244 lines
13 KiB
Rust
244 lines
13 KiB
Rust
use crate::{params::*, reduce::*};
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// Roots of unity in order needed by forward ntt
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pub const ZETAS: [i32; N] = [
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0, 25847, -2608894, -518909, 237124, -777960, -876248, 466468, 1826347,
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2353451, -359251, -2091905, 3119733, -2884855, 3111497, 2680103, 2725464,
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1024112, -1079900, 3585928, -549488, -1119584, 2619752, -2108549, -2118186,
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-3859737, -1399561, -3277672, 1757237, -19422, 4010497, 280005, 2706023,
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95776, 3077325, 3530437, -1661693, -3592148, -2537516, 3915439, -3861115,
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-3043716, 3574422, -2867647, 3539968, -300467, 2348700, -539299, -1699267,
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-1643818, 3505694, -3821735, 3507263, -2140649, -1600420, 3699596, 811944,
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531354, 954230, 3881043, 3900724, -2556880, 2071892, -2797779, -3930395,
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-1528703, -3677745, -3041255, -1452451, 3475950, 2176455, -1585221, -1257611,
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1939314, -4083598, -1000202, -3190144, -3157330, -3632928, 126922, 3412210,
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-983419, 2147896, 2715295, -2967645, -3693493, -411027, -2477047, -671102,
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-1228525, -22981, -1308169, -381987, 1349076, 1852771, -1430430, -3343383,
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264944, 508951, 3097992, 44288, -1100098, 904516, 3958618, -3724342, -8578,
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1653064, -3249728, 2389356, -210977, 759969, -1316856, 189548, -3553272,
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3159746, -1851402, -2409325, -177440, 1315589, 1341330, 1285669, -1584928,
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-812732, -1439742, -3019102, -3881060, -3628969, 3839961, 2091667, 3407706,
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2316500, 3817976, -3342478, 2244091, -2446433, -3562462, 266997, 2434439,
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-1235728, 3513181, -3520352, -3759364, -1197226, -3193378, 900702, 1859098,
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909542, 819034, 495491, -1613174, -43260, -522500, -655327, -3122442,
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2031748, 3207046, -3556995, -525098, -768622, -3595838, 342297, 286988,
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-2437823, 4108315, 3437287, -3342277, 1735879, 203044, 2842341, 2691481,
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-2590150, 1265009, 4055324, 1247620, 2486353, 1595974, -3767016, 1250494,
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2635921, -3548272, -2994039, 1869119, 1903435, -1050970, -1333058, 1237275,
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-3318210, -1430225, -451100, 1312455, 3306115, -1962642, -1279661, 1917081,
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-2546312, -1374803, 1500165, 777191, 2235880, 3406031, -542412, -2831860,
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-1671176, -1846953, -2584293, -3724270, 594136, -3776993, -2013608, 2432395,
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2454455, -164721, 1957272, 3369112, 185531, -1207385, -3183426, 162844,
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1616392, 3014001, 810149, 1652634, -3694233, -1799107, -3038916, 3523897,
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3866901, 269760, 2213111, -975884, 1717735, 472078, -426683, 1723600,
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-1803090, 1910376, -1667432, -1104333, -260646, -3833893, -2939036, -2235985,
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-420899, -2286327, 183443, -976891, 1612842, -3545687, -554416, 3919660,
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-48306, -1362209, 3937738, 1400424, -846154, 1976782,
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];
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/// Name: ntt
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//
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/// Forward NTT, in-place. No modular reduction is performed after
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/// additions or subtractions. Output vector is in bitreversed order.
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//
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/// Arguments: - uint32_t p[N]: input/output coefficient array
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pub fn ntt(a: &mut [i32]) {
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let mut j;
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let mut k = 0usize;
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let mut len = 128;
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let (mut t, mut zeta);
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while len > 0 {
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let mut start = 0;
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while start < N {
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k += 1;
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zeta = ZETAS[k] as i64;
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j = start;
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while j < (start + len) {
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t = montgomery_reduce(zeta * a[j + len] as i64);
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a[j + len] = a[j] - t;
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a[j] += t;
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j += 1;
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}
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start = j + len;
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}
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len >>= 1;
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}
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}
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/// Name: invntt
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//
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/// Inverse NTT and multiplication by Montgomery factor 2^32.
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/// In-place. No modular reductions after additions or
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/// subtractions; input coefficients need to be smaller than
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/// Q in absolute value. Output coefficient are smaller than Q in
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/// absolute value.
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//
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/// Arguments: - uint32_t p[N]: input/output coefficient array
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pub fn invntt_tomont(a: &mut [i32]) {
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let mut j;
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let mut k = 256usize;
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let mut len = 1;
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let (mut t, mut zeta);
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const F: i64 = 41978; // mont^2/256
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while len < N {
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let mut start = 0;
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while start < 256 {
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k -= 1;
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zeta = -ZETAS[k] as i64;
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j = start;
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while j < (start + len) {
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t = a[j];
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a[j] = t + a[j + len];
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a[j + len] = t - a[j + len];
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a[j + len] = montgomery_reduce(zeta * a[j + len] as i64);
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j += 1
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}
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start = j + len;
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}
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len <<= 1;
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}
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for j in 0..N {
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a[j] = montgomery_reduce(F * a[j] as i64);
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}
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}
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mod tests {
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#[test]
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fn ntt() {
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let mut a = [
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-1, 1, -4, -3, -4, 4, 1, 1, 2, 4, 1, 2, -2, 3, 1, 0, -3, 1, -1, -2, 4,
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-4, -1, -3, -4, -3, 3, -3, -1, 0, 0, 2, 3, -4, 3, 4, 1, -3, -1, 3, 0, 0,
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1, -4, -1, -2, -2, 2, 3, 0, 1, 1, 4, 1, 2, 2, 4, 1, -2, 2, 0, 3, 1, -3,
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4, -3, 2, -1, 3, 2, -3, 4, 3, -4, -2, 2, 4, -1, 3, -2, -1, -4, -1, -4,
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-3, 4, -1, -3, -2, 0, -4, 3, -4, -1, -1, 4, -4, 0, 1, -1, 4, 1, -4, 3, 4,
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-3, -2, -2, -3, 0, 3, -1, 2, -4, -3, -2, 1, -3, -3, -3, 1, 1, 4, -1, 2,
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4, 4, -3, 3, 1, -4, 2, -4, -3, 2, -4, -1, 3, 4, -4, 3, -3, 4, 0, -2, 2,
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1, -3, 1, 0, 4, 2, 3, -2, 2, -2, 4, -1, 3, -2, 1, -3, 3, -3, 3, 4, 1, 4,
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3, 3, -1, 0, -2, 1, 3, -4, 2, -1, 4, 1, 0, 2, -1, -2, 1, 4, -4, 0, 0, 3,
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-3, 1, -4, 4, -3, 1, -4, 3, -1, 2, 4, -1, 0, -4, -2, 4, -4, 4, 4, -2, -3,
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3, 2, -2, -4, -1, 3, 1, 3, 1, -4, 2, -3, 2, 4, 4, -3, 3, -4, 3, -4, 0,
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-2, 3, -3, -2, 3, 1, -4, -3, 3, -2, -3, 4, -3, 1, 1, 2, -1, -1, 0, -3,
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-3, 0, -1, 3,
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];
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let a_output = [
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-262661, -8506629, 3427761, 2784265, 3141917, -2372709, -8049215,
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-2353801, 3022212, 7731946, 1644566, 3053540, -255898, -2738860, 876613,
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9132009, 10276178, 7874020, -11588, 1969958, 12632850, 8341150, 8287818,
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3925510, -8773920, -747228, 898118, -2317034, 3897976, -4414032, -834621,
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4071501, -1432521, -9685153, -13990476, -13659378, -7289253, -7755363,
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3791227, -3833707, -9487410, -8901660, -19000363, -13214259, 544413,
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-6844765, -6105586, -11435970, -2978543, -1014713, -5667934, -13166438,
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-5875092, -12621756, -9964452, -5673368, -3935130, -4224380, -7354605,
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-7906865, -4353982, 1618188, 4762265, 2833189, -310581, -3991895,
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-11913640, -5312548, 3570135, -4704135, -3170969, -5592951, 1453785,
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-4560687, -1182968, 2521098, -3751247, -4714079, 301131, -2224209,
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-5642042, 458282, 5403769, 2707403, 12215228, 5224740, 6413907, 6815913,
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4580029, 425581, 1318364, -783726, 7326262, 7568074, 689180, -547668,
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-4653694, -11442820, -7832628, -5377838, -11257920, -8298570, -4596359,
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-4150699, -3065694, -10682906, -2769659, 937211, 1653867, 3120263,
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-1126589, 7211075, -14877134, -18262456, -8293726, -9183292, -10773770,
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-6705792, -5315674, 2787012, -2270115, -9841689, -5051871, -7388413,
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4234814, 1052190, -2471397, -6463519, 10137330, 5496024, 4753901,
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-645043, 7223139, 1246181, 9902026, 8334682, 6254834, 13121436, 5157886,
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5524544, 3335176, -1444146, 7151165, 8213713, 5425362, 2999358, 9659970,
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4975850, 10923812, 12903596, 3807803, 8025009, -5468017, -1536129,
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-2185854, 2751920, 6580366, 4468658, 8981903, 2405433, 8513375, 9863111,
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7777890, 11623292, -484225, 2094367, 6670303, -1190953, -113377, 7560821,
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-1565727, 512851, 2493128, -2496028, -2851481, -11119827, -3547676,
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-6187460, 4743114, -1430434, 8695423, 404053, -5689198, -237334,
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-10292594, -2482562, -4377285, -8964791, -8246037, -13793329, -106937,
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-5784361, 16421657, 16169825, 17295701, 14750529, 15111685, 13365139,
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5665684, 6845556, 3012973, 2469901, -34925, 3554251, 2179597, 9005783,
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11178922, 11448090, 4172918, 6892142, -3097350, -2378354, -2508563,
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-3588283, -7774392, -7426678, 3013820, 8971556, 11583329, 6634515,
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657092, 6937984, -6083813, -1488819, -1315854, 5205578, -7934583,
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-2186897, 6308547, 3324877, 10276044, 2595056, 8209625, 2358083, 6005802,
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2915382, 1471531, -1624379, -3631962, -4158290, 544917, -6606555, 998696,
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584554, 1926740, 844426, 1017867, -3082165, -5819081, -8499759, 521737,
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-7231469, -4117257, -5370457, -6235069, 314971,
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];
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super::ntt(&mut a);
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assert_eq!(a, a_output);
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}
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#[test]
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fn invntt_tomont() {
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let mut a = [
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-410121, -3439227, -1510274, 1543151, -2293562, -1024787, -1768713,
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3416108, -1829266, -39421, 1553720, 383193, -1303564, 2601404, 178534,
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3075833, -1669488, 2938151, 419856, 3374895, -3659025, 2791925, -2014544,
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-4116040, 528058, -460960, -498884, -3726436, 1576721, 1111713, -2404662,
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289307, 3590938, 362196, -2812407, -1463477, 1001050, 2798150, -472041,
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1298972, -601719, -3341683, -2239048, -3200450, -1250550, -2932037,
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-158803, -42310, 1710565, 1768181, 3343337, -4124626, -970397, 2715826,
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650012, -2014903, 4155312, -570039, -1014542, -1136867, -2854295,
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3545986, 3534334, 1775063, 543277, 1440396, -2274992, -1666074, -2522410,
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1374130, 2546411, 2357995, 3246445, -1637839, -3940900, -22882, 3617374,
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3695910, 3135497, 3461903, 321845, 1837065, -4102518, 2025912, 4037956,
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3262194, -1077158, -104681, 1543795, 2067328, -3128599, 3610959, 1154470,
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-1950084, 3161277, -1484341, 3056494, 145395, -2412862, 3811285,
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-2651526, 794539, -1077785, -3775793, 1851954, 925186, -1420046,
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-2129292, -2572721, -1709299, 2466220, -1148025, -631434, 1616317,
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1979838, 1787596, -2046122, 4145612, 2425669, -1207333, -3920849,
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2920839, -1437055, 2250361, -2512504, -2660187, -2934830, 3926550,
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1895481, -763893, 1348485, 3392907, -2603573, 748841, 3508436, -3904020,
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800986, 1434045, 3024446, -2067148, 4058529, -1797892, 2428719, -1661266,
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-1174918, -1085872, -437562, 2040521, 3475996, 35877, 3621178, -1269117,
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-743638, 442376, -278296, -2265303, 1611044, -1440032, 545695, 3186212,
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2126009, -93566, 1381483, -4000405, -1074727, 291811, 3040864, -1459167,
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-3809294, -1446926, -2959019, 1110797, -2346583, 1125183, -1458376,
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476652, 2246737, -1552594, -321172, -328787, 3727158, 2578512, -637322,
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2145686, 124009, 316574, 598758, -2180345, -40300, 1777560, -712912,
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3969900, -837615, 4186858, -1992625, 1592425, 4172055, 1030316, 1732649,
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3365500, -2209545, -2216165, 1598405, 4122715, 4094540, 363060, 369838,
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-1841354, 3772391, 1383675, -1268324, -237400, -3972626, 1314275,
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-128037, -810499, -3799034, -1750396, 766339, 1350337, -519324, -3673999,
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873780, -2497778, 1159808, 3552922, 900408, 3883840, -4073441, 2974189,
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763212, -1033993, -1137934, -3359093, 452287, 2935586, -917124, 608771,
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3625009, -2851574, -207975, -101949, -3075118, -1522612, -3819111,
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3826184, 2419692, 1871952, -1722545, -710127, 3035522, -3436794,
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-2649023, 383072, 2434951, 3052038,
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];
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let a_output = [
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775832, -3236070, 3979117, -477690, -3845958, 3442130, 3288278, 3510572,
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-4059961, 398894, -2353757, 2033799, 1142104, -1503727, -1966738,
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-646014, -1208934, 2807801, 1786267, 77787, -3034606, -2018590, -4138114,
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-119863, -2143281, -2656209, -1161853, -1355718, -3330698, 535482,
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3053760, 1831603, 2290608, 2796725, -2609926, -663097, 1464007, 2958053,
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-2816324, 2906926, 500159, 943996, 524888, -4163949, -834472, 964151,
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2161202, 1983774, -3656476, -3020535, 952201, 2170010, 711358, 1519731,
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-3738927, -3756753, 921738, -3392868, 2699399, 3324418, -1453193,
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1620721, 449384, -39155, 3109821, 1029974, 142649, 921233, 3727107,
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637146, -756794, 34504, -1893151, -603841, 2330154, 1322568, -1191265,
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-748922, 1386438, 2435097, 355691, 705695, -504939, 1785625, 3011361,
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2599030, -721431, 3258978, 826952, 3134195, 1786978, -2063102, 3719340,
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-3791185, 766135, 1412965, 2002641, 344357, -3493197, -3971320, -1589376,
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3333787, -886393, -3473781, 2615969, 258578, -1357515, 31929, -2417061,
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3279057, 623958, 402549, -3223514, 1434146, 2674659, 4184013, 2350081,
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-2255267, 3242948, -2755729, 3141850, -3642170, -410070, -3603228,
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509187, 747235, -2733439, 2951878, 934726, -1464030, -3685617, -177281,
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-2026915, -2014190, 3892744, -2765709, 178393, 1247779, -328544, -647840,
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227976, -1303803, -407239, 2659686, 330785, 22660, 3150838, -49448,
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-3247191, 3366409, 3515827, 2681493, -3955013, 957672, 2270951, -2324620,
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848541, 252308, 2362816, -480849, 1886753, 1946701, -3448907, 3931255,
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-2029213, -3650910, 3939281, 730275, 2214811, 1201755, -694587, -2004861,
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2583875, 3279717, 3819665, 2574119, -2112908, -2400101, -1349537,
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3495414, 1347624, -2225620, -2050682, -2951590, -3996103, -3607935,
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3247458, -2175324, -1553702, -2091666, 1571828, -1878102, 2718529,
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-541427, -662267, -1324341, -370258, -474473, 2224715, 2128310, -345001,
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1208578, -1376070, 3433670, 3140605, 875985, -1831696, 449356, -220450,
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1787974, 2388192, -34248, -3456146, 2415580, 1786863, -2849072, -212492,
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59437, -716203, 1968326, 1107129, 434519, 185631, 3036577, -2325373,
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567821, 1988023, 2839088, -1233636, -3135158, 4161465, -3730607, 1882010,
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-3271303, -2556717, -1387745, -3161242, 1813752, -3561981, 130118,
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-2005282, -3396498, 1716289, -3253036, -1302754, 2500212, -1918240,
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1201565, -1106518, 743553, 902331, 804710, -3047027, 3654086, 911638,
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3708051,
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];
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super::invntt_tomont(&mut a);
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assert_eq!(a, a_output);
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}
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}
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