
if ((err = mp_copy(a, &u3)) != MP_OKAY) {
goto LBL_ERR;
}
/* initialize, (v1,v2,v3) = (0,1,b) */
mp_set(&v2, 1uL);
if ((err = mp_copy(b, &v3)) != MP_OKAY) {
goto LBL_ERR;
}
/* loop while v3 != 0 */
while (mp_iszero(&v3) == MP_NO) {
/* q = u3/v3 */
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) {
goto LBL_ERR;
}
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
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;
}
/* (u1,u2,u3) = (v1,v2,v3) */
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;
}
/* (v1,v2,v3) = (t1,t2,t3) */
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;
}
}
/* make sure U3 >= 0 */
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;
}
}
/* copy result out */
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;
}
/* find the n'th root of an integer
*
* 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. This is not meant to
* find huge roots [square and cube, etc].
*/
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
{
mp_int t1, t2, t3;
int res, neg;
/* input must be positive if b is even */
if ((b & 1) == 0 && a->sign == MP_NEG) {
return MP_VAL;
}
if ((res = mp_init (&t1)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
goto LBL_T2;
}
/* if a is negative fudge the sign but keep track */
neg = a->sign;
a->sign = MP_ZPOS;
/* t2 = 2 */
mp_set (&t2, 2);
do {
/* t1 = t2 */
if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
/* t3 = t1**(b-1) */
if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
goto LBL_T3;
}
/* numerator */
/* t2 = t1**b */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* t2 = t1**b - a */
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
goto LBL_T3;
}
/* denominator */
/* t3 = t1**(b-1) * b */
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
goto LBL_T3;
}
/* t3 = (t1**b - a)/(b * t1**(b-1)) */
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
goto LBL_T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
goto LBL_T3;
}
} while (mp_cmp (&t1, &t2) != MP_EQ);
/* result can be off by a few so check */
for (;;) {
if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
goto LBL_T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}
/* reset the sign of a first */
a->sign = neg;
/* set the result */
mp_exch (&t1, c);
/* set the sign of the result */
c->sign = neg;
res = MP_OKAY;
LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
return res;
}
/**
Verify an ECC signature
@param sig The signature to verify
@param siglen The length of the signature (octets)
@param hash The hash (message digest) that was signed
@param hashlen The length of the hash (octets)
@param stat Result of signature, 1==valid, 0==invalid
@param key The corresponding public ECC key
@return CRYPT_OK if successful (even if the signature is not valid)
*/
int ecc_verify_hash(const unsigned char *sig, unsigned long siglen,
const unsigned char *hash, unsigned long hashlen,
int *stat, ecc_key *key)
{
ecc_point *mG, *mQ;
void *r, *s, *v, *w, *u1, *u2, *e, *p, *m;
void *mp;
int err;
LTC_ARGCHK(sig != NULL);
LTC_ARGCHK(hash != NULL);
LTC_ARGCHK(stat != NULL);
LTC_ARGCHK(key != NULL);
/* default to invalid signature */
*stat = 0;
mp = NULL;
/* is the IDX valid ? */
if (ltc_ecc_is_valid_idx(key->idx) != 1) {
return CRYPT_PK_INVALID_TYPE;
}
/* allocate ints */
if ((err = mp_init_multi(&r, &s, &v, &w, &u1, &u2, &p, &e, &m, NULL)) != CRYPT_OK) {
return CRYPT_MEM;
}
/* allocate points */
mG = ltc_ecc_new_point();
mQ = ltc_ecc_new_point();
if (mQ == NULL || mG == NULL) {
err = CRYPT_MEM;
goto error;
}
/* parse header */
if ((err = der_decode_sequence_multi(sig, siglen,
LTC_ASN1_INTEGER, 1UL, r,
LTC_ASN1_INTEGER, 1UL, s,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto error;
}
/* get the order */
if ((err = mp_read_radix(p, (char *)key->dp->order, 16)) != CRYPT_OK) { goto error; }
/* get the modulus */
if ((err = mp_read_radix(m, (char *)key->dp->prime, 16)) != CRYPT_OK) { goto error; }
/* check for zero */
if (mp_iszero(r) || mp_iszero(s) || mp_cmp(r, p) != LTC_MP_LT || mp_cmp(s, p) != LTC_MP_LT) {
err = CRYPT_INVALID_PACKET;
goto error;
}
/* read hash */
if ((err = mp_read_unsigned_bin(e, (unsigned char *)hash, (int)hashlen)) != CRYPT_OK) { goto error; }
/* w = s^-1 mod n */
if ((err = mp_invmod(s, p, w)) != CRYPT_OK) { goto error; }
/* u1 = ew */
if ((err = mp_mulmod(e, w, p, u1)) != CRYPT_OK) { goto error; }
/* u2 = rw */
if ((err = mp_mulmod(r, w, p, u2)) != CRYPT_OK) { goto error; }
/* find mG and mQ */
if ((err = mp_read_radix(mG->x, (char *)key->dp->Gx, 16)) != CRYPT_OK) { goto error; }
if ((err = mp_read_radix(mG->y, (char *)key->dp->Gy, 16)) != CRYPT_OK) { goto error; }
if ((err = mp_set(mG->z, 1)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.x, mQ->x)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.y, mQ->y)) != CRYPT_OK) { goto error; }
if ((err = mp_copy(key->pubkey.z, mQ->z)) != CRYPT_OK) { goto error; }
/* compute u1*mG + u2*mQ = mG */
if (ltc_mp.ecc_mul2add == NULL) {
if ((err = ltc_mp.ecc_ptmul(u1, mG, mG, m, 0)) != CRYPT_OK) { goto error; }
if ((err = ltc_mp.ecc_ptmul(u2, mQ, mQ, m, 0)) != CRYPT_OK) { goto error; }
/* find the montgomery mp */
if ((err = mp_montgomery_setup(m, &mp)) != CRYPT_OK) { goto error; }
/* add them */
if ((err = ltc_mp.ecc_ptadd(mQ, mG, mG, m, mp)) != CRYPT_OK) { goto error; }
/* reduce */
if ((err = ltc_mp.ecc_map(mG, m, mp)) != CRYPT_OK) { goto error; }
} else {
/* use Shamir's trick to compute u1*mG + u2*mQ using half of the doubles */
if ((err = ltc_mp.ecc_mul2add(mG, u1, mQ, u2, mG, m)) != CRYPT_OK) { goto error; }
}
/* v = X_x1 mod n */
if ((err = mp_mod(mG->x, p, v)) != CRYPT_OK) { goto error; }
/* does v == r */
if (mp_cmp(v, r) == LTC_MP_EQ) {
*stat = 1;
}
/* clear up and return */
err = CRYPT_OK;
error:
ltc_ecc_del_point(mG);
ltc_ecc_del_point(mQ);
mp_clear_multi(r, s, v, w, u1, u2, p, e, m, NULL);
if (mp != NULL) {
mp_montgomery_free(mp);
}
return err;
}
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
* From HAC pp.604 Algorithm 14.42
*/
int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
{
mp_int q;
int res, um = USED(m);
/* q = x */
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
return res;
}
/* q1 = x / b**(k-1) */
mp_rshd (&q, um - 1);
/* according to HAC this optimization is ok */
if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
} else {
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
#else
{
res = MP_VAL;
goto CLEANUP;
}
#endif
}
/* q3 = q2 / b**(k+1) */
mp_rshd (&q, um + 1);
/* x = x mod b**(k+1), quick (no division) */
if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
goto CLEANUP;
}
/* q = q * m mod b**(k+1), quick (no division) */
if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
goto CLEANUP;
}
/* x = x - q */
if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
goto CLEANUP;
}
/* If x < 0, add b**(k+1) to it */
if (mp_cmp_d (x, 0) == MP_LT) {
mp_set (&q, 1);
if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
goto CLEANUP;
if ((res = mp_add (x, &q, x)) != MP_OKAY)
goto CLEANUP;
}
/* Back off if it's too big */
while (mp_cmp (x, m) != MP_LT) {
if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
goto CLEANUP;
}
}
CLEANUP:
mp_clear (&q);
return res;
}
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
int err, res, x, y;
mp_digit res_tab[PRIME_SIZE], step, kstep;
mp_int b;
/* ensure t is valid */
if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
/* force positive */
a->sign = MP_ZPOS;
/* simple algo if a is less than the largest prime in the table */
if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
/* find which prime it is bigger than */
for (x = PRIME_SIZE - 2; x >= 0; x--) {
if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
if (bbs_style == 1) {
/* ok we found a prime smaller or
* equal [so the next is larger]
*
* however, the prime must be
* congruent to 3 mod 4
*/
if ((ltm_prime_tab[x + 1] & 3) != 3) {
/* scan upwards for a prime congruent to 3 mod 4 */
for (y = x + 1; y < PRIME_SIZE; y++) {
if ((ltm_prime_tab[y] & 3) == 3) {
mp_set(a, ltm_prime_tab[y]);
return MP_OKAY;
}
}
}
} else {
mp_set(a, ltm_prime_tab[x + 1]);
return MP_OKAY;
}
}
}
/* at this point a maybe 1 */
if (mp_cmp_d(a, 1) == MP_EQ) {
mp_set(a, 2);
return MP_OKAY;
}
/* fall through to the sieve */
}
/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
if (bbs_style == 1) {
kstep = 4;
} else {
kstep = 2;
}
/* at this point we will use a combination of a sieve and Miller-Rabin */
if (bbs_style == 1) {
/* if a mod 4 != 3 subtract the correct value to make it so */
if ((a->dp[0] & 3) != 3) {
if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
}
} else {
if (mp_iseven(a) == 1) {
/* force odd */
if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
return err;
}
}
}
/* generate the restable */
for (x = 1; x < PRIME_SIZE; x++) {
if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
return err;
}
}
/* init temp used for Miller-Rabin Testing */
if ((err = mp_init(&b)) != MP_OKAY) {
return err;
}
for (;;) {
/* skip to the next non-trivially divisible candidate */
step = 0;
do {
/* y == 1 if any residue was zero [e.g. cannot be prime] */
y = 0;
/* increase step to next candidate */
step += kstep;
/* compute the new residue without using division */
for (x = 1; x < PRIME_SIZE; x++) {
/* add the step to each residue */
res_tab[x] += kstep;
/* subtract the modulus [instead of using division] */
if (res_tab[x] >= ltm_prime_tab[x]) {
res_tab[x] -= ltm_prime_tab[x];
}
/* set flag if zero */
if (res_tab[x] == 0) {
y = 1;
}
}
} while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
/* add the step */
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
goto LBL_ERR;
}
/* if didn't pass sieve and step == MAX then skip test */
if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
continue;
}
/* is this prime? */
for (x = 0; x < t; x++) {
mp_set(&b, ltm_prime_tab[t]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_ERR;
}
if (res == MP_NO) {
break;
}
}
if (res == MP_YES) {
break;
}
}
err = MP_OKAY;
LBL_ERR:
mp_clear(&b);
return err;
}
int
is_mersenne (long s, int *pp)
{
mp_int n, u;
int res, k;
*pp = 0;
if ((res = mp_init (&n)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&u)) != MP_OKAY) {
goto LBL_N;
}
/* n = 2^s - 1 */
if ((res = mp_2expt(&n, s)) != MP_OKAY) {
goto LBL_MU;
}
if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
goto LBL_MU;
}
/* set u=4 */
mp_set (&u, 4);
/* for k=1 to s-2 do */
for (k = 1; k <= s - 2; k++) {
/* u = u^2 - 2 mod n */
if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
goto LBL_MU;
}
if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
goto LBL_MU;
}
/* make sure u is positive */
while (u.sign == MP_NEG) {
if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
goto LBL_MU;
}
}
/* reduce */
if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
goto LBL_MU;
}
}
/* if u == 0 then its prime */
if (mp_iszero (&u) == 1) {
mp_prime_is_prime(&n, 8, pp);
if (*pp != 1) printf("FAILURE\n");
}
res = MP_OKAY;
LBL_MU:mp_clear (&u);
LBL_N:mp_clear (&n);
return res;
}
int main(void)
{
mp_int a, b, c, d, e, f;
unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n, t;
unsigned rr;
int i, n, err, cnt, ix, old_kara_m, old_kara_s;
mp_digit mp;
mp_init(&a);
mp_init(&b);
mp_init(&c);
mp_init(&d);
mp_init(&e);
mp_init(&f);
srand(time(NULL));
#if 0
// test montgomery
printf("Testing montgomery...\n");
for (i = 1; i < 10; i++) {
printf("Testing digit size: %d\n", i);
for (n = 0; n < 1000; n++) {
mp_rand(&a, i);
a.dp[0] |= 1;
// let's see if R is right
mp_montgomery_calc_normalization(&b, &a);
mp_montgomery_setup(&a, &mp);
// now test a random reduction
for (ix = 0; ix < 100; ix++) {
mp_rand(&c, 1 + abs(rand()) % (2*i));
mp_copy(&c, &d);
mp_copy(&c, &e);
mp_mod(&d, &a, &d);
mp_montgomery_reduce(&c, &a, mp);
mp_mulmod(&c, &b, &a, &c);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("d = e mod a, c = e MOD a\n");
mp_todecimal(&a, buf); printf("a = %s\n", buf);
mp_todecimal(&e, buf); printf("e = %s\n", buf);
mp_todecimal(&d, buf); printf("d = %s\n", buf);
mp_todecimal(&c, buf); printf("c = %s\n", buf);
printf("compare no compare!\n"); exit(EXIT_FAILURE); }
}
}
}
printf("done\n");
// test mp_get_int
printf("Testing: mp_get_int\n");
for (i = 0; i < 1000; ++i) {
t = ((unsigned long) rand() * rand() + 1) & 0xFFFFFFFF;
mp_set_int(&a, t);
if (t != mp_get_int(&a)) {
printf("mp_get_int() bad result!\n");
return 1;
}
}
mp_set_int(&a, 0);
if (mp_get_int(&a) != 0) {
printf("mp_get_int() bad result!\n");
return 1;
}
mp_set_int(&a, 0xffffffff);
if (mp_get_int(&a) != 0xffffffff) {
printf("mp_get_int() bad result!\n");
return 1;
}
// test mp_sqrt
printf("Testing: mp_sqrt\n");
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
n = (rand() & 15) + 1;
mp_rand(&a, n);
if (mp_sqrt(&a, &b) != MP_OKAY) {
printf("mp_sqrt() error!\n");
return 1;
}
mp_n_root(&a, 2, &a);
if (mp_cmp_mag(&b, &a) != MP_EQ) {
printf("mp_sqrt() bad result!\n");
return 1;
}
}
printf("\nTesting: mp_is_square\n");
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
/* test mp_is_square false negatives */
n = (rand() & 7) + 1;
mp_rand(&a, n);
mp_sqr(&a, &a);
if (mp_is_square(&a, &n) != MP_OKAY) {
printf("fn:mp_is_square() error!\n");
return 1;
}
if (n == 0) {
printf("fn:mp_is_square() bad result!\n");
return 1;
}
/* test for false positives */
mp_add_d(&a, 1, &a);
if (mp_is_square(&a, &n) != MP_OKAY) {
printf("fp:mp_is_square() error!\n");
return 1;
}
if (n == 1) {
printf("fp:mp_is_square() bad result!\n");
return 1;
}
}
printf("\n\n");
/* test for size */
for (ix = 10; ix < 128; ix++) {
printf("Testing (not safe-prime): %9d bits \r", ix);
fflush(stdout);
err =
mp_prime_random_ex(&a, 8, ix,
(rand() & 1) ? LTM_PRIME_2MSB_OFF :
LTM_PRIME_2MSB_ON, myrng, NULL);
if (err != MP_OKAY) {
printf("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits(&a) != ix) {
printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
return EXIT_FAILURE;
}
}
for (ix = 16; ix < 128; ix++) {
printf("Testing ( safe-prime): %9d bits \r", ix);
fflush(stdout);
err =
mp_prime_random_ex(&a, 8, ix,
((rand() & 1) ? LTM_PRIME_2MSB_OFF :
LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng,
NULL);
if (err != MP_OKAY) {
printf("failed with err code %d\n", err);
return EXIT_FAILURE;
}
if (mp_count_bits(&a) != ix) {
printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
return EXIT_FAILURE;
}
/* let's see if it's really a safe prime */
mp_sub_d(&a, 1, &a);
mp_div_2(&a, &a);
mp_prime_is_prime(&a, 8, &cnt);
if (cnt != MP_YES) {
printf("sub is not prime!\n");
return EXIT_FAILURE;
}
}
printf("\n\n");
mp_read_radix(&a, "123456", 10);
mp_toradix_n(&a, buf, 10, 3);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 4);
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 30);
printf("a == %s\n", buf);
#if 0
for (;;) {
fgets(buf, sizeof(buf), stdin);
mp_read_radix(&a, buf, 10);
mp_prime_next_prime(&a, 5, 1);
mp_toradix(&a, buf, 10);
printf("%s, %lu\n", buf, a.dp[0] & 3);
}
#endif
/* test mp_cnt_lsb */
printf("testing mp_cnt_lsb...\n");
mp_set(&a, 1);
for (ix = 0; ix < 1024; ix++) {
if (mp_cnt_lsb(&a) != ix) {
printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
return 0;
}
mp_mul_2(&a, &a);
}
/* test mp_reduce_2k */
printf("Testing mp_reduce_2k...\n");
for (cnt = 3; cnt <= 128; ++cnt) {
mp_digit tmp;
mp_2expt(&a, cnt);
mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */
printf("\nTesting %4d bits", cnt);
printf("(%d)", mp_reduce_is_2k(&a));
mp_reduce_2k_setup(&a, &tmp);
printf("(%d)", tmp);
for (ix = 0; ix < 1000; ix++) {
if (!(ix & 127)) {
printf(".");
fflush(stdout);
}
mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2);
mp_copy(&c, &b);
mp_mod(&c, &a, &c);
mp_reduce_2k(&b, &a, 2);
if (mp_cmp(&c, &b)) {
printf("FAILED\n");
exit(0);
}
}
}
/* test mp_div_3 */
printf("Testing mp_div_3...\n");
mp_set(&d, 3);
for (cnt = 0; cnt < 10000;) {
mp_digit r1, r2;
if (!(++cnt & 127))
printf("%9d\r", cnt);
mp_rand(&a, abs(rand()) % 128 + 1);
mp_div(&a, &d, &b, &e);
mp_div_3(&a, &c, &r2);
if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
printf("\n\nmp_div_3 => Failure\n");
}
}
printf("\n\nPassed div_3 testing\n");
/* test the DR reduction */
printf("testing mp_dr_reduce...\n");
for (cnt = 2; cnt < 32; cnt++) {
printf("%d digit modulus\n", cnt);
mp_grow(&a, cnt);
mp_zero(&a);
for (ix = 1; ix < cnt; ix++) {
a.dp[ix] = MP_MASK;
}
a.used = cnt;
a.dp[0] = 3;
mp_rand(&b, cnt - 1);
mp_copy(&b, &c);
rr = 0;
do {
if (!(rr & 127)) {
printf("%9lu\r", rr);
fflush(stdout);
}
mp_sqr(&b, &b);
mp_add_d(&b, 1, &b);
mp_copy(&b, &c);
mp_mod(&b, &a, &b);
mp_dr_reduce(&c, &a, (((mp_digit) 1) << DIGIT_BIT) - a.dp[0]);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("Failed on trial %lu\n", rr);
exit(-1);
}
} while (++rr < 500);
printf("Passed DR test for %d digits\n", cnt);
}
#endif
/* test the mp_reduce_2k_l code */
#if 0
#if 0
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
mp_2expt(&a, 1024);
mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
mp_sub(&a, &b, &a);
#elif 1
/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */
mp_2expt(&a, 2048);
mp_read_radix(&b,
"1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
16);
mp_sub(&a, &b, &a);
#endif
mp_todecimal(&a, buf);
printf("p==%s\n", buf);
/* now mp_reduce_is_2k_l() should return */
if (mp_reduce_is_2k_l(&a) != 1) {
printf("mp_reduce_is_2k_l() return 0, should be 1\n");
return EXIT_FAILURE;
}
mp_reduce_2k_setup_l(&a, &d);
/* now do a million square+1 to see if it varies */
mp_rand(&b, 64);
mp_mod(&b, &a, &b);
mp_copy(&b, &c);
printf("testing mp_reduce_2k_l...");
fflush(stdout);
for (cnt = 0; cnt < (1UL << 20); cnt++) {
mp_sqr(&b, &b);
mp_add_d(&b, 1, &b);
mp_reduce_2k_l(&b, &a, &d);
mp_sqr(&c, &c);
mp_add_d(&c, 1, &c);
mp_mod(&c, &a, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("mp_reduce_2k_l() failed at step %lu\n", cnt);
mp_tohex(&b, buf);
printf("b == %s\n", buf);
mp_tohex(&c, buf);
printf("c == %s\n", buf);
return EXIT_FAILURE;
}
}
printf("...Passed\n");
#endif
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
sub_d_n = 0;
/* force KARA and TOOM to enable despite cutoffs */
KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;
for (;;) {
/* randomly clear and re-init one variable, this has the affect of triming the alloc space */
switch (abs(rand()) % 7) {
case 0:
mp_clear(&a);
mp_init(&a);
break;
case 1:
mp_clear(&b);
mp_init(&b);
break;
case 2:
mp_clear(&c);
mp_init(&c);
break;
case 3:
mp_clear(&d);
mp_init(&d);
break;
case 4:
mp_clear(&e);
mp_init(&e);
break;
case 5:
mp_clear(&f);
mp_init(&f);
break;
case 6:
break; /* don't clear any */
}
printf
("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
fgets(cmd, 4095, stdin);
cmd[strlen(cmd) - 1] = 0;
printf("%s ]\r", cmd);
fflush(stdout);
if (!strcmp(cmd, "mul2d")) {
++mul2d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_mul_2d(&a, rr, &a);
a.sign = b.sign;
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mul2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "div2d")) {
++div2d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_div_2d(&a, rr, &a, &e);
a.sign = b.sign;
if (a.used == b.used && a.used == 0) {
a.sign = b.sign = MP_ZPOS;
}
if (mp_cmp(&a, &b) != MP_EQ) {
printf("div2d failed, rr == %d\n", rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "add")) {
++add_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_add(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("add %lu failure!\n", add_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
/* test the sign/unsigned storage functions */
rr = mp_signed_bin_size(&c);
mp_to_signed_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mp_signed_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
rr = mp_unsigned_bin_size(&c);
mp_to_unsigned_bin(&c, (unsigned char *) cmd);
memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
if (mp_cmp_mag(&c, &d) != MP_EQ) {
printf("mp_unsigned_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "sub")) {
++sub_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_sub(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("sub %lu failure!\n", sub_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "mul")) {
++mul_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_mul(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mul %lu failure!\n", mul_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "div")) {
++div_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&d, buf, 64);
mp_div(&a, &b, &e, &f);
if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
mp_cmp(&d, &f));
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
draw(&f);
return 0;
}
} else if (!strcmp(cmd, "sqr")) {
++sqr_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_copy(&a, &c);
mp_sqr(&c, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sqr %lu failure!\n", sqr_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "gcd")) {
++gcd_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_gcd(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("gcd %lu failure!\n", gcd_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "lcm")) {
++lcm_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_copy(&a, &d);
mp_lcm(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("lcm %lu failure!\n", lcm_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "expt")) {
++expt_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&d, buf, 64);
mp_copy(&a, &e);
mp_exptmod(&e, &b, &c, &e);
if (mp_cmp(&d, &e) != MP_EQ) {
printf("expt %lu failure!\n", expt_n);
draw(&a);
draw(&b);
draw(&c);
draw(&d);
draw(&e);
return 0;
}
} else if (!strcmp(cmd, "invmod")) {
++inv_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&c, buf, 64);
mp_invmod(&a, &b, &d);
mp_mulmod(&d, &a, &b, &e);
if (mp_cmp_d(&e, 1) != MP_EQ) {
printf("inv [wrong value from MPI?!] failure\n");
draw(&a);
draw(&b);
draw(&c);
draw(&d);
mp_gcd(&a, &b, &e);
draw(&e);
return 0;
}
} else if (!strcmp(cmd, "div2")) {
++div2_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_div_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("div_2 %lu failure\n", div2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "mul2")) {
++mul2_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_mul_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("mul_2 %lu failure\n", mul2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "add_d")) {
++add_d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &ix);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_add_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("add_d %lu failure\n", add_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return 0;
}
} else if (!strcmp(cmd, "sub_d")) {
++sub_d_n;
fgets(buf, 4095, stdin);
mp_read_radix(&a, buf, 64);
fgets(buf, 4095, stdin);
sscanf(buf, "%d", &ix);
fgets(buf, 4095, stdin);
mp_read_radix(&b, buf, 64);
mp_sub_d(&a, ix, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sub_d %lu failure\n", sub_d_n);
draw(&a);
draw(&b);
draw(&c);
printf("d == %d\n", ix);
return 0;
}
}
}
return 0;
}
int main(void)
{
ulong64 tt, gg, CLK_PER_SEC;
FILE *log, *logb, *logc, *logd;
mp_int a, b, c, d, e, f;
int n, cnt, ix, old_kara_m, old_kara_s;
unsigned rr;
mp_init(&a);
mp_init(&b);
mp_init(&c);
mp_init(&d);
mp_init(&e);
mp_init(&f);
srand(time(NULL));
/* temp. turn off TOOM */
TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;
CLK_PER_SEC = TIMFUNC();
sleep(1);
CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;
printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
goto exptmod;
log = fopen("logs/add.log", "w");
for (cnt = 8; cnt <= 128; cnt += 8) {
SLEEP;
mp_rand(&a, cnt);
mp_rand(&b, cnt);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_add(&a, &b, &c));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 100000);
printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
fflush(log);
}
fclose(log);
log = fopen("logs/sub.log", "w");
for (cnt = 8; cnt <= 128; cnt += 8) {
SLEEP;
mp_rand(&a, cnt);
mp_rand(&b, cnt);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_sub(&a, &b, &c));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 100000);
printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
fflush(log);
}
fclose(log);
/* do mult/square twice, first without karatsuba and second with */
multtest:
old_kara_m = KARATSUBA_MUL_CUTOFF;
old_kara_s = KARATSUBA_SQR_CUTOFF;
for (ix = 0; ix < 2; ix++) {
printf("With%s Karatsuba\n", (ix == 0) ? "out" : "");
KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m;
KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s;
log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w");
for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
SLEEP;
mp_rand(&a, cnt);
mp_rand(&b, cnt);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_mul(&a, &b, &c));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 100);
printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
fflush(log);
}
fclose(log);
log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w");
for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
SLEEP;
mp_rand(&a, cnt);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_sqr(&a, &b));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 100);
printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
fflush(log);
}
fclose(log);
}
exptmod:
{
char *primes[] = {
/* 2K large moduli */
"179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
"32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
"1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
/* 2K moduli mersenne primes */
"6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
"531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
"10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
"1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
"259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
"190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
/* DR moduli */
"14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
"101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
"736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
"38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
"542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
"1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
"1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
/* generic unrestricted moduli */
"17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
"2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
"347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
"47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
"436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
"11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
"1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
NULL
};
log = fopen("logs/expt.log", "w");
logb = fopen("logs/expt_dr.log", "w");
logc = fopen("logs/expt_2k.log", "w");
logd = fopen("logs/expt_2kl.log", "w");
for (n = 0; primes[n]; n++) {
SLEEP;
mp_read_radix(&a, primes[n], 10);
mp_zero(&b);
for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
mp_mul_2(&b, &b);
b.dp[0] |= lbit();
b.used += 1;
}
mp_sub_d(&a, 1, &c);
mp_mod(&b, &c, &b);
mp_set(&c, 3);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_exptmod(&c, &b, &a, &d));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 10);
mp_sub_d(&a, 1, &e);
mp_sub(&e, &b, &b);
mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */
mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */
if (mp_cmp_d(&d, 1)) {
printf("Different (%d)!!!\n", mp_count_bits(&a));
draw(&d);
exit(0);
}
printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
"%d %9llu\n", mp_count_bits(&a), tt);
}
}
fclose(log);
fclose(logb);
fclose(logc);
fclose(logd);
log = fopen("logs/invmod.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
SLEEP;
mp_rand(&a, cnt);
mp_rand(&b, cnt);
do {
mp_add_d(&b, 1, &b);
mp_gcd(&a, &b, &c);
} while (mp_cmp_d(&c, 1) != MP_EQ);
rr = 0;
tt = -1;
do {
gg = TIMFUNC();
DO(mp_invmod(&b, &a, &c));
gg = (TIMFUNC() - gg) >> 1;
if (tt > gg)
tt = gg;
} while (++rr < 1000);
mp_mulmod(&b, &c, &a, &d);
if (mp_cmp_d(&d, 1) != MP_EQ) {
printf("Failed to invert\n");
return 0;
}
printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
mp_count_bits(&a), CLK_PER_SEC / tt, tt);
fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
}
fclose(log);
return 0;
}
/* Do modular exponentiation using integer multiply code. */
mp_err mp_exptmod_i(const mp_int * montBase,
const mp_int * exponent,
const mp_int * modulus,
mp_int * result,
mp_mont_modulus *mmm,
int nLen,
mp_size bits_in_exponent,
mp_size window_bits,
mp_size odd_ints)
{
mp_int *pa1, *pa2, *ptmp;
mp_size i;
mp_err res;
int expOff;
mp_int accum1, accum2, power2, oddPowers[MAX_ODD_INTS];
/* power2 = base ** 2; oddPowers[i] = base ** (2*i + 1); */
/* oddPowers[i] = base ** (2*i + 1); */
MP_DIGITS(&accum1) = 0;
MP_DIGITS(&accum2) = 0;
MP_DIGITS(&power2) = 0;
for (i = 0; i < MAX_ODD_INTS; ++i) {
MP_DIGITS(oddPowers + i) = 0;
}
MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
MP_CHECKOK( mp_init_copy(&oddPowers[0], montBase) );
mp_init_size(&power2, nLen + 2 * MP_USED(montBase) + 2);
MP_CHECKOK( mp_sqr(montBase, &power2) ); /* power2 = montBase ** 2 */
MP_CHECKOK( s_mp_redc(&power2, mmm) );
for (i = 1; i < odd_ints; ++i) {
mp_init_size(oddPowers + i, nLen + 2 * MP_USED(&power2) + 2);
MP_CHECKOK( mp_mul(oddPowers + (i - 1), &power2, oddPowers + i) );
MP_CHECKOK( s_mp_redc(oddPowers + i, mmm) );
}
/* set accumulator to montgomery residue of 1 */
mp_set(&accum1, 1);
MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
pa1 = &accum1;
pa2 = &accum2;
for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
mp_size smallExp;
MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
smallExp = (mp_size)res;
if (window_bits == 1) {
if (!smallExp) {
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 1) {
SQR(pa1,pa2); MUL(0,pa2,pa1);
} else {
ABORT;
}
} else if (window_bits == 4) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/2, pa1,pa2); SWAPPA;
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/8,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 8) {
SQR(pa1,pa2); MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else {
ABORT;
}
} else if (window_bits == 5) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); MUL(smallExp/2,pa2,pa1);
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/4,pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/8,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 8) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/16,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 0x10) {
SQR(pa1,pa2); MUL(smallExp/32,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
} else {
ABORT;
}
} else if (window_bits == 6) {
if (!smallExp) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SQR(pa2,pa1);
} else if (smallExp & 1) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/2,pa1,pa2); SWAPPA;
} else if (smallExp & 2) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 4) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
MUL(smallExp/8,pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 8) {
SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2);
MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 0x10) {
SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/32,pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else if (smallExp & 0x20) {
SQR(pa1,pa2); MUL(smallExp/64,pa2,pa1); SQR(pa1,pa2);
SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
} else {
ABORT;
}
} else {
ABORT;
}
}
res = s_mp_redc(pa1, mmm);
mp_exch(pa1, result);
CLEANUP:
mp_clear(&accum1);
mp_clear(&accum2);
mp_clear(&power2);
for (i = 0; i < odd_ints; ++i) {
mp_clear(oddPowers + i);
}
return res;
}
/* Do modular exponentiation using floating point multiply code. */
mp_err mp_exptmod_f(const mp_int * montBase,
const mp_int * exponent,
const mp_int * modulus,
mp_int * result,
mp_mont_modulus *mmm,
int nLen,
mp_size bits_in_exponent,
mp_size window_bits,
mp_size odd_ints)
{
mp_digit *mResult;
double *dBuf = 0, *dm1, *dn, *dSqr, *d16Tmp, *dTmp;
double dn0;
mp_size i;
mp_err res;
int expOff;
int dSize = 0, oddPowSize, dTmpSize;
mp_int accum1;
double *oddPowers[MAX_ODD_INTS];
/* function for computing n0prime only works if n0 is odd */
MP_DIGITS(&accum1) = 0;
for (i = 0; i < MAX_ODD_INTS; ++i)
oddPowers[i] = 0;
MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
mp_set(&accum1, 1);
MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
MP_CHECKOK( s_mp_pad(&accum1, nLen) );
oddPowSize = 2 * nLen + 1;
dTmpSize = 2 * oddPowSize;
dSize = sizeof(double) * (nLen * 4 + 1 +
((odd_ints + 1) * oddPowSize) + dTmpSize);
dBuf = (double *)malloc(dSize);
dm1 = dBuf; /* array of d32 */
dn = dBuf + nLen; /* array of d32 */
dSqr = dn + nLen; /* array of d32 */
d16Tmp = dSqr + nLen; /* array of d16 */
dTmp = d16Tmp + oddPowSize;
for (i = 0; i < odd_ints; ++i) {
oddPowers[i] = dTmp;
dTmp += oddPowSize;
}
mResult = (mp_digit *)(dTmp + dTmpSize); /* size is nLen + 1 */
/* Make dn and dn0 */
conv_i32_to_d32(dn, MP_DIGITS(modulus), nLen);
dn0 = (double)(mmm->n0prime & 0xffff);
/* Make dSqr */
conv_i32_to_d32_and_d16(dm1, oddPowers[0], MP_DIGITS(montBase), nLen);
mont_mulf_noconv(mResult, dm1, oddPowers[0],
dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
conv_i32_to_d32(dSqr, mResult, nLen);
for (i = 1; i < odd_ints; ++i) {
mont_mulf_noconv(mResult, dSqr, oddPowers[i - 1],
dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
conv_i32_to_d16(oddPowers[i], mResult, nLen);
}
s_mp_copy(MP_DIGITS(&accum1), mResult, nLen); /* from, to, len */
for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
mp_size smallExp;
MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
smallExp = (mp_size)res;
if (window_bits == 1) {
if (!smallExp) {
SQR;
} else if (smallExp & 1) {
SQR; MUL(0);
} else {
ABORT;
}
} else if (window_bits == 4) {
if (!smallExp) {
SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else {
ABORT;
}
} else if (window_bits == 5) {
if (!smallExp) {
SQR; SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else if (smallExp & 0x10) {
SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
} else {
ABORT;
}
} else if (window_bits == 6) {
if (!smallExp) {
SQR; SQR; SQR; SQR; SQR; SQR;
} else if (smallExp & 1) {
SQR; SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
} else if (smallExp & 2) {
SQR; SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
} else if (smallExp & 4) {
SQR; SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
} else if (smallExp & 8) {
SQR; SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
} else if (smallExp & 0x10) {
SQR; SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
} else if (smallExp & 0x20) {
SQR; MUL(smallExp/64); SQR; SQR; SQR; SQR; SQR;
} else {
ABORT;
}
} else {
ABORT;
}
}
s_mp_copy(mResult, MP_DIGITS(&accum1), nLen); /* from, to, len */
res = s_mp_redc(&accum1, mmm);
mp_exch(&accum1, result);
CLEANUP:
mp_clear(&accum1);
if (dBuf) {
if (dSize)
memset(dBuf, 0, dSize);
free(dBuf);
}
return res;
}
/**
Verify an ECC signature
@param sig The signature to verify
@param siglen The length of the signature (octets)
@param hash The hash (message digest) that was signed
@param hashlen The length of the hash (octets)
@param stat Result of signature, 1==valid, 0==invalid
@param key The corresponding public ECC key
@return CRYPT_OK if successful (even if the signature is not valid)
*/
int ecc_verify_hash(const unsigned char *sig, unsigned long siglen,
const unsigned char *hash, unsigned long hashlen,
int *stat, ecc_key *key)
{
ecc_point *mG, *mQ;
mp_int r, s, v, w, u1, u2, e, p, m;
mp_digit mp;
int err;
LTC_ARGCHK(sig != NULL);
LTC_ARGCHK(hash != NULL);
LTC_ARGCHK(stat != NULL);
LTC_ARGCHK(key != NULL);
/* default to invalid signature */
*stat = 0;
/* is the IDX valid ? */
if (is_valid_idx(key->idx) != 1) {
return CRYPT_PK_INVALID_TYPE;
}
/* allocate ints */
if ((err = mp_init_multi(&r, &s, &v, &w, &u1, &u2, &p, &e, &m, NULL)) != MP_OKAY) {
return CRYPT_MEM;
}
/* allocate points */
mG = new_point();
mQ = new_point();
if (mQ == NULL || mG == NULL) {
err = CRYPT_MEM;
goto done;
}
/* parse header */
if ((err = der_decode_sequence_multi(sig, siglen,
LTC_ASN1_INTEGER, 1UL, &r,
LTC_ASN1_INTEGER, 1UL, &s,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
/* get the order */
if ((err = mp_read_radix(&p, (char *)sets[key->idx].order, 64)) != MP_OKAY) { goto error; }
/* get the modulus */
if ((err = mp_read_radix(&m, (char *)sets[key->idx].prime, 64)) != MP_OKAY) { goto error; }
/* check for zero */
if (mp_iszero(&r) || mp_iszero(&s) || mp_cmp(&r, &p) != MP_LT || mp_cmp(&s, &p) != MP_LT) {
err = CRYPT_INVALID_PACKET;
goto done;
}
/* read hash */
if ((err = mp_read_unsigned_bin(&e, (unsigned char *)hash, (int)hashlen)) != MP_OKAY) { goto error; }
/* w = s^-1 mod n */
if ((err = mp_invmod(&s, &p, &w)) != MP_OKAY) { goto error; }
/* u1 = ew */
if ((err = mp_mulmod(&e, &w, &p, &u1)) != MP_OKAY) { goto error; }
/* u2 = rw */
if ((err = mp_mulmod(&r, &w, &p, &u2)) != MP_OKAY) { goto error; }
/* find mG = u1*G */
if ((err = mp_read_radix(&mG->x, (char *)sets[key->idx].Gx, 64)) != MP_OKAY) { goto error; }
if ((err = mp_read_radix(&mG->y, (char *)sets[key->idx].Gy, 64)) != MP_OKAY) { goto error; }
mp_set(&mG->z, 1);
if ((err = ecc_mulmod(&u1, mG, mG, &m, 0)) != CRYPT_OK) { goto done; }
/* find mQ = u2*Q */
if ((err = mp_copy(&key->pubkey.x, &mQ->x)) != MP_OKAY) { goto error; }
if ((err = mp_copy(&key->pubkey.y, &mQ->y)) != MP_OKAY) { goto error; }
if ((err = mp_copy(&key->pubkey.z, &mQ->z)) != MP_OKAY) { goto error; }
if ((err = ecc_mulmod(&u2, mQ, mQ, &m, 0)) != CRYPT_OK) { goto done; }
/* find the montgomery mp */
if ((err = mp_montgomery_setup(&m, &mp)) != MP_OKAY) { goto error; }
/* add them */
if ((err = add_point(mQ, mG, mG, &m, mp)) != CRYPT_OK) { goto done; }
/* reduce */
if ((err = ecc_map(mG, &m, mp)) != CRYPT_OK) { goto done; }
/* v = X_x1 mod n */
if ((err = mp_mod(&mG->x, &p, &v)) != CRYPT_OK) { goto done; }
/* does v == r */
if (mp_cmp(&v, &r) == MP_EQ) {
*stat = 1;
}
/* clear up and return */
err = CRYPT_OK;
goto done;
error:
err = mpi_to_ltc_error(err);
done:
del_point(mG);
del_point(mQ);
mp_clear_multi(&r, &s, &v, &w, &u1, &u2, &p, &e, &m, NULL);
return err;
}
/**
* Kopiert die src Variabel in die target Variabel
* @param target Ziel-MPZ
* @param src Quell-MPZ
*/
void mp_copy(MPZ * target, MPZ src) {
if (target->array != src.array)
mp_allocate(target, src.len);
mp_set(target,src.array,src.sign);
}
/* Greatest Common Divisor using the binary method [Algorithm B, page 338, vol2 of TAOCP]
*/
int
mp_gcd (mp_int * a, mp_int * b, mp_int * c)
{
mp_int u, v, t;
int k, res, neg;
/* either zero than gcd is the largest */
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
return mp_copy (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
return mp_copy (a, c);
}
if (mp_iszero (a) == 1 && mp_iszero (b) == 1) {
mp_set (c, 1);
return MP_OKAY;
}
/* if both are negative they share (-1) as a common divisor */
neg = (a->sign == b->sign) ? a->sign : MP_ZPOS;
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
goto __U;
}
/* must be positive for the remainder of the algorithm */
u.sign = v.sign = MP_ZPOS;
if ((res = mp_init (&t)) != MP_OKAY) {
goto __V;
}
/* B1. Find power of two */
k = 0;
while (mp_iseven(&u) == 1 && mp_iseven(&v) == 1) {
++k;
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
goto __T;
}
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
goto __T;
}
}
/* B2. Initialize */
if (mp_isodd(&u) == 1) {
/* t = -v */
if ((res = mp_copy (&v, &t)) != MP_OKAY) {
goto __T;
}
t.sign = MP_NEG;
} else {
/* t = u */
if ((res = mp_copy (&u, &t)) != MP_OKAY) {
goto __T;
}
}
do {
/* B3 (and B4). Halve t, if even */
while (t.used != 0 && mp_iseven(&t) == 1) {
if ((res = mp_div_2 (&t, &t)) != MP_OKAY) {
goto __T;
}
}
/* B5. if t>0 then u=t otherwise v=-t */
if (t.used != 0 && t.sign != MP_NEG) {
if ((res = mp_copy (&t, &u)) != MP_OKAY) {
goto __T;
}
} else {
if ((res = mp_copy (&t, &v)) != MP_OKAY) {
goto __T;
}
v.sign = (v.sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
}
/* B6. t = u - v, if t != 0 loop otherwise terminate */
if ((res = mp_sub (&u, &v, &t)) != MP_OKAY) {
goto __T;
}
} while (mp_iszero(&t) == 0);
/* multiply by 2^k which we divided out at the beginning */
if ((res = mp_mul_2d (&u, k, &u)) != MP_OKAY) {
goto __T;
}
mp_exch (&u, c);
c->sign = neg;
res = MP_OKAY;
__T:
mp_clear (&t);
__V:
mp_clear (&u);
__U:
mp_clear (&v);
return res;
}
//http://numbers.computation.free.fr/Constants/Algorithms/splitting.html
int mp_acoth_binary_splitting(mp_int * q, mp_int * a, mp_int * b, mp_int * P,
mp_int * Q, mp_int * R)
{
int err;
mp_int p1, q1, r1, p2, q2, r2, t1, t2, one;
if ((err =
mp_init_multi(&p1, &q1, &r1, &p2, &q2, &r2, &t1, &t2, &one,
NULL)) != MP_OKAY) {
return err;
}
err = MP_OKAY;
mp_set(&one, 1);
if ((err = mp_sub(b, a, &t1)) != MP_OKAY) {
goto _ERR;
}
if (mp_cmp(&t1, &one) == MP_EQ) {
if ((err = mp_mul_2d(a, 1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_add_d(&t1, 3, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_set_int(P, 1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_sqr(q, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_mul(&t1, &t2, Q)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_copy(&t1, R)) != MP_OKAY) {
goto _ERR;
}
goto _ERR;
}
if ((err = mp_add(a, b, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_div_2d(&t1, 1, &t1, NULL)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_acoth_binary_splitting(q, a, &t1, &p1, &q1, &r1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_acoth_binary_splitting(q, &t1, b, &p2, &q2, &r2)) != MP_OKAY) {
goto _ERR;
}
//P = q2*p1 + r1*p2
if ((err = mp_mul(&q2, &p1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_mul(&r1, &p2, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mp_add(&t1, &t2, P)) != MP_OKAY) {
goto _ERR;
}
//Q = q1*q2
if ((err = mp_mul(&q1, &q2, Q)) != MP_OKAY) {
goto _ERR;
}
//R = r1*r2
if ((err = mp_mul(&r1, &r2, R)) != MP_OKAY) {
goto _ERR;
}
_ERR:
mp_clear_multi(&p1, &q1, &r1, &p2, &q2, &r2, &t1, &t2, &one, NULL);
return err;
}
/**
Import an ECC key from a binary packet, using user supplied domain params rather than one of the NIST ones
@param in The packet to import
@param inlen The length of the packet
@param key [out] The destination of the import
@param dp pointer to user supplied params; must be the same as the params used when exporting
@return CRYPT_OK if successful, upon error all allocated memory will be freed
*/
int ecc_import_ex(const unsigned char *in, unsigned long inlen, ecc_key *key, const ltc_ecc_set_type *dp)
{
unsigned long key_size;
unsigned char flags[1];
int err;
LTC_ARGCHK(in != NULL);
LTC_ARGCHK(key != NULL);
LTC_ARGCHK(ltc_mp.name != NULL);
/* init key */
if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, NULL) != CRYPT_OK) {
return CRYPT_MEM;
}
/* find out what type of key it is */
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, &flags,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
if (flags[0] == 1) {
/* private key */
key->type = PK_PRIVATE;
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_INTEGER, 1UL, key->k,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
} else {
/* public key */
key->type = PK_PUBLIC;
if ((err = der_decode_sequence_multi(in, inlen,
LTC_ASN1_BIT_STRING, 1UL, flags,
LTC_ASN1_SHORT_INTEGER, 1UL, &key_size,
LTC_ASN1_INTEGER, 1UL, key->pubkey.x,
LTC_ASN1_INTEGER, 1UL, key->pubkey.y,
LTC_ASN1_EOL, 0UL, NULL)) != CRYPT_OK) {
goto done;
}
}
if (dp == NULL) {
/* find the idx */
for (key->idx = 0; ltc_ecc_sets[key->idx].size && (unsigned long)ltc_ecc_sets[key->idx].size != key_size; ++key->idx);
if (ltc_ecc_sets[key->idx].size == 0) {
err = CRYPT_INVALID_PACKET;
goto done;
}
key->dp = <c_ecc_sets[key->idx];
} else {
key->idx = -1;
key->dp = dp;
}
/* set z */
if ((err = mp_set(key->pubkey.z, 1)) != CRYPT_OK) { goto done; }
/* is it a point on the curve? */
if ((err = is_point(key)) != CRYPT_OK) {
goto done;
}
/* we're good */
return CRYPT_OK;
done:
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
return err;
}
int ecc_make_key_ex(prng_state *prng, int wprng, ecc_key *key, const ltc_ecc_set_type *dp)
{
int err;
ecc_point *base;
void *prime, *order, *a;
unsigned char *buf;
int keysize, orderbits;
LTC_ARGCHK(key != NULL);
LTC_ARGCHK(ltc_mp.name != NULL);
LTC_ARGCHK(dp != NULL);
/* good prng? */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
key->idx = -1;
key->dp = dp;
keysize = dp->size;
/* allocate ram */
base = NULL;
buf = XMALLOC(ECC_MAXSIZE);
if (buf == NULL) {
return CRYPT_MEM;
}
/* make up random string */
if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
err = CRYPT_ERROR_READPRNG;
goto ERR_BUF;
}
/* setup the key variables */
if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, &prime, &order, &a, NULL)) != CRYPT_OK) {
goto ERR_BUF;
}
base = ltc_ecc_new_point();
if (base == NULL) {
err = CRYPT_MEM;
goto errkey;
}
/* read in the specs for this key */
if ((err = mp_read_radix(prime, (char *)key->dp->prime, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_radix(order, (char *)key->dp->order, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_radix(base->x, (char *)key->dp->Gx, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_radix(base->y, (char *)key->dp->Gy, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_set(base->z, 1)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_unsigned_bin(key->k, (unsigned char *)buf, keysize)) != CRYPT_OK) { goto errkey; }
/* ECC key pair generation according to FIPS-186-4 (B.4.2 Key Pair Generation by Testing Candidates):
* the generated private key k should be the range [1, order–1]
* a/ N = bitlen(order)
* b/ generate N random bits and convert them into big integer k
* c/ if k not in [1, order-1] go to b/
* e/ Q = k*G
*/
orderbits = mp_count_bits(order);
do {
if ((err = rand_bn_bits(key->k, orderbits, prng, wprng)) != CRYPT_OK) { goto errkey; }
} while (mp_iszero(key->k) || mp_cmp(key->k, order) != LTC_MP_LT);
/* make the public key */
if ((err = mp_read_radix(a, (char *)key->dp->A, 16)) != CRYPT_OK) { goto errkey; }
if ((err = ltc_mp.ecc_ptmul(key->k, base, &key->pubkey, a, prime, 1)) != CRYPT_OK) { goto errkey; }
key->type = PK_PRIVATE;
/* free up ram */
err = CRYPT_OK;
goto cleanup;
errkey:
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
cleanup:
ltc_ecc_del_point(base);
mp_clear_multi(prime, order, a, NULL);
ERR_BUF:
#ifdef LTC_CLEAN_STACK
zeromem(buf, ECC_MAXSIZE);
#endif
XFREE(buf);
return err;
}
SECStatus
DH_GenParam(int primeLen, DHParams **params)
{
PLArenaPool *arena;
DHParams *dhparams;
unsigned char *pb = NULL;
unsigned char *ab = NULL;
unsigned long counter = 0;
mp_int p, q, a, h, psub1, test;
mp_err err = MP_OKAY;
SECStatus rv = SECSuccess;
if (!params || primeLen < 0) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
arena = PORT_NewArena(NSS_FREEBL_DEFAULT_CHUNKSIZE);
if (!arena) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
return SECFailure;
}
dhparams = (DHParams *)PORT_ArenaZAlloc(arena, sizeof(DHParams));
if (!dhparams) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
PORT_FreeArena(arena, PR_TRUE);
return SECFailure;
}
dhparams->arena = arena;
MP_DIGITS(&p) = 0;
MP_DIGITS(&q) = 0;
MP_DIGITS(&a) = 0;
MP_DIGITS(&h) = 0;
MP_DIGITS(&psub1) = 0;
MP_DIGITS(&test) = 0;
CHECK_MPI_OK( mp_init(&p) );
CHECK_MPI_OK( mp_init(&q) );
CHECK_MPI_OK( mp_init(&a) );
CHECK_MPI_OK( mp_init(&h) );
CHECK_MPI_OK( mp_init(&psub1) );
CHECK_MPI_OK( mp_init(&test) );
/* generate prime with MPI, uses Miller-Rabin to generate strong prime. */
pb = PORT_Alloc(primeLen);
CHECK_SEC_OK( RNG_GenerateGlobalRandomBytes(pb, primeLen) );
pb[0] |= 0x80; /* set high-order bit */
pb[primeLen-1] |= 0x01; /* set low-order bit */
CHECK_MPI_OK( mp_read_unsigned_octets(&p, pb, primeLen) );
CHECK_MPI_OK( mpp_make_prime(&p, primeLen * 8, PR_TRUE, &counter) );
/* construct Sophie-Germain prime q = (p-1)/2. */
CHECK_MPI_OK( mp_sub_d(&p, 1, &psub1) );
CHECK_MPI_OK( mp_div_2(&psub1, &q) );
/* construct a generator from the prime. */
ab = PORT_Alloc(primeLen);
/* generate a candidate number a in p's field */
CHECK_SEC_OK( RNG_GenerateGlobalRandomBytes(ab, primeLen) );
CHECK_MPI_OK( mp_read_unsigned_octets(&a, ab, primeLen) );
/* force a < p (note that quot(a/p) <= 1) */
if ( mp_cmp(&a, &p) > 0 )
CHECK_MPI_OK( mp_sub(&a, &p, &a) );
do {
/* check that a is in the range [2..p-1] */
if ( mp_cmp_d(&a, 2) < 0 || mp_cmp(&a, &psub1) >= 0) {
/* a is outside of the allowed range. Set a=3 and keep going. */
mp_set(&a, 3);
}
/* if a**q mod p != 1 then a is a generator */
CHECK_MPI_OK( mp_exptmod(&a, &q, &p, &test) );
if ( mp_cmp_d(&test, 1) != 0 )
break;
/* increment the candidate and try again. */
CHECK_MPI_OK( mp_add_d(&a, 1, &a) );
} while (PR_TRUE);
MPINT_TO_SECITEM(&p, &dhparams->prime, arena);
MPINT_TO_SECITEM(&a, &dhparams->base, arena);
*params = dhparams;
cleanup:
mp_clear(&p);
mp_clear(&q);
mp_clear(&a);
mp_clear(&h);
mp_clear(&psub1);
mp_clear(&test);
if (pb) PORT_ZFree(pb, primeLen);
if (ab) PORT_ZFree(ab, primeLen);
if (err) {
MP_TO_SEC_ERROR(err);
rv = SECFailure;
}
if (rv)
PORT_FreeArena(arena, PR_TRUE);
return rv;
}
/**
Make a new ECC key
@param prng An active PRNG state
@param wprng The index of the PRNG you wish to use
@param keysize The keysize for the new key (in octets from 20 to 65 bytes)
@param key [out] Destination of the newly created key
@return CRYPT_OK if successful, upon error all allocated memory will be freed
*/
int ecc_make_key(prng_state *prng, int wprng, int keysize, ecc_key *key)
{
int x, err;
ecc_point *base;
void *prime;
unsigned char *buf;
LTC_ARGCHK(key != NULL);
LTC_ARGCHK(ltc_mp.name != NULL);
/* good prng? */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
/* find key size */
for (x = 0; (keysize > ltc_ecc_sets[x].size) && (ltc_ecc_sets[x].size != 0); x++);
keysize = ltc_ecc_sets[x].size;
if (keysize > ECC_MAXSIZE || ltc_ecc_sets[x].size == 0) {
return CRYPT_INVALID_KEYSIZE;
}
key->idx = x;
/* allocate ram */
base = NULL;
buf = XMALLOC(ECC_MAXSIZE);
if (buf == NULL) {
return CRYPT_MEM;
}
/* make up random string */
if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
err = CRYPT_ERROR_READPRNG;
goto LBL_ERR2;
}
/* setup the key variables */
if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, &prime, NULL)) != CRYPT_OK) {
goto done;
}
base = ltc_ecc_new_point();
if (base == NULL) {
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, prime, NULL);
err = CRYPT_MEM;
goto done;
}
/* read in the specs for this key */
if ((err = mp_read_radix(prime, (char *)ltc_ecc_sets[key->idx].prime, 16)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(base->x, (char *)ltc_ecc_sets[key->idx].Gx, 16)) != CRYPT_OK) { goto done; }
if ((err = mp_read_radix(base->y, (char *)ltc_ecc_sets[key->idx].Gy, 16)) != CRYPT_OK) { goto done; }
mp_set(base->z, 1);
if ((err = mp_read_unsigned_bin(key->k, (unsigned char *)buf, keysize)) != CRYPT_OK) { goto done; }
/* make the public key */
if ((err = ltc_mp.ecc_ptmul(key->k, base, &key->pubkey, prime, 1)) != CRYPT_OK) { goto done; }
key->type = PK_PRIVATE;
/* free up ram */
err = CRYPT_OK;
done:
ltc_ecc_del_point(base);
mp_clear(prime);
LBL_ERR2:
#ifdef LTC_CLEAN_STACK
zeromem(buf, ECC_MAXSIZE);
#endif
XFREE(buf);
return err;
}
int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
{
mp_int M[TAB_SIZE], res;
mp_digit buf, mp;
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
/* use a pointer to the reduction algorithm. This allows us to use
* one of many reduction algorithms without modding the guts of
* the code with if statements everywhere.
*/
int (*redux)(mp_int*,mp_int*,mp_digit);
/* find window size */
x = mp_count_bits (X);
if (x <= 7) {
winsize = 2;
} else if (x <= 36) {
winsize = 3;
} else if (x <= 140) {
winsize = 4;
} else if (x <= 450) {
winsize = 5;
} else if (x <= 1303) {
winsize = 6;
} else if (x <= 3529) {
winsize = 7;
} else {
winsize = 8;
}
#ifdef MP_LOW_MEM
if (winsize > 5) {
winsize = 5;
}
#endif
/* init M array */
/* init first cell */
if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
return err;
}
/* now init the second half of the array */
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
if ((err = mp_init_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;
}
}
/* determine and setup reduction code */
if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto LBL_M;
}
#else
err = MP_VAL;
goto LBL_M;
#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if ((((P->used * 2) + 1) < MP_WARRAY) &&
(P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
redux = fast_mp_montgomery_reduce;
} else
#endif
{
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
#else
err = MP_VAL;
goto LBL_M;
#endif
}
} else if (redmode == 1) {
#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
#else
err = MP_VAL;
goto LBL_M;
#endif
} else {
#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto LBL_M;
}
redux = mp_reduce_2k;
#else
err = MP_VAL;
goto LBL_M;
#endif
}
/* setup result */
if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
goto LBL_M;
}
/* create M table
*
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto LBL_RES;
}
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
goto LBL_RES;
}
#else
err = MP_VAL;
goto LBL_RES;
#endif
} else {
mp_set(&res, 1);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
goto LBL_RES;
}
}
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* create upper table */
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* set initial mode and bit cnt */
mode = 0;
bitcnt = 1;
buf = 0;
digidx = X->used - 1;
bitcpy = 0;
bitbuf = 0;
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
/* if digidx == -1 we are out of digits so break */
if (digidx == -1) {
break;
}
/* read next digit and reset bitcnt */
buf = X->dp[digidx--];
bitcnt = (int)DIGIT_BIT;
}
/* grab the next msb from the exponent */
y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
buf <<= (mp_digit)1;
/* if the bit is zero and mode == 0 then we ignore it
* These represent the leading zero bits before the first 1 bit
* in the exponent. Technically this opt is not required but it
* does lower the # of trivial squaring/reductions used
*/
if ((mode == 0) && (y == 0)) {
continue;
}
/* if the bit is zero and mode == 1 then we square */
if ((mode == 1) && (y == 0)) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
continue;
}
/* else we add it to the window */
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
if (bitcpy == winsize) {
/* ok window is filled so square as required and multiply */
/* square first */
for (x = 0; x < winsize; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* then multiply */
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
/* empty window and reset */
bitcpy = 0;
bitbuf = 0;
mode = 1;
}
}
/* if bits remain then square/multiply */
if ((mode == 2) && (bitcpy > 0)) {
/* square then multiply if the bit is set */
for (x = 0; x < bitcpy; x++) {
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
/* get next bit of the window */
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
}
}
if (redmode == 0) {
/* fixup result if Montgomery reduction is used
* recall that any value in a Montgomery system is
* actually multiplied by R mod n. So we have
* to reduce one more time to cancel out the factor
* of R.
*/
if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* swap res with Y */
mp_exch (&res, Y);
err = MP_OKAY;
LBL_RES:mp_clear (&res);
LBL_M:
mp_clear(&M[1]);
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear (&M[x]);
}
return err;
}
/*
** Performs an ECDH key derivation by computing the scalar point
** multiplication of privateValue and publicValue (with or without the
** cofactor) and returns the x-coordinate of the resulting elliptic
** curve point in derived secret. If successful, derivedSecret->data
** is set to the address of the newly allocated buffer containing the
** derived secret, and derivedSecret->len is the size of the secret
** produced. It is the caller's responsibility to free the allocated
** buffer containing the derived secret.
*/
SECStatus
ECDH_Derive(SECItem *publicValue,
ECParams *ecParams,
SECItem *privateValue,
PRBool withCofactor,
SECItem *derivedSecret)
{
SECStatus rv = SECFailure;
#ifndef NSS_DISABLE_ECC
unsigned int len = 0;
SECItem pointQ = { siBuffer, NULL, 0 };
mp_int k; /* to hold the private value */
mp_int cofactor;
mp_err err = MP_OKAY;
#if EC_DEBUG
int i;
#endif
if (!publicValue || !ecParams || !privateValue || !derivedSecret ||
!ecParams->name) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
/* Perform curve specific multiplication using ECMethod */
if (ecParams->fieldID.type == ec_field_plain) {
const ECMethod *method;
memset(derivedSecret, 0, sizeof(*derivedSecret));
derivedSecret = SECITEM_AllocItem(NULL, derivedSecret, ecParams->pointSize);
if (derivedSecret == NULL) {
PORT_SetError(SEC_ERROR_NO_MEMORY);
return SECFailure;
}
method = ec_get_method_from_name(ecParams->name);
if (method == NULL || method->validate == NULL ||
method->mul == NULL) {
PORT_SetError(SEC_ERROR_UNSUPPORTED_ELLIPTIC_CURVE);
return SECFailure;
}
if (method->validate(publicValue) != SECSuccess) {
PORT_SetError(SEC_ERROR_BAD_KEY);
return SECFailure;
}
return method->mul(derivedSecret, privateValue, publicValue);
}
/*
* We fail if the public value is the point at infinity, since
* this produces predictable results.
*/
if (ec_point_at_infinity(publicValue)) {
PORT_SetError(SEC_ERROR_BAD_KEY);
return SECFailure;
}
MP_DIGITS(&k) = 0;
memset(derivedSecret, 0, sizeof *derivedSecret);
len = (ecParams->fieldID.size + 7) >> 3;
pointQ.len = ecParams->pointSize;
if ((pointQ.data = PORT_Alloc(ecParams->pointSize)) == NULL)
goto cleanup;
CHECK_MPI_OK(mp_init(&k));
CHECK_MPI_OK(mp_read_unsigned_octets(&k, privateValue->data,
(mp_size)privateValue->len));
if (withCofactor && (ecParams->cofactor != 1)) {
/* multiply k with the cofactor */
MP_DIGITS(&cofactor) = 0;
CHECK_MPI_OK(mp_init(&cofactor));
mp_set(&cofactor, ecParams->cofactor);
CHECK_MPI_OK(mp_mul(&k, &cofactor, &k));
}
/* Multiply our private key and peer's public point */
if (ec_points_mul(ecParams, NULL, &k, publicValue, &pointQ) != SECSuccess) {
goto cleanup;
}
if (ec_point_at_infinity(&pointQ)) {
PORT_SetError(SEC_ERROR_BAD_KEY); /* XXX better error code? */
goto cleanup;
}
/* Allocate memory for the derived secret and copy
* the x co-ordinate of pointQ into it.
*/
SECITEM_AllocItem(NULL, derivedSecret, len);
memcpy(derivedSecret->data, pointQ.data + 1, len);
rv = SECSuccess;
#if EC_DEBUG
printf("derived_secret:\n");
for (i = 0; i < derivedSecret->len; i++)
printf("%02x:", derivedSecret->data[i]);
printf("\n");
#endif
cleanup:
mp_clear(&k);
if (err) {
MP_TO_SEC_ERROR(err);
}
if (pointQ.data) {
PORT_ZFree(pointQ.data, ecParams->pointSize);
}
#else
PORT_SetError(SEC_ERROR_UNSUPPORTED_KEYALG);
#endif /* NSS_DISABLE_ECC */
return rv;
}
/* makes a prime of at least k bits */
int
pprime (int k, int li, mp_int * p, mp_int * q)
{
mp_int a, b, c, n, x, y, z, v;
int res, ii;
static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
/* single digit ? */
if (k <= (int) DIGIT_BIT) {
mp_set (p, prime_digit ());
return MP_OKAY;
}
if ((res = mp_init (&c)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&v)) != MP_OKAY) {
goto LBL_C;
}
/* product of first 50 primes */
if ((res =
mp_read_radix (&v,
"19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
10)) != MP_OKAY) {
goto LBL_V;
}
if ((res = mp_init (&a)) != MP_OKAY) {
goto LBL_V;
}
/* set the prime */
mp_set (&a, prime_digit ());
if ((res = mp_init (&b)) != MP_OKAY) {
goto LBL_A;
}
if ((res = mp_init (&n)) != MP_OKAY) {
goto LBL_B;
}
if ((res = mp_init (&x)) != MP_OKAY) {
goto LBL_N;
}
if ((res = mp_init (&y)) != MP_OKAY) {
goto LBL_X;
}
if ((res = mp_init (&z)) != MP_OKAY) {
goto LBL_Y;
}
/* now loop making the single digit */
while (mp_count_bits (&a) < k) {
fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
fflush (stderr);
top:
mp_set (&b, prime_digit ());
/* now compute z = a * b * 2 */
if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */
goto LBL_Z;
}
if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */
goto LBL_Z;
}
if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
goto LBL_Z;
}
/* n = z + 1 */
if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */
goto LBL_Z;
}
/* check (n, v) == 1 */
if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
goto LBL_Z;
}
if (mp_cmp_d (&y, 1) != MP_EQ)
goto top;
/* now try base x=bases[ii] */
for (ii = 0; ii < li; ii++) {
mp_set (&x, bases[ii]);
/* compute x^a mod n */
if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */
goto LBL_Z;
}
/* if y == 1 loop */
if (mp_cmp_d (&y, 1) == MP_EQ)
continue;
/* now x^2a mod n */
if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
goto LBL_Z;
}
if (mp_cmp_d (&y, 1) == MP_EQ)
continue;
/* compute x^b mod n */
if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
goto LBL_Z;
}
/* if y == 1 loop */
if (mp_cmp_d (&y, 1) == MP_EQ)
continue;
/* now x^2b mod n */
if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
goto LBL_Z;
}
if (mp_cmp_d (&y, 1) == MP_EQ)
continue;
/* compute x^c mod n == x^ab mod n */
if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */
goto LBL_Z;
}
/* if y == 1 loop */
if (mp_cmp_d (&y, 1) == MP_EQ)
continue;
/* now compute (x^c mod n)^2 */
if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
goto LBL_Z;
}
/* y should be 1 */
if (mp_cmp_d (&y, 1) != MP_EQ)
continue;
break;
}
/* no bases worked? */
if (ii == li)
goto top;
{
char buf[4096];
mp_toradix(&n, buf, 10);
printf("Certificate of primality for:\n%s\n\n", buf);
mp_toradix(&a, buf, 10);
printf("A == \n%s\n\n", buf);
mp_toradix(&b, buf, 10);
printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
printf("----------------------------------------------------------------\n");
}
/* a = n */
mp_copy (&n, &a);
}
/* get q to be the order of the large prime subgroup */
mp_sub_d (&n, 1, q);
mp_div_2 (q, q);
mp_div (q, &b, q, NULL);
mp_exch (&n, p);
res = MP_OKAY;
LBL_Z:mp_clear (&z);
LBL_Y:mp_clear (&y);
LBL_X:mp_clear (&x);
LBL_N:mp_clear (&n);
LBL_B:mp_clear (&b);
LBL_A:mp_clear (&a);
LBL_V:mp_clear (&v);
LBL_C:mp_clear (&c);
return res;
}
/**
Create a DSA key
@param prng An active PRNG state
@param wprng The index of the PRNG desired
@param group_size Size of the multiplicative group (octets)
@param modulus_size Size of the modulus (octets)
@param key [out] Where to store the created key
@return CRYPT_OK if successful, upon error this function will free all allocated memory
*/
int dsa_make_key(prng_state *prng, int wprng, int group_size, int modulus_size, dsa_key *key)
{
void *tmp, *tmp2;
int err, res;
unsigned char *buf;
LTC_ARGCHK(key != NULL);
LTC_ARGCHK(ltc_mp.name != NULL);
/* check prng */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
/* check size */
if (group_size >= MDSA_MAX_GROUP || group_size <= 15 ||
group_size >= modulus_size || (modulus_size - group_size) >= MDSA_DELTA) {
return CRYPT_INVALID_ARG;
}
/* allocate ram */
buf = XMALLOC(MDSA_DELTA);
if (buf == NULL) {
return CRYPT_MEM;
}
/* init mp_ints */
if ((err = mp_init_multi(&tmp, &tmp2, &key->g, &key->q, &key->p, &key->x, &key->y, NULL)) != CRYPT_OK) {
XFREE(buf);
return err;
}
/* make our prime q */
if ((err = rand_prime(key->q, group_size, prng, wprng)) != CRYPT_OK) { goto error; }
/* double q */
if ((err = mp_add(key->q, key->q, tmp)) != CRYPT_OK) { goto error; }
/* now make a random string and multply it against q */
if (prng_descriptor[wprng].read(buf+1, modulus_size - group_size, prng) != (unsigned long)(modulus_size - group_size)) {
err = CRYPT_ERROR_READPRNG;
goto error;
}
/* force magnitude */
buf[0] |= 0xC0;
/* force even */
buf[modulus_size - group_size - 1] &= ~1;
if ((err = mp_read_unsigned_bin(tmp2, buf, modulus_size - group_size)) != CRYPT_OK) { goto error; }
if ((err = mp_mul(key->q, tmp2, key->p)) != CRYPT_OK) { goto error; }
if ((err = mp_add_d(key->p, 1, key->p)) != CRYPT_OK) { goto error; }
/* now loop until p is prime */
for (;;) {
if ((err = mp_prime_is_prime(key->p, 8, &res)) != CRYPT_OK) { goto error; }
if (res == LTC_MP_YES) break;
/* add 2q to p and 2 to tmp2 */
if ((err = mp_add(tmp, key->p, key->p)) != CRYPT_OK) { goto error; }
if ((err = mp_add_d(tmp2, 2, tmp2)) != CRYPT_OK) { goto error; }
}
/* now p = (q * tmp2) + 1 is prime, find a value g for which g^tmp2 != 1 */
mp_set(key->g, 1);
do {
if ((err = mp_add_d(key->g, 1, key->g)) != CRYPT_OK) { goto error; }
if ((err = mp_exptmod(key->g, tmp2, key->p, tmp)) != CRYPT_OK) { goto error; }
} while (mp_cmp_d(tmp, 1) == LTC_MP_EQ);
/* at this point tmp generates a group of order q mod p */
mp_exch(tmp, key->g);
/* so now we have our DH structure, generator g, order q, modulus p
Now we need a random exponent [mod q] and it's power g^x mod p
*/
do {
if (prng_descriptor[wprng].read(buf, group_size, prng) != (unsigned long)group_size) {
err = CRYPT_ERROR_READPRNG;
goto error;
}
if ((err = mp_read_unsigned_bin(key->x, buf, group_size)) != CRYPT_OK) { goto error; }
} while (mp_cmp_d(key->x, 1) != LTC_MP_GT);
if ((err = mp_exptmod(key->g, key->x, key->p, key->y)) != CRYPT_OK) { goto error; }
key->type = PK_PRIVATE;
key->qord = group_size;
#ifdef LTC_CLEAN_STACK
zeromem(buf, MDSA_DELTA);
#endif
err = CRYPT_OK;
goto done;
error:
mp_clear_multi(key->g, key->q, key->p, key->x, key->y, NULL);
done:
mp_clear_multi(tmp, tmp2, NULL);
XFREE(buf);
return err;
}
/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, A, B, C, D;
int res;
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
return res;
}
/* x = a, y = b */
if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (b, &y)) != MP_OKAY) {
goto LBL_ERR;
}
/* 2. [modified] if x,y are both even then return an error! */
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto LBL_ERR;
}
mp_set (&A, 1);
mp_set (&D, 1);
top:
/* 4. while u is even do */
while (mp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
goto LBL_ERR;
}
/* 4.2 if A or B is odd then */
if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* A = A/2, B = B/2 */
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 5. while v is even do */
while (mp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
goto LBL_ERR;
}
/* 5.2 if C or D is odd then */
if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, A = A - C, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, C = C - A, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero (&u) == 0)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
goto LBL_ERR;
}
/* if its too low */
while (mp_cmp_d(&C, 0) == MP_LT) {
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* too big */
while (mp_cmp_mag(&C, b) != MP_LT) {
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C is now the inverse */
mp_exch (&C, c);
res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
}
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
* Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
mp_int x, y, u, v, B, D;
int res, neg;
/* 2. [modified] b must be odd */
if (mp_iseven (b) == 1) {
return MP_VAL;
}
/* init all our temps */
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return res;
}
/* x == modulus, y == value to invert */
if ((res = mp_copy (b, &x)) != MP_OKAY) {
goto LBL_ERR;
}
/* we need y = |a| */
if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
goto LBL_ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
goto LBL_ERR;
}
mp_set (&D, 1);
top:
/* 4. while u is even do */
while (mp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
goto LBL_ERR;
}
/* 4.2 if B is odd then */
if (mp_isodd (&B) == 1) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* B = B/2 */
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 5. while v is even do */
while (mp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
goto LBL_ERR;
}
/* 5.2 if D is odd then */
if (mp_isodd (&D) == 1) {
/* D = (D-x)/2 */
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* 6. if u >= v then */
if (mp_cmp (&u, &v) != MP_LT) {
/* u = u - v, B = B - D */
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
goto LBL_ERR;
}
} else {
/* v - v - u, D = D - B */
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* if not zero goto step 4 */
if (mp_iszero (&u) == 0) {
goto top;
}
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d (&v, 1) != MP_EQ) {
res = MP_VAL;
goto LBL_ERR;
}
/* b is now the inverse */
neg = a->sign;
while (D.sign == MP_NEG) {
if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_exch (&D, c);
c->sign = neg;
res = MP_OKAY;
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
/*
** Performs an ECDH key derivation by computing the scalar point
** multiplication of privateValue and publicValue (with or without the
** cofactor) and returns the x-coordinate of the resulting elliptic
** curve point in derived secret. If successful, derivedSecret->data
** is set to the address of the newly allocated buffer containing the
** derived secret, and derivedSecret->len is the size of the secret
** produced. It is the caller's responsibility to free the allocated
** buffer containing the derived secret.
*/
SECStatus
ECDH_Derive(SECItem *publicValue,
ECParams *ecParams,
SECItem *privateValue,
PRBool withCofactor,
SECItem *derivedSecret)
{
SECStatus rv = SECFailure;
#ifndef NSS_DISABLE_ECC
unsigned int len = 0;
SECItem pointQ = {siBuffer, NULL, 0};
mp_int k; /* to hold the private value */
mp_int cofactor;
mp_err err = MP_OKAY;
#if EC_DEBUG
int i;
#endif
if (!publicValue || !ecParams || !privateValue ||
!derivedSecret) {
PORT_SetError(SEC_ERROR_INVALID_ARGS);
return SECFailure;
}
MP_DIGITS(&k) = 0;
memset(derivedSecret, 0, sizeof *derivedSecret);
len = (ecParams->fieldID.size + 7) >> 3;
pointQ.len = 2*len + 1;
if ((pointQ.data = PORT_Alloc(2*len + 1)) == NULL) goto cleanup;
CHECK_MPI_OK( mp_init(&k) );
CHECK_MPI_OK( mp_read_unsigned_octets(&k, privateValue->data,
(mp_size) privateValue->len) );
if (withCofactor && (ecParams->cofactor != 1)) {
/* multiply k with the cofactor */
MP_DIGITS(&cofactor) = 0;
CHECK_MPI_OK( mp_init(&cofactor) );
mp_set(&cofactor, ecParams->cofactor);
CHECK_MPI_OK( mp_mul(&k, &cofactor, &k) );
}
/* Multiply our private key and peer's public point */
if (ec_points_mul(ecParams, NULL, &k, publicValue, &pointQ) != SECSuccess)
goto cleanup;
if (ec_point_at_infinity(&pointQ)) {
PORT_SetError(SEC_ERROR_BAD_KEY); /* XXX better error code? */
goto cleanup;
}
/* Allocate memory for the derived secret and copy
* the x co-ordinate of pointQ into it.
*/
SECITEM_AllocItem(NULL, derivedSecret, len);
memcpy(derivedSecret->data, pointQ.data + 1, len);
rv = SECSuccess;
#if EC_DEBUG
printf("derived_secret:\n");
for (i = 0; i < derivedSecret->len; i++)
printf("%02x:", derivedSecret->data[i]);
printf("\n");
#endif
cleanup:
mp_clear(&k);
if (err) {
MP_TO_SEC_ERROR(err);
}
if (pointQ.data) {
PORT_ZFree(pointQ.data, 2*len + 1);
}
#else
PORT_SetError(SEC_ERROR_UNSUPPORTED_KEYALG);
#endif /* NSS_DISABLE_ECC */
return rv;
}
int ecc_test_shamir(void)
{
void *modulus, *mp, *kA, *kB, *rA, *rB;
ecc_point *G, *A, *B, *C1, *C2;
int x, y, z;
unsigned char buf[ECC_BUF_SIZE];
DO(mp_init_multi(&kA, &kB, &rA, &rB, &modulus, NULL));
LTC_ARGCHK((G = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((A = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((B = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((C1 = ltc_ecc_new_point()) != NULL);
LTC_ARGCHK((C2 = ltc_ecc_new_point()) != NULL);
for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
/* get the base point */
for (z = 0; ltc_ecc_sets[z].name; z++) {
if (sizes[z] < ltc_ecc_sets[z].size) break;
}
LTC_ARGCHK(ltc_ecc_sets[z].name != NULL);
/* load it */
DO(mp_read_radix(G->x, ltc_ecc_sets[z].Gx, 16));
DO(mp_read_radix(G->y, ltc_ecc_sets[z].Gy, 16));
DO(mp_set(G->z, 1));
DO(mp_read_radix(modulus, ltc_ecc_sets[z].prime, 16));
DO(mp_montgomery_setup(modulus, &mp));
/* do 100 random tests */
for (y = 0; y < 100; y++) {
/* pick a random r1, r2 */
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(rA, buf, sizes[x]));
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(rB, buf, sizes[x]));
/* compute rA * G = A */
DO(ltc_mp.ecc_ptmul(rA, G, A, modulus, 1));
/* compute rB * G = B */
DO(ltc_mp.ecc_ptmul(rB, G, B, modulus, 1));
/* pick a random kA, kB */
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(kA, buf, sizes[x]));
LTC_ARGCHK(yarrow_read(buf, sizes[x], &yarrow_prng) == sizes[x]);
DO(mp_read_unsigned_bin(kB, buf, sizes[x]));
/* now, compute kA*A + kB*B = C1 using the older method */
DO(ltc_mp.ecc_ptmul(kA, A, C1, modulus, 0));
DO(ltc_mp.ecc_ptmul(kB, B, C2, modulus, 0));
DO(ltc_mp.ecc_ptadd(C1, C2, C1, modulus, mp));
DO(ltc_mp.ecc_map(C1, modulus, mp));
/* now compute using mul2add */
DO(ltc_mp.ecc_mul2add(A, kA, B, kB, C2, modulus));
/* is they the sames? */
if ((mp_cmp(C1->x, C2->x) != LTC_MP_EQ) || (mp_cmp(C1->y, C2->y) != LTC_MP_EQ) || (mp_cmp(C1->z, C2->z) != LTC_MP_EQ)) {
fprintf(stderr, "ECC failed shamir test: size=%d, testno=%d\n", sizes[x], y);
return 1;
}
}
mp_montgomery_free(mp);
}
ltc_ecc_del_point(C2);
ltc_ecc_del_point(C1);
ltc_ecc_del_point(B);
ltc_ecc_del_point(A);
ltc_ecc_del_point(G);
mp_clear_multi(kA, kB, rA, rB, modulus, NULL);
return 0;
}
/* slower bit-bang division... also smaller */
int mp_div MPA(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
mp_int ta, tb, tq, q;
int res, n, n2;
/* is divisor zero ? */
if (mp_iszero (b) == 1) {
return MP_VAL;
}
/* if a < b then q=0, r = a */
if (mp_cmp_mag (a, b) == MP_LT) {
if (d != NULL) {
res = mp_copy (a, d);
} else {
res = MP_OKAY;
}
if (c != NULL) {
mp_zero (c);
}
return res;
}
/* init our temps */
if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
return res;
}
mp_set(&tq, 1);
n = mp_count_bits(a) - mp_count_bits(b);
if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
((res = mp_abs(b, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
goto LBL_ERR;
}
while (n-- >= 0) {
if (mp_cmp(&tb, &ta) != MP_GT) {
if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
goto LBL_ERR;
}
}
if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
goto LBL_ERR;
}
}
/* now q == quotient and ta == remainder */
n = a->sign;
n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
if (c != NULL) {
mp_exch(c, &q);
c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
}
if (d != NULL) {
mp_exch(d, &ta);
d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
}
LBL_ERR:
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
return res;
}
int ecc_make_key_ex(prng_state *prng, int wprng, ecc_key *key, const ltc_ecc_set_type *dp)
{
int err;
ecc_point *base;
void *prime;
unsigned char *buf;
int keysize;
LTC_ARGCHK(key != NULL);
LTC_ARGCHK(ltc_mp.name != NULL);
LTC_ARGCHK(dp != NULL);
/* good prng? */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
key->idx = -1;
key->dp = dp;
keysize = dp->size;
/* allocate ram */
base = NULL;
buf = XMALLOC(ECC_MAXSIZE);
if (buf == NULL) {
return CRYPT_MEM;
}
/* make up random string */
if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
err = CRYPT_ERROR_READPRNG;
goto ERR_BUF;
}
/* setup the key variables */
if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k, &prime, NULL)) != CRYPT_OK) {
goto ERR_BUF;
}
base = ltc_ecc_new_point();
if (base == NULL) {
err = CRYPT_MEM;
goto errkey;
}
/* read in the specs for this key */
if ((err = mp_read_radix(prime, (char *)key->dp->prime, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_radix(base->x, (char *)key->dp->Gx, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_radix(base->y, (char *)key->dp->Gy, 16)) != CRYPT_OK) { goto errkey; }
if ((err = mp_set(base->z, 1)) != CRYPT_OK) { goto errkey; }
if ((err = mp_read_unsigned_bin(key->k, (unsigned char *)buf, keysize)) != CRYPT_OK) { goto errkey; }
/* make the public key */
if ((err = ltc_mp.ecc_ptmul(key->k, base, &key->pubkey, prime, 1)) != CRYPT_OK) { goto errkey; }
key->type = PK_PRIVATE;
/* free up ram */
err = CRYPT_OK;
goto cleanup;
errkey:
mp_clear_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z, key->k, NULL);
cleanup:
ltc_ecc_del_point(base);
mp_clear(prime);
ERR_BUF:
#ifdef LTC_CLEAN_STACK
zeromem(buf, ECC_MAXSIZE);
#endif
XFREE(buf);
return err;
}
