Algoritma RSA di C??!!

oke, kalau udah baca keterangan dan algoritma RSA,, nih saya dapet surce code untuk implementasi di C,, tapi saya juga blom ngerti2 amat,, sedang saya pelajari ^_^ Moga-moga berguna yuph..
C implementation:

#include “includes.h”

#include

#include

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 > 0×70000000)

{ /* 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(φ);

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(φ, &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, φ, &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, φ);

}

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(φ);

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 */