Problem - Kevin Tafuro

static int passes_rabin_miller_once(BIGNUM *p) {
BIGNUM a, m, z, tmp;
BN_CTX *ctx;
unsigned int b, i;
/* Initialize a, m, z and tmp properly. */
BN_init(&a);
BN_init(&m);
BN_init(&z);
BN_init(&tmp);
ctx = BN_CTX_new( );
b = calc_b_and_m(p, &m);
/* a is a random number less than p: */
if (!BN_rand_range(&a, p)) abort( );
/* z = a^m mod p. */
if (!BN_mod_exp(&z, &a, &m, p, ctx)) abort( );
/* if z = 1 at the start, pass. */
if (BN_is_one(&z)) return 1;
for (i = 0; i < b; i++) {
if (BN_is_one(&z)) return 0;
/* if z = p-1, pass! */
BN_copy(&tmp, &z);
if (!BN_add_word(&tmp, 1)) abort( );
if (!BN_cmp(&tmp, p)) return 1;
/* z = z^2 mod p */
BN_mod_sqr(&tmp, &z, p, ctx);
BN_copy(&z, &tmp);
}
/* if z = p-1, pass! */
BN_copy(&tmp, &z);
if (!BN_add_word(&tmp, 1)) abort( );
if (!BN_cmp(&tmp, p)) return 1;
/* Fail! */
return 0;
}
/* b = How many times does 2 divide p - 1? This gets returned.
* m is (p-1)/(2^b).
*/
static unsigned int calc_b_and_m(BIGNUM *p, BIGNUM *x) {
unsigned int b;
if (!BN_copy(x, p)) abort( );
if (!BN_sub_word(x, 1)) abort( );
326 | Chapter 7: Public Key Cryptography
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