Key Generation -- ML-DSA-65
seed: 72C3C5E0CC9F332F49D0FC0FD6399DA75645A3E33DBF56F1E96897662D0A9B37
rho: 88C93DEB901A24A945FA94AE54DBAF46D81CACA943FBE320421C61B33204849F
rhoPrime: DC6A3A1A9734E79B41C2ED6F988BE18802726D9B975E35A656E6303C3FE798EAF9049E0DDEBBC32902605BCE6F2536B9AC71E124827025A1C4E4524CA6E39459
k: 9B2E348E4865616680FC184376A8CCB8DBE598365A23A2723944F5351F42F474

aHat: [[[3482139, 8186163, 2372395, 3386819, 1143206, 2532484, 8052453, 4473490, 106443, 7179739, 507086, 3597062, 3935196, 4173570, 4894936, 73631, 3923816, 485984, 8303229, 418498, 4036494, 3329435, 87822, 2247277, 952450, 1978109, 2997645, 5170958, 7137052, 498572, 6902549, 5000158, 4440102, 6172438, 8254652, 7211061, 5854442, 3139758, 5893400, 7655936, 4531127, 2920492, 694997, 3700280, 1015307, 7330957, 6698948, 8190071, 7370326, 5031935, 6475609, 7449364, 821181, 2258657, 8177579, 342859, 1927209, 621786, 2591863, 8005111, 6471577, 2890207, 1607020, 1722749, 2444680, 1525424, 874519, 2912496, 3122222, 8121488, 14954, 6974534, 853039, 5043046, 2563397, 2968386, 7990895, 1126735, 4798433, 2401947, 1275283, 868219, 6004047, 2208907, 2722238, 2340420, 4128269, 6331126, 1974241, 7439181, 8252773, 1219710, 62405, 2800555, 5705387, 2872004, 41065, 493061, 2544170, 1158560, 4009348, 3142805, 7476154, 6828659, 7691796, 3548866, 8134542, 7765604, 5718455, 2342255, 510863, 5388852, 3800516, 938253, 6663034, 7645963, 242746, 5025356, 1847800, 2410227, 6437351, 4054057, 2058288, 1105810, 7244758, 5549033, 2838854, 7376749, 648271, 6116217, 3156383, 5607076, 7100285, 7217664, 1365942, 6316618, 4417786, 1418305, 8017787, 1921823, 2737106, 1977270, 7909604, 1659612, 2263825, 4223224, 4903412, 1092262, 3918378, 1438847, 1125058, 8347845, 1579301, 7446952, 7852836, 1225947, 977321, 3498691, 7212891, 918627, 1612511, 3803396, 8085172, 3891699, 5743866, 6941716, 219579, 6278823, 1585468, 8099873, 4315795, 8096204, 6503682, 3710042, 7627375, 2627448, 5126134, 6861330, 7140328, 5252709, 1481849, 2143309, 5989699, 1243249, 859264, 5272237, 1536840, 5653399, 6191690, 5659837, 435597, 4255912, 6260676, 7436604, 4285241, 458782, 6386431, 2374394, 538345, 7694314, 1454040, 416175, 4678198, 3575352, 6429995, 3545291, 3173558, 7889992, 3746243, 7911255, 1957610, 701184, 2995003, 3222046, 7941019, 5678653, 304959, 1450925, 7836173, 1066653, 4162595, 3349735, 5519259, 1610239, 527540, 5141930, 863259, 509637, 7725149, 6503527, 7635929, 5341698, 2869, 6057974, 7824865, 4185418, 6940188, 4827490, 3875104, 3278037, 6563827, 4940836, 1466788, 5790742, 4260142, 3825122, 6317302, 4911489, 6390531, 4276141, 3475545, 4800230, 3691606, 4956359, 3900278, 1672013],
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NTTInverse(aHat * s1Hat): [[830897, 2049833, 6969400, 7713335, 5408488, 7739107, 6814387, 5445045, 4299840, 4623630, 5600489, 970754, 6088905, 5234075, 4265145, 4827235, 6985528, 8132429, 7904641, 2124141, 2214658, 1990802, 6491209, 1466042, 3906849, 422790, 2844497, 5635218, 3052908, 3693638, 7069807, 5149612, 6793090, 6316831, 5223556, 4906560, 2640758, 6259040, 4603354, 350630, 2676843, 642972, 1194346, 5057399, 1197066, 7592819, 6001672, 8183194, 7914878, 5330704, 6947177, 2890033, 2528985, 8237993, 910660, 2104710, 6815144, 483063, 3043336, 4341116, 3620738, 254071, 2265370, 6178683, 7489213, 401005, 867999, 1172157, 1815764, 4059760, 5383393, 3043078, 473863, 6728410, 808005, 3000087, 2826274, 2287193, 1175760, 720220, 2434523, 862109, 2667457, 5338582, 6495963, 5491680, 4325993, 754733, 1906144, 4680928, 6780178, 7492093, 5356156, 6345635, 7283384, 1417413, 5550317, 5304042, 4624792, 649064, 3151665, 8139938, 1415280, 5185361, 4359608, 822499, 5057029, 3453267, 6898914, 372767, 664304, 6781702, 3473923, 3631653, 5954646, 6724674, 1149409, 3956638, 5627577, 7636946, 3706592, 1746907, 7734756, 3722467, 827361, 903702, 31090, 5772814, 1665351, 7000261, 6776039, 8351822, 5804027, 1694323, 574486, 6736393, 3280669, 2804553, 7022444, 5492468, 5300019, 4706983, 1476604, 8333644, 4385118, 8290495, 6378992, 1211684, 120187, 7583559, 3761388, 7679430, 4506238, 979295, 8258427, 1039168, 6552448, 5942033, 7114669, 3915990, 6195466, 4623256, 5115335, 6476043, 1516424, 5987993, 2962237, 2153131, 903430, 7822971, 4335736, 7340380, 7347333, 2846393, 5789183, 4324995, 5359805, 2574489, 7943831, 7250479, 5355207, 2097405, 6511510, 2891214, 1544013, 2468945, 2261919, 6923981, 785750, 7168456, 3889771, 6802616, 4866776, 4838100, 5467167, 2599498, 3843348, 3080907, 8035389, 5510313, 6180840, 7198481, 1425344, 325996, 6144076, 1213298, 7716704, 7830318, 6511496, 2575529, 3832433, 4768048, 4599869, 4430115, 1424196, 7910434, 3210195, 7904069, 5251564, 3872663, 3962856, 2958241, 6415110, 5314643, 4718362, 2957079, 6361575, 3624111, 632494, 1766540, 5904115, 5307677, 7778880, 6385387, 5668306, 3031461, 7408523, 1107530, 7262246, 5641663, 5909338, 4632800, 5274126, 3773435, 7142527, 7746948, 2683311, 5237050, 5615659, 5852448, 6063504, 3077534, 6186557, 1497080, 4197381, 5483691],
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