static int
tfm_rsa_private_calculate(fp_int * in, fp_int * p, fp_int * q,
fp_int * dmp1, fp_int * dmq1, fp_int * iqmp,
fp_int * out)
{
fp_int vp, vq, u;
fp_init_multi(&vp, &vq, &u, NULL);
/* vq = c ^ (d mod (q - 1)) mod q */
/* vp = c ^ (d mod (p - 1)) mod p */
fp_mod(in, p, &u);
fp_exptmod(&u, dmp1, p, &vp);
fp_mod(in, q, &u);
fp_exptmod(&u, dmq1, q, &vq);
/* C2 = 1/q mod p (iqmp) */
/* u = (vp - vq)C2 mod p. */
fp_sub(&vp, &vq, &u);
if (fp_isneg(&u))
fp_add(&u, p, &u);
fp_mul(&u, iqmp, &u);
fp_mod(&u, p, &u);
/* c ^ d mod n = vq + u q */
fp_mul(&u, q, &u);
fp_add(&u, &vq, out);
fp_zero_multi(&vp, &vq, &u, NULL);
return 0;
}
/* d = a - b (mod c) */
int fp_submod(fp_int *a, fp_int *b, fp_int *c, fp_int *d)
{
fp_int tmp;
fp_zero(&tmp);
fp_sub(a, b, &tmp);
return fp_mod(&tmp, c, d);
}
/* c = (a, b) */
void fp_gcd(fp_int *a, fp_int *b, fp_int *c)
{
fp_int u, v, r;
/* either zero than gcd is the largest */
if (fp_iszero (a) == 1 && fp_iszero (b) == 0) {
fp_abs (b, c);
return;
}
if (fp_iszero (a) == 0 && fp_iszero (b) == 1) {
fp_abs (a, c);
return;
}
/* optimized. At this point if a == 0 then
* b must equal zero too
*/
if (fp_iszero (a) == 1) {
fp_zero(c);
return;
}
/* sort inputs */
if (fp_cmp_mag(a, b) != FP_LT) {
fp_init_copy(&u, a);
fp_init_copy(&v, b);
} else {
fp_init_copy(&u, b);
fp_init_copy(&v, a);
}
fp_zero(&r);
while (fp_iszero(&v) == FP_NO) {
fp_mod(&u, &v, &r);
fp_copy(&v, &u);
fp_copy(&r, &v);
}
fp_copy(&u, c);
}
static int
tfm_rsa_generate_key(RSA *rsa, int bits, BIGNUM *e, BN_GENCB *cb)
{
fp_int el, p, q, n, d, dmp1, dmq1, iqmp, t1, t2, t3;
int counter, ret, bitsp;
if (bits < 789)
return -1;
bitsp = (bits + 1) / 2;
ret = -1;
fp_init_multi(&el, &p, &q, &n, &n, &d, &dmp1, &dmq1, &iqmp, &t1, &t2, &t3, NULL);
BN2mpz(&el, e);
/* generate p and q so that p != q and bits(pq) ~ bits */
counter = 0;
do {
BN_GENCB_call(cb, 2, counter++);
CHECK(random_num(&p, bitsp), 0);
CHECK(fp_find_prime(&p), FP_YES);
fp_sub_d(&p, 1, &t1);
fp_gcd(&t1, &el, &t2);
} while(fp_cmp_d(&t2, 1) != 0);
BN_GENCB_call(cb, 3, 0);
counter = 0;
do {
BN_GENCB_call(cb, 2, counter++);
CHECK(random_num(&q, bits - bitsp), 0);
CHECK(fp_find_prime(&q), FP_YES);
if (fp_cmp(&p, &q) == 0) /* don't let p and q be the same */
continue;
fp_sub_d(&q, 1, &t1);
fp_gcd(&t1, &el, &t2);
} while(fp_cmp_d(&t2, 1) != 0);
/* make p > q */
if (fp_cmp(&p, &q) < 0) {
fp_int c;
fp_copy(&p, &c);
fp_copy(&q, &p);
fp_copy(&c, &q);
}
BN_GENCB_call(cb, 3, 1);
/* calculate n, n = p * q */
fp_mul(&p, &q, &n);
/* calculate d, d = 1/e mod (p - 1)(q - 1) */
fp_sub_d(&p, 1, &t1);
fp_sub_d(&q, 1, &t2);
fp_mul(&t1, &t2, &t3);
fp_invmod(&el, &t3, &d);
/* calculate dmp1 dmp1 = d mod (p-1) */
fp_mod(&d, &t1, &dmp1);
/* calculate dmq1 dmq1 = d mod (q-1) */
fp_mod(&d, &t2, &dmq1);
/* calculate iqmp iqmp = 1/q mod p */
fp_invmod(&q, &p, &iqmp);
/* fill in RSA key */
rsa->e = mpz2BN(&el);
rsa->p = mpz2BN(&p);
rsa->q = mpz2BN(&q);
rsa->n = mpz2BN(&n);
rsa->d = mpz2BN(&d);
rsa->dmp1 = mpz2BN(&dmp1);
rsa->dmq1 = mpz2BN(&dmq1);
rsa->iqmp = mpz2BN(&iqmp);
ret = 1;
out:
fp_zero_multi(&el, &p, &q, &n, &d, &dmp1,
&dmq1, &iqmp, &t1, &t2, &t3, NULL);
return ret;
}
static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
{
fp_int x, y, u, v, A, B, C, D;
int res;
/* b cannot be negative */
if (b->sign == FP_NEG || fp_iszero(b) == 1) {
return FP_VAL;
}
/* init temps */
fp_init(&x); fp_init(&y);
fp_init(&u); fp_init(&v);
fp_init(&A); fp_init(&B);
fp_init(&C); fp_init(&D);
/* x = a, y = b */
if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
return res;
}
fp_copy(b, &y);
/* 2. [modified] if x,y are both even then return an error! */
if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
return FP_VAL;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
fp_copy (&x, &u);
fp_copy (&y, &v);
fp_set (&A, 1);
fp_set (&D, 1);
top:
/* 4. while u is even do */
while (fp_iseven (&u) == 1) {
/* 4.1 u = u/2 */
fp_div_2 (&u, &u);
/* 4.2 if A or B is odd then */
if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
/* A = (A+y)/2, B = (B-x)/2 */
fp_add (&A, &y, &A);
fp_sub (&B, &x, &B);
}
/* A = A/2, B = B/2 */
fp_div_2 (&A, &A);
fp_div_2 (&B, &B);
}
/* 5. while v is even do */
while (fp_iseven (&v) == 1) {
/* 5.1 v = v/2 */
fp_div_2 (&v, &v);
/* 5.2 if C or D is odd then */
if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
/* C = (C+y)/2, D = (D-x)/2 */
fp_add (&C, &y, &C);
fp_sub (&D, &x, &D);
}
/* C = C/2, D = D/2 */
fp_div_2 (&C, &C);
fp_div_2 (&D, &D);
}
/* 6. if u >= v then */
if (fp_cmp (&u, &v) != FP_LT) {
/* u = u - v, A = A - C, B = B - D */
fp_sub (&u, &v, &u);
fp_sub (&A, &C, &A);
fp_sub (&B, &D, &B);
} else {
/* v - v - u, C = C - A, D = D - B */
fp_sub (&v, &u, &v);
fp_sub (&C, &A, &C);
fp_sub (&D, &B, &D);
}
/* if not zero goto step 4 */
if (fp_iszero (&u) == 0)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (fp_cmp_d (&v, 1) != FP_EQ) {
return FP_VAL;
}
/* if its too low */
while (fp_cmp_d(&C, 0) == FP_LT) {
fp_add(&C, b, &C);
}
/* too big */
while (fp_cmp_mag(&C, b) != FP_LT) {
fp_sub(&C, b, &C);
}
/* C is now the inverse */
fp_copy(&C, c);
return FP_OKAY;
}
