// precomp.go - Precomputed NTT constants.
//
// To the extent possible under law, Yawning Angel has waived all copyright
// and related or neighboring rights to the software, using the Creative
// Commons "CC0" public domain dedication. See LICENSE or
// <http://creativecommons.org/publicdomain/zero/1.0/> for full details.

package kyber

// Precomputed constants for the forward NTT and inverse NTT.
// Computed using Pari/GP as follows:
//
// brv=[0,128,64,192,32,160,96,224,16,144,80,208,48,176,112,240, \
//      8,136,72,200,40,168,104,232,24,152,88,216,56,184,120,248, \
//      4,132,68,196,36,164,100,228,20,148,84,212,52,180,116,244, \
//      12,140,76,204,44,172,108,236,28,156,92,220,60,188,124,252, \
//      2,130,66,194,34,162,98,226,18,146,82,210,50,178,114,242, \
//      10,138,74,202,42,170,106,234,26,154,90,218,58,186,122,250, \
//      6,134,70,198,38,166,102,230,22,150,86,214,54,182,118,246, \
//      14,142,78,206,46,174,110,238,30,158,94,222,62,190,126,254, \
//      1,129,65,193,33,161,97,225,17,145,81,209,49,177,113,241, \
//      9,137,73,201,41,169,105,233,25,153,89,217,57,185,121,249, \
//      5,133,69,197,37,165,101,229,21,149,85,213,53,181,117,245, \
//      13,141,77,205,45,173,109,237,29,157,93,221,61,189,125,253, \
//      3,131,67,195,35,163,99,227,19,147,83,211,51,179,115,243, \
//      11,139,75,203,43,171,107,235,27,155,91,219,59,187,123,251, \
//      7,135,71,199,39,167,103,231,23,151,87,215,55,183,119,247, \
//      15,143,79,207,47,175,111,239,31,159,95,223,63,191,127,255];
//
// q = 7681;
// n = 256;
// mont = Mod(2^18,q);
//
// g=0; for(i=2,q-1,if(znorder(Mod(i,q)) == 2*n, g=Mod(i,q); break))
//
// zetas = lift(vector(n, i, g^(brv[i])*mont))
// omegas_inv_bitrev_montgomery = lift(vector(n/2, i, (g^2)^(-brv[2*(i-1)+1])*mont))
// psis_inv_montgomery = lift(vector(n, i, g^(-(i-1))/n*mont))

var zetas = [kyberN]uint16{
	990, 7427, 2634, 6819, 578, 3281, 2143, 1095, 484, 6362, 3336, 5382, 6086, 3823, 877, 5656,
	3583, 7010, 6414, 263, 1285, 291, 7143, 7338, 1581, 5134, 5184, 5932, 4042, 5775, 2468, 3,
	606, 729, 5383, 962, 3240, 7548, 5129, 7653, 5929, 4965, 2461, 641, 1584, 2666, 1142, 157,
	7407, 5222, 5602, 5142, 6140, 5485, 4931, 1559, 2085, 5284, 2056, 3538, 7269, 3535, 7190, 1957,
	3465, 6792, 1538, 4664, 2023, 7643, 3660, 7673, 1694, 6905, 3995, 3475, 5939, 1859, 6910, 4434,
	1019, 1492, 7087, 4761, 657, 4859, 5798, 2640, 1693, 2607, 2782, 5400, 6466, 1010, 957, 3851,
	2121, 6392, 7319, 3367, 3659, 3375, 6430, 7583, 1549, 5856, 4773, 6084, 5544, 1650, 3997, 4390,
	6722, 2915, 4245, 2635, 6128, 7676, 5737, 1616, 3457, 3132, 7196, 4702, 6239, 851, 2122, 3009,
	7613, 7295, 2007, 323, 5112, 3716, 2289, 6442, 6965, 2713, 7126, 3401, 963, 6596, 607, 5027,
	7078, 4484, 5937, 944, 2860, 2680, 5049, 1777, 5850, 3387, 6487, 6777, 4812, 4724, 7077, 186,
	6848, 6793, 3463, 5877, 1174, 7116, 3077, 5945, 6591, 590, 6643, 1337, 6036, 3991, 1675, 2053,
	6055, 1162, 1679, 3883, 4311, 2106, 6163, 4486, 6374, 5006, 4576, 4288, 5180, 4102, 282, 6119,
	7443, 6330, 3184, 4971, 2530, 5325, 4171, 7185, 5175, 5655, 1898, 382, 7211, 43, 5965, 6073,
	1730, 332, 1577, 3304, 2329, 1699, 6150, 2379, 5113, 333, 3502, 4517, 1480, 1172, 5567, 651,
	925, 4573, 599, 1367, 4109, 1863, 6929, 1605, 3866, 2065, 4048, 839, 5764, 2447, 2022, 3345,
	1990, 4067, 2036, 2069, 3567, 7371, 2368, 339, 6947, 2159, 654, 7327, 2768, 6676, 987, 2214,
}

var omegasInvBitrevMontgomery = [kyberN / 2]uint16{
	990, 254, 862, 5047, 6586, 5538, 4400, 7103, 2025, 6804, 3858, 1595, 2299, 4345, 1319, 7197,
	7678, 5213, 1906, 3639, 1749, 2497, 2547, 6100, 343, 538, 7390, 6396, 7418, 1267, 671, 4098,
	5724, 491, 4146, 412, 4143, 5625, 2397, 5596, 6122, 2750, 2196, 1541, 2539, 2079, 2459, 274,
	7524, 6539, 5015, 6097, 7040, 5220, 2716, 1752, 28, 2552, 133, 4441, 6719, 2298, 6952, 7075,
	4672, 5559, 6830, 1442, 2979, 485, 4549, 4224, 6065, 1944, 5, 1553, 5046, 3436, 4766, 959,
	3291, 3684, 6031, 2137, 1597, 2908, 1825, 6132, 98, 1251, 4306, 4022, 4314, 362, 1289, 5560,
	3830, 6724, 6671, 1215, 2281, 4899, 5074, 5988, 5041, 1883, 2822, 7024, 2920, 594, 6189, 6662,
	3247, 771, 5822, 1742, 4206, 3686, 776, 5987, 8, 4021, 38, 5658, 3017, 6143, 889, 4216,
}

var psisInvMontgomery = [kyberN]uint16{
	1024, 4972, 5779, 6907, 4943, 4168, 315, 5580, 90, 497, 1123, 142, 4710, 5527, 2443, 4871,
	698, 2489, 2394, 4003, 684, 2241, 2390, 7224, 5072, 2064, 4741, 1687, 6841, 482, 7441, 1235,
	2126, 4742, 2802, 5744, 6287, 4933, 699, 3604, 1297, 2127, 5857, 1705, 3868, 3779, 4397, 2177,
	159, 622, 2240, 1275, 640, 6948, 4572, 5277, 209, 2605, 1157, 7328, 5817, 3191, 1662, 2009,
	4864, 574, 2487, 164, 6197, 4436, 7257, 3462, 4268, 4281, 3414, 4515, 3170, 1290, 2003, 5855,
	7156, 6062, 7531, 1732, 3249, 4884, 7512, 3590, 1049, 2123, 1397, 6093, 3691, 6130, 6541, 3946,
	6258, 3322, 1788, 4241, 4900, 2309, 1400, 1757, 400, 502, 6698, 2338, 3011, 668, 7444, 4580,
	6516, 6795, 2959, 4136, 3040, 2279, 6355, 3943, 2913, 6613, 7416, 4084, 6508, 5556, 4054, 3782,
	61, 6567, 2212, 779, 632, 5709, 5667, 4923, 4911, 6893, 4695, 4164, 3536, 2287, 7594, 2848,
	3267, 1911, 3128, 546, 1991, 156, 4958, 5531, 6903, 483, 875, 138, 250, 2234, 2266, 7222,
	2842, 4258, 812, 6703, 232, 5207, 6650, 2585, 1900, 6225, 4932, 7265, 4701, 3173, 4635, 6393,
	227, 7313, 4454, 4284, 6759, 1224, 5223, 1447, 395, 2608, 4502, 4037, 189, 3348, 54, 6443,
	2210, 6230, 2826, 1780, 3002, 5995, 1955, 6102, 6045, 3938, 5019, 4417, 1434, 1262, 1507, 5847,
	5917, 7157, 7177, 6434, 7537, 741, 4348, 1309, 145, 374, 2236, 4496, 5028, 6771, 6923, 7421,
	1978, 1023, 3857, 6876, 1102, 7451, 4704, 6518, 1344, 765, 384, 5705, 1207, 1630, 4734, 1563,
	6839, 5933, 1954, 4987, 7142, 5814, 7527, 4953, 7637, 4707, 2182, 5734, 2818, 541, 4097, 5641,
}