prime.c

这个是RSA密钥对生成器

/*
    PRIME.C - primality-testing routines
    Copyright(C) 2002 by charry, [e-mail]
    RSAEURO - RSA Library compatible with RSAREF(tm) 2.0.

    Uses a small primes factor test and the Fermat Test to determine if
    the number is probable prime number.
 */

#include "rsaeuro.h"
#include "r_random.h"
#include "nn.h"
#include "prime.h"

#define SMALL_PRIME_COUNT 1027

static int probableprime PROTO_LIST ((NN_DIGIT *, unsigned int));

/* Generates a probable prime a between b and c such that a-1 is
   divisible by d.

   Assumes b < c, digits < MAX_NN_DIGITS.
   Returns RE_NEED_RANDOM if randomStruct not seeded, RE_DATA if
   unsuccessful.
 */

int GeneratePrime(a, b, c, d, digits, randomStruct)
NN_DIGIT *a, *b, *c, *d;
unsigned int digits;
R_RANDOM_STRUCT *randomStruct; /* random structure */
{
    int status;
    unsigned char block[MAX_NN_DIGITS * NN_DIGIT_LEN];
    NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];

    /* Generate random number between b and c. */

    status = R_GenerateBytes(block, digits * NN_DIGIT_LEN, randomStruct);
    if(status)
        return(status);

    NN_Decode(a, digits, block, digits * NN_DIGIT_LEN);
    NN_Sub(t, c, b, digits);
    NN_ASSIGN_DIGIT(u, 1, digits);
    NN_Add(t, t, u, digits);
    NN_Mod(a, a, digits, t, digits);
    NN_Add(a, a, b, digits);

    /* Adjust so that a-1 is divisible by d. */

    NN_Mod(t, a, digits, d, digits);
    NN_Sub(a, a, t, digits);
    NN_Add(a, a, u, digits);
    if(NN_Cmp(a, b, digits) < 0)
        NN_Add(a, a, d, digits);
    if(NN_Cmp(a, c, digits) > 0)
        NN_Sub(a, a, d, digits);

    /* Search to c in steps of d. */

    NN_Assign(t, c, digits);
    NN_Sub(t, t, d, digits);

    while(!probableprime (a, digits)) {
        if(NN_Cmp (a, t, digits) > 0)
            return(RE_DATA);
        NN_Add(a, a, d, digits);
    }

    return(ID_OK);
}

/* Returns nonzero iff a is a probable prime.

   Does small factor test and a fermat test witness 2.
 */

static int probableprime(a, aDigits)
NN_DIGIT *a;
unsigned int aDigits;
{

    int status;
    NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];

    /* This table can be reduced in size but the smaller
         the table the slower the testing.
     */

    static unsigned int SMALL_PRIMES[] = {
        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
    };

    unsigned int i;

    status = 1;

    NN_AssignZero(t, aDigits);

    /* Small Primes test, weed out junk numbers before slower Fermat's */

    for(i = 0; *(SMALL_PRIMES+i); i++) {
        *t = *(SMALL_PRIMES+i);
        if(aDigits == 1)
            if(NN_Cmp (a, t, 1) == 0)
                break;
        NN_Mod(t, a, aDigits, t, 1);
        if(NN_Zero (t, 1)) {
            status = 0;
            break;
        }
    }

    /* Clear sensitive information. */

    i = 0;
    R_memset((POINTER)t, 0, sizeof(t));

    /* Fermat's test for witness 2.
         (All primes pass the test, and nearly all composites fail.)
     */

    if(status) {
        NN_ASSIGN_DIGIT(t, 2, aDigits);
        NN_ModExp(u, t, a, aDigits, a, aDigits);

        status = NN_EQUAL(t, u, aDigits);

    /* Clear sensitive information. */

    R_memset((POINTER)u, 0, sizeof(u));
    }

    return(status ? TRUE : FALSE);
}