paillier_common/
keygen.rs

1//! Key generation following standard recommendations.
2
3use rust_bigint::traits::{BitManipulation, Modulo, NumberTests, Samplable};
4#[cfg(feature = "num_bigint")]
5use num_integer::Integer;
6#[cfg(feature = "num_bigint")]
7use num_traits::{One, Zero};
8
9use crate::traits::*;
10use crate::{BigInt, Keypair, Paillier};
11
12impl KeyGeneration<Keypair> for Paillier {
13    fn keypair_with_modulus_size(bit_length: usize) -> Keypair {
14        let p = BigInt::sample_prime(bit_length / 2);
15        let q = BigInt::sample_prime(bit_length / 2);
16        Keypair { p, q }
17    }
18
19    fn keypair_safe_primes_with_modulus_size(bit_length: usize) -> Keypair {
20        let p = BigInt::sample_safe_prime(bit_length / 2);
21        let q = BigInt::sample_safe_prime(bit_length / 2);
22        Keypair { p, q }
23    }
24}
25
26pub trait PrimeSampable {
27    fn sample_prime(bitsize: usize) -> Self;
28    fn sample_safe_prime(bitsize: usize) -> Self;
29}
30
31impl PrimeSampable for BigInt {
32    fn sample_prime(bitsize: usize) -> Self {
33        // See Practical Considerations section inside the section 11.5 "Prime Number Generation"
34        // Applied Cryptography, Bruce Schneier.
35        let one = BigInt::one();
36        let two = &one + &one;
37
38        loop {
39            let mut candidate = Self::sample(bitsize);
40            // We flip the LSB to make sure tue candidate is odd.
41            //  BitManipulation::set_bit(&mut candidate, 0, true);
42            BigInt::set_bit(&mut candidate, 0, true);
43
44            // To ensure the appropiate size
45            // we set the MSB of the candidate.
46            BitManipulation::set_bit(&mut candidate, bitsize - 1, true);
47            // If no prime number is found in 500 iterations,
48            // restart the loop (re-seed).
49            // FIXME: Why 500?
50            for _ in 0..500 {
51                if is_prime(&candidate) {
52                    return candidate;
53                }
54                candidate += &two;
55            }
56        }
57    }
58
59    fn sample_safe_prime(bitsize: usize) -> Self {
60        // q = 2p + 1;
61        let two = BigInt::from(2);
62        loop {
63            let q = PrimeSampable::sample_prime(bitsize);
64            let tmp: BigInt = &q - BigInt::one();
65            let p = tmp.div_floor(&two);
66            if is_prime(&p) {
67                return q;
68            };
69        }
70    }
71}
72
73// Runs the following three tests on a given `candidate` to determine
74// primality:
75//
76// 1. Divide the candidate by the first 999 small prime numbers.
77// 2. Run Fermat's Little Theorem against the candidate.
78// 3. Run five rounds of the Miller-Rabin test on the candidate.
79pub fn is_prime(candidate: &BigInt) -> bool {
80    // First, simple trial divide
81    for p in SMALL_PRIMES.iter() {
82        let prime = BigInt::from(*p);
83        let r = candidate % &prime;
84        if !NumberTests::is_zero(&r) {
85            continue;
86        } else {
87            return false;
88        }
89    }
90    // Second, do a little Fermat test on the candidate
91    if !fermat(candidate) {
92        return false;
93    }
94
95    // Finally, do a Miller-Rabin test
96    // NIST recommendation is 5 rounds for 512 and 1024 bits. For 1536 bits, the recommendation is 4 rounds.
97    if !miller_rabin(candidate, 5) {
98        return false;
99    }
100    true
101}
102
103/// Perform test based on Fermat's little theorem
104/// This might be performed more than once, see Handbook of Applied Cryptography [Algorithm 4.9 p136]
105fn fermat(candidate: &BigInt) -> bool {
106    let random = BigInt::sample_below(candidate);
107    let result = BigInt::mod_pow(&random, &(candidate - &BigInt::one()), candidate);
108
109    result == BigInt::one()
110}
111
112/// Perform Miller-Rabin primality test
113fn miller_rabin(candidate: &BigInt, limit: usize) -> bool {
114    // Iterations recommended for which  p < (1/2)^{80}
115    //  500 bits => 6 iterations
116    // 1000 bits => 3 iterations
117    // 2000 bits => 2 iterations
118
119    let (s, d) = rewrite(&(candidate - &BigInt::one()));
120    let one = BigInt::one();
121    let two = &one + &one;
122
123    for _ in 0..limit {
124        let basis = BigInt::sample_range(&two, &(candidate - &two));
125        let mut y = BigInt::mod_pow(&basis, &d, candidate);
126
127        if y == one || y == (candidate - &one) {
128            continue;
129        } else {
130            let mut counter = BigInt::one();
131            while counter < (&s - &one) {
132                y = BigInt::mod_pow(&y, &two, candidate);
133                if y == one {
134                    return false;
135                } else if y == candidate - &one {
136                    break;
137                }
138                counter += BigInt::one();
139            }
140            return false;
141        }
142    }
143    true
144}
145
146/// Rewrite a number n = 2^s * d
147/// (i.e., 2^s is the largest power of 2 that divides the candidate).
148fn rewrite(n: &BigInt) -> (BigInt, BigInt) {
149    let mut d = n.clone();
150    let mut s = BigInt::zero();
151    let one = BigInt::one();
152
153    while NumberTests::is_even(&d) {
154        d >>= 1_usize;
155        s = &s + &one;
156    }
157
158    (s, d)
159}
160
161// BoringSSL's table.
162// https://boringssl.googlesource.com/boringssl/+/master/crypto/bn/prime.c
163#[rustfmt::skip]
164static SMALL_PRIMES: [u32; 2048] = [
165    2,     3,     5,     7,     11,    13,    17,    19,    23,    29,    31,
166    37,    41,    43,    47,    53,    59,    61,    67,    71,    73,    79,
167    83,    89,    97,    101,   103,   107,   109,   113,   127,   131,   137,
168    139,   149,   151,   157,   163,   167,   173,   179,   181,   191,   193,
169    197,   199,   211,   223,   227,   229,   233,   239,   241,   251,   257,
170    263,   269,   271,   277,   281,   283,   293,   307,   311,   313,   317,
171    331,   337,   347,   349,   353,   359,   367,   373,   379,   383,   389,
172    397,   401,   409,   419,   421,   431,   433,   439,   443,   449,   457,
173    461,   463,   467,   479,   487,   491,   499,   503,   509,   521,   523,
174    541,   547,   557,   563,   569,   571,   577,   587,   593,   599,   601,
175    607,   613,   617,   619,   631,   641,   643,   647,   653,   659,   661,
176    673,   677,   683,   691,   701,   709,   719,   727,   733,   739,   743,
177    751,   757,   761,   769,   773,   787,   797,   809,   811,   821,   823,
178    827,   829,   839,   853,   857,   859,   863,   877,   881,   883,   887,
179    907,   911,   919,   929,   937,   941,   947,   953,   967,   971,   977,
180    983,   991,   997,   1009,  1013,  1019,  1021,  1031,  1033,  1039,  1049,
181    1051,  1061,  1063,  1069,  1087,  1091,  1093,  1097,  1103,  1109,  1117,
182    1123,  1129,  1151,  1153,  1163,  1171,  1181,  1187,  1193,  1201,  1213,
183    1217,  1223,  1229,  1231,  1237,  1249,  1259,  1277,  1279,  1283,  1289,
184    1291,  1297,  1301,  1303,  1307,  1319,  1321,  1327,  1361,  1367,  1373,
185    1381,  1399,  1409,  1423,  1427,  1429,  1433,  1439,  1447,  1451,  1453,
186    1459,  1471,  1481,  1483,  1487,  1489,  1493,  1499,  1511,  1523,  1531,
187    1543,  1549,  1553,  1559,  1567,  1571,  1579,  1583,  1597,  1601,  1607,
188    1609,  1613,  1619,  1621,  1627,  1637,  1657,  1663,  1667,  1669,  1693,
189    1697,  1699,  1709,  1721,  1723,  1733,  1741,  1747,  1753,  1759,  1777,
190    1783,  1787,  1789,  1801,  1811,  1823,  1831,  1847,  1861,  1867,  1871,
191    1873,  1877,  1879,  1889,  1901,  1907,  1913,  1931,  1933,  1949,  1951,
192    1973,  1979,  1987,  1993,  1997,  1999,  2003,  2011,  2017,  2027,  2029,
193    2039,  2053,  2063,  2069,  2081,  2083,  2087,  2089,  2099,  2111,  2113,
194    2129,  2131,  2137,  2141,  2143,  2153,  2161,  2179,  2203,  2207,  2213,
195    2221,  2237,  2239,  2243,  2251,  2267,  2269,  2273,  2281,  2287,  2293,
196    2297,  2309,  2311,  2333,  2339,  2341,  2347,  2351,  2357,  2371,  2377,
197    2381,  2383,  2389,  2393,  2399,  2411,  2417,  2423,  2437,  2441,  2447,
198    2459,  2467,  2473,  2477,  2503,  2521,  2531,  2539,  2543,  2549,  2551,
199    2557,  2579,  2591,  2593,  2609,  2617,  2621,  2633,  2647,  2657,  2659,
200    2663,  2671,  2677,  2683,  2687,  2689,  2693,  2699,  2707,  2711,  2713,
201    2719,  2729,  2731,  2741,  2749,  2753,  2767,  2777,  2789,  2791,  2797,
202    2801,  2803,  2819,  2833,  2837,  2843,  2851,  2857,  2861,  2879,  2887,
203    2897,  2903,  2909,  2917,  2927,  2939,  2953,  2957,  2963,  2969,  2971,
204    2999,  3001,  3011,  3019,  3023,  3037,  3041,  3049,  3061,  3067,  3079,
205    3083,  3089,  3109,  3119,  3121,  3137,  3163,  3167,  3169,  3181,  3187,
206    3191,  3203,  3209,  3217,  3221,  3229,  3251,  3253,  3257,  3259,  3271,
207    3299,  3301,  3307,  3313,  3319,  3323,  3329,  3331,  3343,  3347,  3359,
208    3361,  3371,  3373,  3389,  3391,  3407,  3413,  3433,  3449,  3457,  3461,
209    3463,  3467,  3469,  3491,  3499,  3511,  3517,  3527,  3529,  3533,  3539,
210    3541,  3547,  3557,  3559,  3571,  3581,  3583,  3593,  3607,  3613,  3617,
211    3623,  3631,  3637,  3643,  3659,  3671,  3673,  3677,  3691,  3697,  3701,
212    3709,  3719,  3727,  3733,  3739,  3761,  3767,  3769,  3779,  3793,  3797,
213    3803,  3821,  3823,  3833,  3847,  3851,  3853,  3863,  3877,  3881,  3889,
214    3907,  3911,  3917,  3919,  3923,  3929,  3931,  3943,  3947,  3967,  3989,
215    4001,  4003,  4007,  4013,  4019,  4021,  4027,  4049,  4051,  4057,  4073,
216    4079,  4091,  4093,  4099,  4111,  4127,  4129,  4133,  4139,  4153,  4157,
217    4159,  4177,  4201,  4211,  4217,  4219,  4229,  4231,  4241,  4243,  4253,
218    4259,  4261,  4271,  4273,  4283,  4289,  4297,  4327,  4337,  4339,  4349,
219    4357,  4363,  4373,  4391,  4397,  4409,  4421,  4423,  4441,  4447,  4451,
220    4457,  4463,  4481,  4483,  4493,  4507,  4513,  4517,  4519,  4523,  4547,
221    4549,  4561,  4567,  4583,  4591,  4597,  4603,  4621,  4637,  4639,  4643,
222    4649,  4651,  4657,  4663,  4673,  4679,  4691,  4703,  4721,  4723,  4729,
223    4733,  4751,  4759,  4783,  4787,  4789,  4793,  4799,  4801,  4813,  4817,
224    4831,  4861,  4871,  4877,  4889,  4903,  4909,  4919,  4931,  4933,  4937,
225    4943,  4951,  4957,  4967,  4969,  4973,  4987,  4993,  4999,  5003,  5009,
226    5011,  5021,  5023,  5039,  5051,  5059,  5077,  5081,  5087,  5099,  5101,
227    5107,  5113,  5119,  5147,  5153,  5167,  5171,  5179,  5189,  5197,  5209,
228    5227,  5231,  5233,  5237,  5261,  5273,  5279,  5281,  5297,  5303,  5309,
229    5323,  5333,  5347,  5351,  5381,  5387,  5393,  5399,  5407,  5413,  5417,
230    5419,  5431,  5437,  5441,  5443,  5449,  5471,  5477,  5479,  5483,  5501,
231    5503,  5507,  5519,  5521,  5527,  5531,  5557,  5563,  5569,  5573,  5581,
232    5591,  5623,  5639,  5641,  5647,  5651,  5653,  5657,  5659,  5669,  5683,
233    5689,  5693,  5701,  5711,  5717,  5737,  5741,  5743,  5749,  5779,  5783,
234    5791,  5801,  5807,  5813,  5821,  5827,  5839,  5843,  5849,  5851,  5857,
235    5861,  5867,  5869,  5879,  5881,  5897,  5903,  5923,  5927,  5939,  5953,
236    5981,  5987,  6007,  6011,  6029,  6037,  6043,  6047,  6053,  6067,  6073,
237    6079,  6089,  6091,  6101,  6113,  6121,  6131,  6133,  6143,  6151,  6163,
238    6173,  6197,  6199,  6203,  6211,  6217,  6221,  6229,  6247,  6257,  6263,
239    6269,  6271,  6277,  6287,  6299,  6301,  6311,  6317,  6323,  6329,  6337,
240    6343,  6353,  6359,  6361,  6367,  6373,  6379,  6389,  6397,  6421,  6427,
241    6449,  6451,  6469,  6473,  6481,  6491,  6521,  6529,  6547,  6551,  6553,
242    6563,  6569,  6571,  6577,  6581,  6599,  6607,  6619,  6637,  6653,  6659,
243    6661,  6673,  6679,  6689,  6691,  6701,  6703,  6709,  6719,  6733,  6737,
244    6761,  6763,  6779,  6781,  6791,  6793,  6803,  6823,  6827,  6829,  6833,
245    6841,  6857,  6863,  6869,  6871,  6883,  6899,  6907,  6911,  6917,  6947,
246    6949,  6959,  6961,  6967,  6971,  6977,  6983,  6991,  6997,  7001,  7013,
247    7019,  7027,  7039,  7043,  7057,  7069,  7079,  7103,  7109,  7121,  7127,
248    7129,  7151,  7159,  7177,  7187,  7193,  7207,  7211,  7213,  7219,  7229,
249    7237,  7243,  7247,  7253,  7283,  7297,  7307,  7309,  7321,  7331,  7333,
250    7349,  7351,  7369,  7393,  7411,  7417,  7433,  7451,  7457,  7459,  7477,
251    7481,  7487,  7489,  7499,  7507,  7517,  7523,  7529,  7537,  7541,  7547,
252    7549,  7559,  7561,  7573,  7577,  7583,  7589,  7591,  7603,  7607,  7621,
253    7639,  7643,  7649,  7669,  7673,  7681,  7687,  7691,  7699,  7703,  7717,
254    7723,  7727,  7741,  7753,  7757,  7759,  7789,  7793,  7817,  7823,  7829,
255    7841,  7853,  7867,  7873,  7877,  7879,  7883,  7901,  7907,  7919,  7927,
256    7933,  7937,  7949,  7951,  7963,  7993,  8009,  8011,  8017,  8039,  8053,
257    8059,  8069,  8081,  8087,  8089,  8093,  8101,  8111,  8117,  8123,  8147,
258    8161,  8167,  8171,  8179,  8191,  8209,  8219,  8221,  8231,  8233,  8237,
259    8243,  8263,  8269,  8273,  8287,  8291,  8293,  8297,  8311,  8317,  8329,
260    8353,  8363,  8369,  8377,  8387,  8389,  8419,  8423,  8429,  8431,  8443,
261    8447,  8461,  8467,  8501,  8513,  8521,  8527,  8537,  8539,  8543,  8563,
262    8573,  8581,  8597,  8599,  8609,  8623,  8627,  8629,  8641,  8647,  8663,
263    8669,  8677,  8681,  8689,  8693,  8699,  8707,  8713,  8719,  8731,  8737,
264    8741,  8747,  8753,  8761,  8779,  8783,  8803,  8807,  8819,  8821,  8831,
265    8837,  8839,  8849,  8861,  8863,  8867,  8887,  8893,  8923,  8929,  8933,
266    8941,  8951,  8963,  8969,  8971,  8999,  9001,  9007,  9011,  9013,  9029,
267    9041,  9043,  9049,  9059,  9067,  9091,  9103,  9109,  9127,  9133,  9137,
268    9151,  9157,  9161,  9173,  9181,  9187,  9199,  9203,  9209,  9221,  9227,
269    9239,  9241,  9257,  9277,  9281,  9283,  9293,  9311,  9319,  9323,  9337,
270    9341,  9343,  9349,  9371,  9377,  9391,  9397,  9403,  9413,  9419,  9421,
271    9431,  9433,  9437,  9439,  9461,  9463,  9467,  9473,  9479,  9491,  9497,
272    9511,  9521,  9533,  9539,  9547,  9551,  9587,  9601,  9613,  9619,  9623,
273    9629,  9631,  9643,  9649,  9661,  9677,  9679,  9689,  9697,  9719,  9721,
274    9733,  9739,  9743,  9749,  9767,  9769,  9781,  9787,  9791,  9803,  9811,
275    9817,  9829,  9833,  9839,  9851,  9857,  9859,  9871,  9883,  9887,  9901,
276    9907,  9923,  9929,  9931,  9941,  9949,  9967,  9973,  10007, 10009, 10037,
277    10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133,
278    10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223,
279    10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313,
280    10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429,
281    10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529,
282    10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639,
283    10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733,
284    10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859,
285    10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957,
286    10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071,
287    11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171,
288    11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279,
289    11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393,
290    11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491,
291    11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617,
292    11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731,
293    11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831,
294    11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933,
295    11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037,
296    12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119,
297    12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241,
298    12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343,
299    12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437,
300    12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527,
301    12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613,
302    12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713,
303    12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823,
304    12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923,
305    12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009,
306    13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127,
307    13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229,
308    13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337,
309    13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457,
310    13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577,
311    13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687,
312    13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759,
313    13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877,
314    13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967,
315    13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083,
316    14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221,
317    14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347,
318    14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447,
319    14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551,
320    14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653,
321    14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747,
322    14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831,
323    14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939,
324    14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073,
325    15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161,
326    15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269,
327    15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349,
328    15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443,
329    15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559,
330    15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649,
331    15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749,
332    15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859,
333    15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959,
334    15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069,
335    16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187,
336    16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301,
337    16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421,
338    16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529,
339    16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649,
340    16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747,
341    16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883,
342    16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981,
343    16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077,
344    17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191,
345    17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321,
346    17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401,
347    17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491,
348    17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599,
349    17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729,
350    17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839,
351    17851, 17863 ];
paillier_common/keygen.rs

paillier_common/
keygen.rs
