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ultimatepp/uppdev/rsa/rsa.cpp
cxl 351994a6cc Adding uppdev.... 
git-svn-id: svn://ultimatepp.org/upp/trunk@328 f0d560ea-af0d-0410-9eb7-867de7ffcac7
2008-08-15 08:36:24 +00:00

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#include "includes.h"
#include <gmp.h>
#include <xmalloc.h>
int rsa_verbose = 1;
#define MAX_PRIMES_IN_TABLE 1050 /* must be more than # primes */
static const unsigned int small_primes[MAX_PRIMES_IN_TABLE + 1] =
{ /* 2 is eliminated by trying only odd numbers. */
3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89,
97, 101, 103, 107, 109, 113, 127, 131,
137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223,
227, 229, 233, 239, 241, 251, 257, 263,
269, 271, 277, 281, 283, 293, 307, 311,
313, 317, 331, 337, 347, 349, 353, 359,
367, 373, 379, 383, 389, 397, 401, 409,
419, 421, 431, 433, 439, 443, 449, 457,
461, 463, 467, 479, 487, 491, 499, 503,
509, 521, 523, 541, 547, 557, 563, 569,
571, 577, 587, 593, 599, 601, 607, 613,
617, 619, 631, 641, 643, 647, 653, 659,
661, 673, 677, 683, 691, 701, 709, 719,
727, 733, 739, 743, 751, 757, 761, 769,
773, 787, 797, 809, 811, 821, 823, 827,
829, 839, 853, 857, 859, 863, 877, 881,
883, 887, 907, 911, 919, 929, 937, 941,
947, 953, 967, 971, 977, 983, 991, 997,
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049,
1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097,
1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283,
1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423,
1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459,
1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619,
1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,
1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949,
1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003,
2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203,
2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311,
2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377,
2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,
2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579,
2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657,
2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693,
2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801,
2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861,
2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167,
3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301,
3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347,
3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491,
3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541,
3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797,
3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863,
3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923,
3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003,
4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129,
4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259,
4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337,
4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481,
4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547,
4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621,
4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673,
4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813,
4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909,
4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967,
4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011,
5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233,
5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309,
5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399,
5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507,
5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573,
5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653,
5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711,
5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849,
5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007,
6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073,
6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211,
6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271,
6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329,
6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379,
6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563,
6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637,
6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779,
6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907,
6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971,
6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027,
7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121,
7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253,
7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349,
7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457,
7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621,
7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691,
7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757,
7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853,
7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009,
8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087,
8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161,
8167, 8171, 8179, 8191,
0};
/* Generate a random number of the desired number of bits. */
void rsa_random_integer(MP_INT *ret, RandomState *state, unsigned int bits)
{
unsigned int bytes = (bits + 7) / 8;
char *str = xmalloc(bytes * 2 + 1);
unsigned int i;
/* We first create a random hex number of the desired size, and then
convert it to a mp-int. */
for (i = 0; i < bytes; i++)
sprintf(str + 2 * i, "%02x", random_get_byte(state));
/* Convert it to the internal representation. */
if (mpz_set_str(ret, str, 16) < 0)
fatal("Intenal error, mpz_set_str returned error");
/* Clear extra data. */
memset(str, 0, 2 * bytes);
xfree(str);
/* Reduce it to the desired number of bits. */
mpz_mod_2exp(ret, ret, bits);
}
/* Returns a prime number of the specified number of bits. The number
will have the highest bit set and two lowest bits set. */
void rsa_random_prime(MP_INT *ret, RandomState *state, unsigned int bits)
{
MP_INT start, aux;
unsigned int num_primes;
int *moduli;
long difference;
mpz_init(&start);
mpz_init(&aux);
retry:
/* Pick a random integer of the appropriate size. */
rsa_random_integer(&start, state, bits);
/* Set the two highest bits. */
mpz_set_ui(&aux, 3);
mpz_mul_2exp(&aux, &aux, bits - 2);
mpz_ior(&start, &start, &aux);
/* Set the lowest bit to make it odd. */
mpz_set_ui(&aux, 1);
mpz_ior(&start, &start, &aux);
/* Initialize moduli of the small primes with respect to the given
random number. */
moduli = xmalloc(MAX_PRIMES_IN_TABLE * sizeof(moduli[0]));
if (bits < 16)
num_primes = 0; /* Don\'t use the table for very small numbers. */
else
{
for (num_primes = 0; small_primes[num_primes] != 0; num_primes++)
{
mpz_mod_ui(&aux, &start, small_primes[num_primes]);
moduli[num_primes] = mpz_get_ui(&aux);
}
}
/* Look for numbers that are not evenly divisible by any of the small
primes. */
for (difference = 0; ; difference += 2)
{
unsigned int i;
if (difference > 0x70000000)
{ /* Should never happen, I think... */
if (rsa_verbose)
fprintf(stderr,
"rsa_random_prime: failed to find a prime, retrying.\n");
xfree(moduli);
goto retry;
}
/* Check if it is a multiple of any small prime. Note that this
updates the moduli into negative values as difference grows. */
for (i = 0; i < num_primes; i++)
{
while (moduli[i] + difference >= small_primes[i])
moduli[i] -= small_primes[i];
if (moduli[i] + difference == 0)
break;
}
if (i < num_primes)
continue; /* Multiple of a known prime. */
/* It passed the small prime test (not divisible by any of them). */
if (rsa_verbose)
{
fprintf(stderr, ".");
}
/* Compute the number in question. */
mpz_add_ui(ret, &start, difference);
/* Perform the fermat test for witness 2. This means:
it is not prime if 2^n mod n != 2. */
mpz_set_ui(&aux, 2);
mpz_powm(&aux, &aux, ret, ret);
if (mpz_cmp_ui(&aux, 2) == 0)
{
/* Passed the fermat test for witness 2. */
if (rsa_verbose)
{
fprintf(stderr, "+");
}
/* Perform a more tests. These are probably unnecessary. */
if (mpz_probab_prime_p(ret, 20))
break; /* It is a prime with probability 1 - 2^-40. */
}
}
/* Found a (probable) prime. It is in ret. */
if (rsa_verbose)
{
fprintf(stderr, "+ (distance %ld)\n", difference);
}
/* Free the small prime moduli; they are no longer needed. */
xfree(moduli);
/* Sanity check: does it still have the high bit set (we might have
wrapped around)? */
mpz_div_2exp(&aux, ret, bits - 1);
if (mpz_get_ui(&aux) != 1)
{
if (rsa_verbose)
fprintf(stderr, "rsa_random_prime: high bit not set, retrying.\n");
goto retry;
}
mpz_clear(&start);
mpz_clear(&aux);
/* Return value already set in ret. */
}
/* Computes the multiplicative inverse of a number using Euclids algorithm.
Computes x such that a * x mod n = 1, where 0 < a < n. */
static void mpz_mod_inverse(MP_INT *x, MP_INT *a, MP_INT *n)
{
MP_INT g0, g1, v0, v1, div, mod, aux;
mpz_init_set(&g0, n);
mpz_init_set(&g1, a);
mpz_init_set_ui(&v0, 0);
mpz_init_set_ui(&v1, 1);
mpz_init(&div);
mpz_init(&mod);
mpz_init(&aux);
while (mpz_cmp_ui(&g1, 0) != 0)
{
mpz_divmod(&div, &mod, &g0, &g1);
mpz_mul(&aux, &div, &v1);
mpz_sub(&aux, &v0, &aux);
mpz_set(&v0, &v1);
mpz_set(&v1, &aux);
mpz_set(&g0, &g1);
mpz_set(&g1, &mod);
}
if (mpz_cmp_ui(&v0, 0) < 0)
mpz_add(x, &v0, n);
else
mpz_set(x, &v0);
mpz_clear(&g0);
mpz_clear(&g1);
mpz_clear(&v0);
mpz_clear(&v1);
mpz_clear(&div);
mpz_clear(&mod);
mpz_clear(&aux);
}
/* Given mutual primes p and q, derives RSA key components n, e, d, and u.
The exponent e will be at least ebits bits in size.
p must be smaller than q. */
static void derive_rsa_keys(MP_INT *n, MP_INT *e, MP_INT *d, MP_INT *u,
MP_INT *p, MP_INT *q,
unsigned int ebits)
{
MP_INT p_minus_1, q_minus_1, aux, phi, G, F;
assert(mpz_cmp(p, q) < 0);
mpz_init(&p_minus_1);
mpz_init(&q_minus_1);
mpz_init(&aux);
mpz_init(&phi);
mpz_init(&G);
mpz_init(&F);
/* Compute p-1 and q-1. */
mpz_sub_ui(&p_minus_1, p, 1);
mpz_sub_ui(&q_minus_1, q, 1);
/* phi = (p - 1) * (q - 1); the number of positive integers less than p*q
that are relatively prime to p*q. */
mpz_mul(&phi, &p_minus_1, &q_minus_1);
/* G is the number of "spare key sets" for a given modulus n. The smaller
G is, the better. The smallest G can get is 2. */
mpz_gcd(&G, &p_minus_1, &q_minus_1);
if (rsa_verbose)
{
if (mpz_cmp_ui(&G, 100) >= 0)
{
fprintf(stderr, "Warning: G=");
mpz_out_str(stdout, 10, &G);
fprintf(stderr, " is large (many spare key sets); key may be bad!\n");
}
}
/* F = phi / G; the number of relative prime numbers per spare key set. */
mpz_div(&F, &phi, &G);
/* Find a suitable e (the public exponent). */
mpz_set_ui(e, 1);
mpz_mul_2exp(e, e, ebits);
mpz_sub_ui(e, e, 1); /* make lowest bit 1, and substract 2. */
/* Keep adding 2 until it is relatively prime to (p-1)(q-1). */
do
{
mpz_add_ui(e, e, 2);
mpz_gcd(&aux, e, &phi);
}
while (mpz_cmp_ui(&aux, 1) != 0);
/* d is the multiplicative inverse of e, mod F. Could also be mod
(p-1)(q-1); however, we try to choose the smallest possible d. */
mpz_mod_inverse(d, e, &F);
/* u is the multiplicative inverse of p, mod q, if p < q. It is used
when doing private key RSA operations using the chinese remainder
theorem method. */
mpz_mod_inverse(u, p, q);
/* n = p * q (the public modulus). */
mpz_mul(n, p, q);
/* Clear auxiliary variables. */
mpz_clear(&p_minus_1);
mpz_clear(&q_minus_1);
mpz_clear(&aux);
mpz_clear(&phi);
mpz_clear(&G);
mpz_clear(&F);
}
/* Generates RSA public and private keys. This initializes the data
structures; they should be freed with rsa_clear_private_key and
rsa_clear_public_key. */
void rsa_generate_key(RSAPrivateKey *prv, RSAPublicKey *pub,
RandomState *state, unsigned int bits)
{
MP_INT test, aux;
unsigned int pbits, qbits;
int ret;
mpz_init(&prv->q);
mpz_init(&prv->p);
mpz_init(&prv->e);
mpz_init(&prv->d);
mpz_init(&prv->u);
mpz_init(&prv->n);
mpz_init(&test);
mpz_init(&aux);
/* Compute the number of bits in each prime. */
pbits = bits / 2;
qbits = bits - pbits;
#ifndef RSAREF
retry0:
#endif /* !RSAREF */
if (rsa_verbose)
{
fprintf(stderr, "Generating p: ");
}
/* Generate random number p. */
rsa_random_prime(&prv->p, state, pbits);
retry:
if (rsa_verbose)
{
fprintf(stderr, "Generating q: ");
}
/* Generate random number q. */
rsa_random_prime(&prv->q, state, qbits);
/* Sort them so that p < q. */
ret = mpz_cmp(&prv->p, &prv->q);
if (ret == 0)
{
if (rsa_verbose)
fprintf(stderr, "Generated the same prime twice!\n");
goto retry;
}
if (ret > 0)
{
mpz_set(&aux, &prv->p);
mpz_set(&prv->p, &prv->q);
mpz_set(&prv->q, &aux);
}
/* Make sure that p and q are not too close together (I am not sure if this
is important). */
mpz_sub(&aux, &prv->q, &prv->p);
mpz_div_2exp(&test, &prv->q, 10);
if (mpz_cmp(&aux, &test) < 0)
{
if (rsa_verbose)
fprintf(stderr, "The primes are too close together.\n");
goto retry;
}
/* Make certain p and q are relatively prime (in case one or both were false
positives... Though this is quite impossible). */
mpz_gcd(&aux, &prv->p, &prv->q);
if (mpz_cmp_ui(&aux, 1) != 0)
{
if (rsa_verbose)
fprintf(stderr, "The primes are not relatively prime!\n");
goto retry;
}
/* Derive the RSA private key from the primes. */
if (rsa_verbose)
fprintf(stderr, "Computing the keys...\n");
derive_rsa_keys(&prv->n, &prv->e, &prv->d, &prv->u, &prv->p, &prv->q, 5);
prv->bits = bits;
/* Initialize the public key with public data from the private key. */
pub->bits = bits;
mpz_init_set(&pub->n, &prv->n);
mpz_init_set(&pub->e, &prv->e);
#ifndef RSAREF /* I don't want to kludge these to work with RSAREF. */
/* Test that the key really works. This should never fail (I think). */
if (rsa_verbose)
fprintf(stderr, "Testing the keys...\n");
rsa_random_integer(&test, state, bits);
mpz_mod(&test, &test, &pub->n); /* must be less than n. */
rsa_private(&aux, &test, prv);
rsa_public(&aux, &aux, pub);
if (mpz_cmp(&aux, &test) != 0)
{
if (rsa_verbose)
fprintf(stderr, "**** private+public failed to decrypt.\n");
goto retry0;
}
rsa_public(&aux, &test, pub);
rsa_private(&aux, &aux, prv);
if (mpz_cmp(&aux, &test) != 0)
{
if (rsa_verbose)
fprintf(stderr, "**** public+private failed to decrypt.\n");
goto retry0;
}
#endif /* !RSAREF */
mpz_clear(&aux);
mpz_clear(&test);
if (rsa_verbose)
fprintf(stderr, "Key generation complete.\n");
}
/* Frees any memory associated with the private key. */
void rsa_clear_private_key(RSAPrivateKey *prv)
{
prv->bits = 0;
mpz_clear(&prv->n);
mpz_clear(&prv->e);
mpz_clear(&prv->d);
mpz_clear(&prv->u);
mpz_clear(&prv->p);
mpz_clear(&prv->q);
}
/* Frees any memory associated with the public key. */
void rsa_clear_public_key(RSAPublicKey *pub)
{
pub->bits = 0;
mpz_clear(&pub->e);
mpz_clear(&pub->n);
}
#ifndef RSAREF
/* Performs a private-key RSA operation (encrypt/decrypt). The computation
is done using the Chinese Remainder Theorem, which is faster than
direct modular exponentiation. */
void rsa_private(MP_INT *output, MP_INT *input, RSAPrivateKey *prv)
{
MP_INT dp, dq, p2, q2, k;
/* Initialize temporary variables. */
mpz_init(&dp);
mpz_init(&dq);
mpz_init(&p2);
mpz_init(&q2);
mpz_init(&k);
/* Compute dp = d mod p-1. */
mpz_sub_ui(&dp, &prv->p, 1);
mpz_mod(&dp, &prv->d, &dp);
/* Compute dq = d mod q-1. */
mpz_sub_ui(&dq, &prv->q, 1);
mpz_mod(&dq, &prv->d, &dq);
/* Compute p2 = (input mod p) ^ dp mod p. */
mpz_mod(&p2, input, &prv->p);
mpz_powm(&p2, &p2, &dp, &prv->p);
/* Compute q2 = (input mod q) ^ dq mod q. */
mpz_mod(&q2, input, &prv->q);
mpz_powm(&q2, &q2, &dq, &prv->q);
/* Compute k = ((q2 - p2) mod q) * u mod q. */
mpz_sub(&k, &q2, &p2);
mpz_mul(&k, &k, &prv->u);
mpz_mmod(&k, &k, &prv->q);
/* Compute output = p2 + p * k. */
mpz_mul(output, &prv->p, &k);
mpz_add(output, output, &p2);
/* Clear temporary variables. */
mpz_clear(&dp);
mpz_clear(&dq);
mpz_clear(&p2);
mpz_clear(&q2);
mpz_clear(&k);
}
/* Performs a public-key RSA operation (encrypt/decrypt). */
void rsa_public(MP_INT *output, MP_INT *input, RSAPublicKey *pub)
{
mpz_powm(output, input, &pub->e, &pub->n);
}
#endif /* !RSAREF */
/* Special realloc that zeroes the old memory before freeing it. */
static void *rsa_realloc(void *ptr, size_t old_size, size_t new_size)
{
int s;
void *p = xmalloc(new_size);
s = old_size;
if (old_size > new_size)
s = new_size;
memcpy(p, ptr, s);
memset(ptr, 0, old_size);
xfree(ptr);
return p;
}
/* Special free that zeroes the memory before freeing it. */
static void rsa_free(void *ptr, size_t size)
{
memset(ptr, 0, size);
xfree(ptr);
}
/* Sets MP_INT memory allocation routines to ones that clear any memory
when freed. */
void rsa_set_mp_memory_allocation(void)
{
mp_set_memory_functions(xmalloc, rsa_realloc, rsa_free);
}
/* Set whether to output verbose messages during key generation. */
void rsa_set_verbose(int verbose)
{
rsa_verbose = verbose;
}
/* program ends */
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