Signature Generation -- ML-DSA-44
message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
deterministic: true
sk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rho: 5AE5192442A0894AC775D84419BB7EDE9E8143A6E21CD709A47B58545EAEC7F5
k: 9EAD08050900CBCF4093F9327CAD67B7600D9F8425084B6905BB6550F426F58B
tr: 27B47C434BC194D466D83C14BF5ABEA249E05287EC80D1B56BD0824E4EB84CE1CD4CCD0DBD1BDE59106AE10516E1150E841B03E759DFDD930F6C7BAC85753045
mu: A12A0CBDCEC8AEF5EC6AD85326CA82938BBEA6C371CA19083DC23BED8053940A544CA299C0CF8AF2DD7BDA21A995598DB01944BAEC75E78D9774652CB8CB3250
rnd: 0000000000000000000000000000000000000000000000000000000000000000
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rhoPrime: A9A9F85C9C20C2B207E25FDC800A2E59F41FB874B7A5DB2CA80C3CD2F6FD1DD6D8F945C176A75CCDEE86D21C830C4164C2386D38968EC0F58ECAA2E6C5193BC7
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NTT(y): [[4047304, 6951015, 1424143, 997117, 6879402, 1833717, 7020260, 1181620, 3857346, 5444919, 8194325, 6688481, 3045723, 2553835, 8293136, 4135624, 3903731, 3168071, 7750529, 4203151, 2358050, 4620113, 7261178, 2102960, 7239039, 3563889, 4250473, 5247329, 2095144, 3579081, 1375903, 2824842, 3508276, 583279, 7985971, 6337149, 1733785, 4719941, 4130201, 7606023, 2208405, 698220, 421291, 2862132, 6100156, 4241289, 492684, 6318413, 5386611, 5054202, 8366094, 915437, 2887972, 3733125, 6441182, 151919, 8141130, 6456516, 6048296, 6651902, 5254766, 1766460, 6748660, 4928040, 7969474, 6780814, 1074451, 7522205, 2499719, 2655016, 5433007, 2794576, 6129091, 2260903, 4836517, 2744265, 5586478, 2950576, 6600262, 6411158, 5387029, 4175444, 4875532, 6716643, 3381244, 5659854, 5679166, 1816373, 5944766, 2369891, 7308601, 510008, 498395, 138446, 2276734, 2763675, 2144328, 7539623, 517247, 1571496, 5711698, 3032615, 1384373, 5677335, 3641703, 7040295, 3943525, 5417434, 6430363, 442182, 6129980, 3575821, 5390203, 3176150, 285838, 4963248, 2902075, 4262715, 6259777, 5677937, 7007778, 1059424, 6365813, 7950419, 925573, 8313399, 5292476, 2134967, 7281546, 2717888, 3597495, 3492668, 2062518, 3845010, 7429111, 4335417, 1327773, 7136735, 8187227, 4700109, 6486499, 6211795, 2797058, 2519385, 7015187, 2079427, 6372435, 5317176, 3965252, 2928176, 5876382, 5121900, 1162414, 642330, 6383348, 5893097, 51428, 5835574, 2937850, 5972764, 1855507, 3267790, 7455812, 264858, 5564922, 4758826, 884993, 1607726, 3265364, 7148294, 8091595, 131995, 8061313, 1011446, 3502483, 2229343, 559564, 5125686, 2979146, 1681278, 7104775, 3603982, 658824, 4958666, 1924888, 3487831, 4370447, 7134267, 165753, 4049890, 3586582, 7579657, 7986363, 5025107, 3121885, 7234851, 5940341, 1776020, 1324805, 5778235, 4727508, 509985, 4217559, 5197029, 6112860, 5483161, 7832985, 2735436, 4844039, 5681837, 1624960, 6506659, 4278687, 3165902, 1662950, 4698023, 314344, 5609489, 1436721, 4100014, 4539342, 7637951, 1338933, 5111603, 4160731, 7955561, 7756072, 5026188, 7704780, 3503469, 1545409, 5985360, 2287942, 3539150, 6131328, 5717386, 1338790, 3847046, 5032089, 7919773, 1125763, 2608017, 7687993, 2419895, 6489167, 6157808, 36230, 1243929, 7559586, 1683170, 3551563, 8000633, 5150948, 2086616, 7132968, 7129578],
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aHat * NTT(y): [[4353692, 5048177, 801391, 576865, 5871765, 6252585, 7465370, 186136, 3504805, 6073060, 2228432, 1605873, 7451066, 1616403, 5584379, 4341230, 7359284, 5762964, 4997819, 4456214, 7523576, 2099024, 6130237, 1055023, 8088381, 2282984, 4153079, 5579630, 6962123, 3858284, 6119695, 4457767, 4666119, 228485, 3854215, 8099180, 4643912, 4257606, 3177559, 3135056, 3639849, 7757802, 2096630, 2213004, 7368272, 3772597, 7868678, 5629074, 2174686, 6914100, 7303605, 950259, 8280872, 699475, 4016484, 3322830, 1883449, 3854522, 6006936, 2631445, 8053882, 6674021, 241381, 5048386, 1545904, 3859296, 4783187, 1109343, 6239057, 8285136, 5101044, 7813898, 436930, 8250640, 3110701, 8175078, 4363994, 2100130, 1976302, 3033362, 6644228, 2174377, 3091381, 3247049, 3329611, 6975717, 2924381, 13764, 5896559, 174175, 3855191, 5245158, 343947, 3467010, 5949901, 2454555, 2982182, 6153818, 7862746, 3051280, 1605784, 2958351, 4869784, 8025145, 6097104, 1382431, 6075556, 3084004, 5170117, 1562121, 3535913, 3791005, 4706879, 2629851, 3489184, 112577, 8222955, 2365891, 1005617, 2828492, 7909693, 6017852, 2218640, 5764700, 5461341, 1185790, 2272654, 6711460, 42942, 3515681, 4282320, 6402239, 2142770, 7523713, 3236075, 297844, 1440040, 7094358, 1931694, 139857, 5891260, 1596241, 6535867, 8344683, 3830882, 5106051, 604954, 7429707, 7078697, 6638027, 2540562, 2101819, 1124933, 442161, 6227052, 573461, 154368, 5038560, 8210269, 644696, 6000172, 7171980, 5390423, 8096820, 4895302, 7358454, 2502384, 6260099, 7278040, 3578500, 7694700, 4933454, 5347081, 3417200, 7997460, 2398739, 2869745, 4611598, 2414021, 3577643, 7737332, 2121445, 3247120, 4673961, 3272341, 2355845, 385931, 7275147, 5608293, 5691917, 7303988, 7031679, 530681, 4543860, 513030, 6536974, 532849, 4540802, 3316414, 1450980, 1394302, 5858210, 4373408, 7510238, 2456810, 5650429, 2529673, 8251471, 3834347, 1917675, 3316559, 686638, 689049, 6413634, 7439663, 3701099, 4531644, 2042082, 8005752, 6507205, 7389037, 37450, 3727399, 5461799, 2573871, 4841323, 680402, 7518464, 2138818, 8127928, 6739315, 2970565, 2237299, 7189858, 1205158, 2516134, 100081, 7932786, 6538105, 8299739, 2886258, 5372459, 6513398, 3063269, 1561643, 269133, 1150140, 5906916, 8197992, 3721737, 5695862, 2587735, 5716960, 5793312, 4970017, 8319353],
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w = NTTInverse(aHat * NTT(y)): [[4090552, 3533489, 3040556, 7911513, 7938043, 4498751, 8247264, 4019279, 4489651, 1937009, 2134142, 8254119, 5094448, 5222799, 4576247, 3403906, 2975355, 2140940, 3628608, 5281315, 5109889, 1200233, 195163, 2108850, 6480104, 7855161, 3333152, 7956488, 3193974, 5711179, 7180786, 3453736, 1821842, 2110116, 2878243, 7162500, 4778256, 4585424, 5690153, 7214683, 7867794, 2415723, 2750775, 6199950, 5719012, 2555792, 8356651, 3060335, 2218881, 2981138, 880777, 2010263, 4240860, 3033290, 4162306, 7281551, 5050617, 2706197, 6037641, 2789071, 7542768, 5586676, 1796352, 7117584, 396604, 5672109, 2211396, 7377636, 3191925, 3589697, 3458243, 6379171, 6282224, 7514513, 8093269, 744491, 6530745, 6680303, 7959458, 6468404, 4554613, 1579512, 7291999, 7940063, 5019760, 6110959, 574920, 1509170, 2888154, 1483394, 4374310, 5359784, 8352303, 6983263, 3258247, 6175746, 1484936, 6603038, 4425884, 5388303, 7924352, 2295988, 357783, 6525701, 991874, 541802, 1891087, 1683548, 1436139, 6093709, 4703588, 2636067, 7443210, 3950995, 7438244, 944369, 1009384, 2164098, 1776297, 7705035, 2651433, 4265265, 2499396, 7229014, 4506901, 5760894, 3042795, 2855661, 7863673, 2822996, 4370369, 1689991, 4483121, 7462859, 5232048, 1998726, 6947975, 2216539, 854217, 3298338, 7281699, 67968, 4282308, 5533878, 2648693, 8270748, 7048058, 8080304, 945526, 1061351, 3105094, 6747922, 2060092, 4308541, 7899, 4691965, 1970672, 2573098, 2648528, 4774027, 4483315, 7794077, 5267629, 5118370, 6540218, 3008373, 8351187, 4767263, 5247715, 4942060, 3176502, 188236, 8036029, 468894, 8299608, 1200966, 3396215, 4071474, 7010176, 2333943, 1514853, 5727543, 7097700, 5803346, 747441, 728038, 3038012, 7421953, 3616257, 878509, 1073073, 1471585, 4678718, 6739394, 3823885, 3885780, 2141989, 5404595, 2739157, 3790080, 1495297, 3192452, 7681032, 7973598, 478836, 1872058, 6164948, 1242520, 2012693, 2823987, 4319384, 7352140, 2080489, 4333079, 6387854, 7945174, 3186302, 1021503, 5663058, 2112936, 5241400, 832081, 1374845, 2208928, 550747, 1558786, 118265, 239678, 6818495, 6013688, 7967061, 2194948, 5730629, 8373419, 823721, 6536521, 7935959, 3299061, 1701492, 7337991, 318236, 3178638, 5878875, 5250341, 4727458, 5440170, 5264828, 2273682, 3509101, 8219686, 8352834, 3882307, 3053324, 8316046, 6618579, 1562087],
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w1Encode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

cTilde: 71F7304848C9CF3A3BF5D462212B4725AC2117EE7E420270B25A58AF64729F7F
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95195, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[4119157, 4505652, 6897916, 4806244, 6670663, 3722624, 6104592, 410456, 6916294, 1351624, 1471249, 7817884, 1022432, 2906279, 229580, 4350585, 1067397, 1948128, 2964589, 5087708, 3419462, 1322155, 2258645, 3016736, 743432, 5070822, 6864104, 3603348, 2828350, 2551459, 6506617, 342362, 1697036, 3656135, 3725520, 1936311, 1811542, 5025592, 6414861, 6641330, 2561047, 4460921, 7923163, 3940117, 96960, 6633996, 5044919, 910287, 4079595, 6024926, 999115, 3401211, 7454097, 419511, 8351401, 695330, 484307, 2986984, 1560856, 514990, 1019197, 1210749, 6190490, 6643871, 192851, 1090678, 2361826, 5617893, 466884, 7796394, 1634530, 8125279, 4664464, 3376259, 2872831, 2282116, 1286962, 3414088, 492311, 5610102, 300434, 292767, 5462202, 1855131, 7991776, 961117, 690518, 4861974, 5708212, 1995637, 2025076, 2592836, 1883793, 2316580, 6444558, 6824472, 3735581, 1148536, 2122728, 1920873, 7987369, 2834593, 5849081, 3521554, 577512, 3139555, 3323671, 1864187, 4031715, 4365034, 5080152, 2353044, 8072169, 5048399, 7712099, 857933, 6597723, 2133892, 7874803, 8183691, 3617268, 158021, 7965930, 282924, 2344956, 1661149, 427167, 5194716, 4274496, 2503434, 5563801, 4949620, 2336803, 5144226, 6003183, 1148224, 4348142, 5936750, 3982248, 4761760, 2594613, 8028987, 27396, 4700121, 5419741, 1259523, 2407545, 2710748, 2490245, 340966, 1760188, 3606892, 5125161, 7420018, 7858511, 5399261, 2081486, 3582517, 5635873, 8210355, 4630905, 7209680, 8209364, 2122756, 2950324, 7384872, 7508136, 3072473, 2654368, 3913844, 4926780, 411832, 1831493, 5436967, 7710061, 1773156, 5217831, 7057492, 222078, 5498717, 3073989, 6977501, 1376190, 3696526, 6565670, 4479326, 745986, 898781, 5645806, 4466322, 1543955, 3162952, 3491918, 2269407, 6546127, 1465149, 3843614, 6604748, 4517157, 3026459, 1396261, 7186079, 5187880, 3389548, 6347979, 6050083, 6537771, 7594187, 3478860, 2848109, 6367670, 2832544, 6083968, 1424056, 1963831, 1131804, 8046601, 5960408, 6077217, 4758134, 4639554, 5483511, 7919951, 5552396, 477197, 8362596, 4249042, 3932859, 1819050, 7173639, 5646100, 7127582, 7082270, 6113124, 3874179, 8194942, 7012009, 530398, 2714013, 657657, 1346900, 6937646, 2203649, 2150717, 1750135, 1974680, 1171662, 2920905, 2226089, 5558024, 2979495, 4108312, 481351, 3810077, 6065179, 2498009],
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w = NTTInverse(aHat * NTT(y)): [[5078642, 2908747, 5983117, 5702027, 7014885, 3882278, 8130884, 5111356, 7153298, 6965105, 3536162, 7516375, 6734081, 5132054, 5879000, 298690, 4318561, 8300441, 7316064, 6853806, 813190, 556351, 5616495, 1832475, 742705, 593306, 2248098, 604274, 35882, 4964163, 427852, 3496795, 5195401, 6836862, 486710, 8333642, 5734776, 5710443, 3050693, 583496, 320004, 2659988, 2871312, 4394287, 4144062, 6914101, 7729184, 7582019, 6468579, 650271, 3727687, 4968937, 7739869, 8217743, 7160675, 4796060, 2782841, 1539847, 8133708, 7962487, 3387429, 7262850, 2109712, 6219667, 2320322, 8045416, 6831805, 2823105, 4002186, 1305011, 5493376, 4014920, 3838240, 2553617, 4352803, 6911656, 15171, 5948050, 6395662, 6703949, 361289, 1846084, 3046953, 5360360, 3762914, 3371944, 5620433, 547591, 5283180, 7798896, 7203346, 3439985, 7615941, 5909004, 6818691, 3009435, 830188, 7523762, 7267372, 6276513, 385655, 1930344, 3184713, 5399939, 6662831, 7735333, 1771182, 2836759, 2999780, 3877333, 6867699, 4836826, 3307073, 677380, 177486, 2188234, 443022, 6446584, 5721130, 570766, 1430125, 4861342, 1091892, 1658013, 2527057, 723711, 4160092, 14020, 2444811, 2694966, 7121093, 3249298, 5309347, 860091, 6342579, 3386367, 4057667, 1822788, 2879193, 132195, 3916152, 7377292, 3490373, 3217777, 7613922, 347049, 3169825, 2559024, 7181042, 3869250, 2509875, 7599631, 603858, 5223679, 7107149, 3081018, 5657840, 5009001, 2414698, 3642032, 4414103, 1672424, 3638254, 6298014, 5024707, 2540182, 1664534, 4376282, 1412443, 6799459, 8256582, 2002544, 688379, 5512887, 1288812, 6604015, 6720858, 7453167, 5525606, 8199408, 1477293, 7230410, 1976704, 4331417, 4327270, 6619602, 534318, 954957, 3638641, 6718661, 4806332, 8067070, 8039826, 4878855, 8370793, 569313, 4648473, 3712524, 7846105, 3141332, 8324693, 2000502, 550140, 3094982, 5923140, 4058757, 5420419, 5829087, 7740297, 2340194, 2208284, 4284243, 7111864, 8307775, 5772478, 1267544, 3836435, 1700348, 6645871, 6164883, 122073, 7576509, 4017238, 6431527, 1012940, 3002219, 8069454, 3791742, 3850362, 2197003, 2830291, 6269368, 3237523, 6452242, 3472564, 3057873, 2680688, 3204419, 7117932, 7534801, 595170, 6593692, 6066886, 3755931, 635205, 8230087, 1210291, 201414, 5853041, 5763321, 6085956, 6232046, 5209152, 1690320, 7901696, 3448646],
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w1: [[27, 15, 31, 30, 37, 20, 43, 27, 38, 37, 19, 39, 35, 27, 31, 2, 23, 0, 38, 36, 4, 3, 29, 10, 4, 3, 12, 3, 0, 26, 2, 18, 27, 36, 3, 0, 30, 30, 16, 3, 2, 14, 15, 23, 22, 36, 41, 40, 34, 3, 20, 26, 41, 43, 38, 25, 15, 8, 43, 42, 18, 38, 11, 33, 12, 42, 36, 15, 21, 7, 29, 21, 20, 13, 23, 36, 0, 31, 34, 35, 2, 10, 16, 28, 20, 18, 30, 3, 28, 41, 38, 18, 40, 31, 36, 16, 4, 40, 38, 33, 2, 10, 17, 28, 35, 41, 9, 15, 16, 20, 36, 25, 17, 4, 1, 11, 2, 34, 30, 3, 8, 26, 6, 9, 13, 4, 22, 0, 13, 14, 37, 17, 28, 5, 33, 18, 21, 10, 15, 1, 21, 39, 18, 17, 40, 2, 17, 13, 38, 20, 13, 40, 3, 27, 37, 16, 30, 26, 13, 19, 23, 9, 19, 33, 26, 13, 9, 23, 7, 36, 43, 11, 4, 29, 7, 35, 35, 39, 29, 43, 8, 38, 10, 23, 23, 35, 3, 5, 19, 35, 25, 42, 42, 26, 0, 3, 24, 19, 41, 16, 0, 11, 3, 16, 31, 21, 28, 31, 41, 12, 12, 22, 37, 0, 30, 7, 20, 9, 35, 32, 1, 40, 21, 34, 5, 16, 42, 20, 20, 12, 15, 33, 17, 34, 18, 16, 14, 17, 37, 40, 3, 35, 32, 20, 3, 43, 6, 1, 31, 30, 32, 33, 27, 9, 41, 18],
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w1Encode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

cTilde: 082E83CF5781050B99CD3EE374AF5B0B24E49C82C438150D45051C9C1EB94F2B
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95057, ||r0|| check passed
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[270439, 1411037, 3377986, 78159, 2180123, 1422052, 1539112, 4901871, 3499164, 5202915, 5895461, 6245409, 5661, 5520541, 6963748, 7375972, 357689, 255839, 6953748, 1300170, 5686391, 5381591, 6025671, 692468, 3813346, 7064302, 8265258, 6333634, 641012, 7799324, 7631007, 6778528, 7015864, 6492383, 1546856, 5388201, 7343229, 5795471, 7794468, 5984449, 7704729, 2583493, 5903665, 5290330, 2723371, 4469623, 4634712, 3833999, 229613, 4840059, 5988016, 7869482, 6142921, 4134744, 6728559, 1448930, 2499244, 868269, 3675580, 4128116, 1633331, 5473768, 8039539, 221897, 5449129, 619008, 3186765, 7601650, 6469561, 2649495, 1944846, 2641664, 4413249, 5022101, 4948349, 3763931, 4332795, 2462908, 5609865, 6334703, 6439823, 5716034, 6368697, 3965070, 6553067, 434943, 5269846, 7068965, 2511877, 3869856, 6020334, 2454395, 694163, 6098709, 5894956, 6858074, 7911100, 451403, 2487949, 2857793, 1117452, 531522, 6586000, 7248477, 6161964, 2480315, 1212450, 1535116, 4690555, 5426276, 1978615, 4490013, 4119858, 3139696, 2287571, 265875, 5450308, 5558510, 571996, 7980836, 3117111, 3070862, 4613476, 6358709, 1116687, 3475251, 2324795, 289123, 1753647, 4551872, 7051247, 4271872, 3621759, 307571, 4463206, 5539950, 2758876, 1168112, 4260769, 2489571, 4997475, 1551997, 811992, 3864818, 8189661, 5708611, 5655256, 100693, 7514304, 4502295, 5959216, 4369905, 1689582, 2511305, 3382188, 3003285, 3971609, 7834992, 6441726, 5885280, 2251605, 5341337, 3087824, 6110659, 4923959, 7916180, 7411763, 4411104, 3797597, 1911050, 5999092, 2677961, 6388421, 6838456, 305566, 2188744, 500351, 7288058, 4568389, 1742411, 5735486, 1788148, 5489697, 1683021, 1357541, 1325630, 8040164, 2793414, 2772766, 7870602, 6168526, 1145799, 1403387, 3641817, 1124649, 1233705, 1356142, 5011012, 4678335, 1145790, 7648366, 4981430, 7138199, 6143835, 5431165, 3953282, 4555644, 7447701, 7430096, 5206325, 1649025, 3700212, 4106442, 4062045, 5080650, 1417100, 1759276, 784375, 4667173, 3661887, 4324724, 702200, 5636528, 740386, 6137036, 465242, 356675, 7676519, 1490083, 603059, 3084235, 2758380, 688895, 5368148, 3468603, 3643497, 4278023, 6221160, 1246505, 5649340, 4448393, 1534168, 6312053, 13446, 3798373, 392323, 8097640, 4820757, 501334, 3678061, 906673, 3652378, 5428514, 6829935, 7470838, 2307732],
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w = NTTInverse(aHat * NTT(y)): [[6810060, 5257295, 3345583, 563675, 2836703, 547228, 5361665, 5992755, 5084814, 3315175, 8274605, 1850047, 2172053, 6165931, 1831180, 2584211, 6374627, 6752156, 7824113, 6345678, 6210108, 6552017, 6090444, 1977866, 2095932, 654181, 6135955, 1701793, 2492319, 273562, 2274683, 7605268, 3432616, 6241327, 6090594, 5037093, 2433492, 6492107, 769107, 2249870, 7747152, 862336, 6984462, 2882730, 1481930, 504950, 5428312, 3889903, 3470199, 6075553, 390654, 5432315, 6093208, 5047184, 2750411, 4691774, 6190863, 286665, 6847365, 3074794, 2414883, 3956958, 5826818, 4475784, 8069308, 5763459, 4096128, 3996498, 6622285, 2812756, 5181899, 5511536, 2267672, 4808858, 4539829, 5293998, 352697, 6116656, 3356186, 5077122, 1384863, 4168883, 8204574, 6762031, 7982928, 5971938, 1713792, 257917, 1971971, 7324845, 8318138, 3529583, 8080948, 5350186, 5957622, 6025144, 7982838, 5587477, 3291765, 1816959, 4882010, 5796387, 3951888, 7920334, 4025055, 1951560, 3572826, 4059910, 2681065, 8285583, 5739081, 7640414, 6913583, 2343183, 660858, 8211560, 4467485, 550045, 1176015, 2290350, 4336432, 5102418, 8236768, 6833365, 6682988, 2863085, 3216113, 5654687, 6346513, 2276840, 7087590, 6575819, 7523431, 4854376, 1160149, 617581, 1362257, 4179289, 8308324, 5648908, 7446702, 5451334, 7047349, 5148881, 7459033, 7830470, 2333917, 3138547, 5543837, 876323, 1158376, 735444, 1471120, 613167, 5970922, 6096918, 2754375, 2780955, 4754069, 7468161, 2144640, 2898340, 2251696, 229491, 5460893, 3829178, 5878117, 6319089, 74056, 3297315, 4042048, 4711962, 8204448, 4654703, 1285683, 7434843, 4118231, 3624810, 6890483, 7028958, 6676126, 5416594, 5183184, 1027346, 4484787, 3405892, 8105594, 1022268, 4835352, 6486881, 6076569, 4315027, 6952114, 6668703, 1241352, 2260652, 440881, 6260090, 2925987, 5062999, 1307248, 6426499, 4060110, 4688243, 5182302, 5094896, 7143829, 6201727, 5946744, 8278720, 233488, 2931900, 4836732, 5880504, 7792717, 5685863, 2257945, 4091436, 6640950, 2759011, 5782620, 5098681, 3582628, 4387985, 1511354, 1101721, 5044827, 5759042, 6195504, 1878917, 5374397, 3781938, 5400091, 2313818, 4471911, 3887175, 7337812, 8215304, 5189572, 589717, 315656, 1611167, 6553875, 6539852, 6037350, 905324, 6905269, 2860728, 217119, 4128930, 6671457, 6165801, 3488346, 7781498, 3904266, 102617],
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w1Encode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

cTilde: 514431DDB2E1846A8D7E7CA6543AE52B63590653C400244B65C052909997240B
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95181, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[4946737, 845782, 1559526, 8335667, 3407129, 4933664, 2761395, 6672771, 874466, 5867726, 2523764, 2765908, 3497667, 1539861, 7683077, 4722136, 6858841, 7211166, 3562719, 2882723, 6248910, 472321, 6670792, 1913046, 3856250, 5929995, 150807, 4736183, 5352223, 6723871, 2280633, 1561864, 2100896, 519135, 915066, 6843621, 2357894, 2929465, 4320527, 5276221, 6656497, 1873276, 3201035, 6849237, 7994573, 5745780, 4114676, 7622475, 1777318, 4368203, 5465261, 5613018, 5497636, 7136683, 795994, 2777378, 4588710, 5493003, 2996020, 1789223, 5955445, 2576807, 3938630, 7010195, 5076035, 3997168, 4983322, 7905237, 6417185, 7999271, 8006, 6761598, 5505574, 4260583, 6600774, 7830212, 5882870, 4771662, 4790878, 5254779, 4755870, 4467430, 6282857, 1779331, 7325943, 4266007, 3824501, 5168151, 7252459, 408600, 6553433, 7033739, 7107435, 2774113, 2090424, 8346081, 4070443, 6590615, 5388604, 2972163, 3176509, 3575050, 871073, 5171238, 6034564, 3173694, 3054140, 5619210, 1171631, 4896615, 4342768, 220191, 3792269, 2156196, 2842568, 1935021, 5328539, 3866114, 1769682, 5588814, 7732816, 2231250, 1632133, 6950883, 1902644, 5930521, 1293356, 2097873, 3530525, 5401087, 1729109, 4613127, 7076361, 5684740, 7253529, 5680583, 3066257, 8344958, 922463, 1131181, 2999254, 1907012, 7416375, 3620789, 7163258, 623893, 4532111, 2647565, 4104861, 1740964, 1784912, 4987996, 6356033, 6193247, 5443522, 7079401, 5526497, 4705707, 7620683, 2526306, 6322050, 1663724, 4054203, 2120567, 6810554, 6942048, 522200, 3996688, 1460005, 15384, 2205386, 7786965, 5460260, 6981979, 1671354, 963357, 4074913, 8373224, 6492471, 6133984, 2739653, 6573893, 8075045, 7403250, 4169618, 2401844, 1217765, 8330038, 8378862, 2693721, 170122, 7696923, 7185482, 8119334, 4096712, 7291634, 1565455, 8216957, 5353402, 568336, 5869384, 6848083, 3374591, 2570617, 3629696, 2411900, 4859814, 4266005, 8278792, 7909137, 846162, 7877092, 2068332, 3047397, 5423389, 2102968, 7912992, 3718370, 5170029, 3274728, 4049041, 4062950, 7705442, 7734371, 3297273, 2155931, 6230075, 7956930, 2222954, 3044967, 89727, 4209169, 3349491, 7699952, 6359710, 7499918, 4995913, 7890109, 1591660, 2518401, 3943964, 6759184, 4756583, 3933237, 5566099, 5661894, 3326897, 3931476, 4373550, 6670646, 4977688, 1364389, 904723, 4386915, 5404205, 4442927],
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w = NTTInverse(aHat * NTT(y)): [[384297, 6873945, 1386044, 2707825, 4559028, 2345590, 1683029, 1381050, 5089217, 3858970, 8019333, 3719928, 7464499, 7143460, 8105520, 1063256, 2548649, 1476973, 4350521, 2814281, 1508160, 4620286, 5180416, 7961135, 8225186, 3436312, 3714798, 7248949, 8298613, 8234534, 6859250, 4834875, 6723519, 2908776, 1765330, 6519002, 1012802, 7740560, 6984048, 7534774, 5825376, 2377367, 7942804, 4052306, 5218815, 1712928, 957401, 1780227, 7353810, 2118962, 7115201, 1880031, 6924059, 258994, 700325, 4238821, 2032152, 853084, 2577443, 8132969, 806977, 7437962, 1360762, 6068262, 5545002, 579247, 4573212, 6229825, 4742393, 3472733, 6512657, 5314650, 3505281, 1607405, 6208821, 5900245, 2082369, 5242485, 7341542, 2511261, 6318313, 2429960, 6747446, 3759011, 7754808, 4159981, 4276212, 1893140, 2578155, 3038470, 7861094, 1026404, 6559112, 2466912, 6577860, 1735792, 6954936, 7205356, 6971862, 1538204, 381363, 282689, 6010091, 5355177, 352437, 632023, 5694484, 3224744, 7926001, 1201795, 1133243, 6852869, 247980, 4419696, 1140960, 5448889, 3507329, 7238974, 4716909, 5819154, 4245481, 2047430, 1128026, 6358186, 3084430, 4292302, 1714621, 983565, 5290978, 7373954, 4630718, 4210511, 4017742, 4145022, 7587880, 1701233, 2900207, 5885413, 4970306, 4139781, 4769134, 1820499, 39552, 7446936, 2681521, 5467058, 2152606, 4386839, 943603, 1817360, 3637246, 2928438, 7963438, 1668737, 6793018, 2043501, 1957277, 2300163, 6189583, 114118, 916470, 5995015, 446183, 3129002, 6671328, 3739236, 4155878, 1055199, 5628665, 7249467, 5718543, 676044, 649659, 174601, 2359910, 796011, 4966122, 2256388, 5138789, 5032867, 5860372, 2961710, 338446, 8330407, 1937794, 4670589, 8181875, 2284908, 3484818, 1858094, 1810442, 2548024, 3420709, 3671454, 6324763, 452103, 7981056, 6500201, 7612513, 994103, 2026537, 3222001, 1420137, 8365497, 2643148, 3934467, 6763875, 5772453, 1272716, 2659307, 7484352, 1717158, 6652654, 5404123, 6214385, 8244224, 3289993, 4910941, 2557381, 5130820, 6678523, 4624846, 5941665, 655869, 344273, 5330639, 1185874, 6020131, 5949271, 8013347, 2593802, 7982732, 3743065, 6183643, 4322109, 2229748, 1460397, 5093994, 4556072, 2474659, 4354542, 4329187, 7590766, 7717689, 6825646, 7994716, 731457, 7260114, 5070493, 827616, 8187697, 5118243, 767756, 4731125, 4455502, 2724432],
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w1Encode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

cTilde: 57784A952DCB8E648F8610F9EF0BF01F0AED20707F445BB525753E5D7096C63F
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95174, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[6533041, 4978568, 3370532, 6220292, 3901369, 6214572, 6998023, 716133, 6077287, 3371588, 1641879, 3983513, 3955445, 986729, 6954844, 7808485, 7615992, 4784384, 2273506, 5251509, 1650658, 2689858, 7923026, 6986888, 539118, 5074688, 3073707, 1735510, 3510830, 1438052, 3826115, 966673, 6964892, 111884, 3213582, 3893747, 2527836, 3551616, 7673060, 1003320, 8234706, 4233522, 332909, 2565736, 7983619, 8267085, 5619020, 884872, 5837840, 507974, 4325726, 150971, 654692, 6563968, 6251928, 8234231, 4748927, 3323408, 2142394, 1586430, 3130892, 6631469, 1859370, 7796618, 237977, 443393, 2544291, 888629, 7309188, 6366079, 4932192, 6709741, 5112339, 5976309, 360744, 3395692, 8128798, 2942396, 1283671, 5350247, 4686769, 2885742, 251649, 7979569, 5047314, 5108623, 3840666, 8071260, 7010538, 3035792, 6936554, 7240073, 1612734, 5576337, 805551, 4008321, 8038060, 93604, 1453154, 4673060, 1516622, 1054031, 7381111, 3435904, 4220341, 1896686, 735951, 4793369, 2992738, 4778101, 4073536, 5058825, 3282291, 7912741, 7833204, 6439701, 104308, 1762208, 7998391, 202249, 1975504, 6324511, 5992913, 2437577, 7526985, 5016077, 7878786, 5363826, 4552235, 4256743, 2190020, 5788940, 3017025, 7415010, 8032817, 2659571, 2870194, 7550703, 1012315, 4181781, 4636527, 1916780, 4563021, 3587252, 1896096, 2245647, 8157996, 2362183, 5706924, 2926869, 1877585, 5995487, 8289226, 8263843, 448340, 3130955, 7851088, 6175721, 1467954, 3017018, 7990704, 2753527, 490463, 2827201, 3333923, 6431425, 7167706, 7327028, 6199863, 698983, 5231059, 8002549, 5705935, 1774098, 2722494, 7728766, 7628580, 6086759, 5320544, 6573614, 4662815, 1998081, 1797426, 5137509, 4444260, 871225, 1629143, 6334782, 2681479, 7046293, 1463326, 4576918, 65603, 859158, 3145799, 8362192, 2951433, 3016486, 6616137, 3138220, 2620797, 6281896, 4238003, 4098585, 2369621, 8174965, 1902641, 1700464, 6419015, 4674669, 2181507, 491553, 4239209, 1145563, 4723270, 7774326, 7969732, 1614053, 5659464, 8172280, 6885516, 3244039, 2887656, 8326545, 3807638, 7999758, 4758900, 8216958, 2247160, 7397121, 6447949, 2827955, 4315566, 1258054, 6415657, 1723761, 2204062, 5017345, 6113323, 940113, 6059584, 6765072, 2655110, 242943, 2739807, 6769400, 4867737, 7905510, 7167983, 1433446, 3958473, 7460339, 6248184, 1648762, 4815250, 7661469],
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w = NTTInverse(aHat * NTT(y)): [[3162481, 1697673, 4795824, 611569, 5434330, 1733082, 7251102, 4971247, 3910715, 2491782, 6324776, 81764, 2665637, 5536158, 273698, 1225182, 6230352, 7073809, 3597226, 7105208, 1714198, 8268058, 4370687, 4216584, 4389790, 930140, 434608, 7635755, 6653037, 4988225, 1234291, 778829, 7794607, 1618222, 1726968, 8330580, 8181288, 6394094, 273133, 7297185, 4150606, 3325362, 4174099, 2994253, 2846796, 884598, 1933530, 5047139, 4475193, 4730936, 8050743, 5261280, 8308984, 3839276, 5709353, 5743170, 4958291, 5166310, 6277131, 5757650, 2681421, 6960950, 2720794, 2111752, 7558120, 6242284, 5081355, 192063, 4958582, 4402889, 166667, 3428552, 5463493, 5364845, 2201207, 661550, 6637816, 5842826, 3744334, 2840855, 5316258, 8320816, 7934531, 596600, 1541260, 6202393, 203019, 4655597, 2866581, 7949499, 2482488, 6898190, 7232233, 983996, 7867320, 4350042, 3991883, 2151726, 6456207, 494293, 7168151, 5392469, 2838659, 582866, 369227, 4684167, 2925490, 292945, 8048522, 7535096, 6109971, 412070, 153460, 735813, 1787653, 6286676, 2215016, 6076533, 6034893, 4735293, 7938870, 6296716, 6598983, 890835, 1734070, 7033988, 4387759, 4020565, 7398045, 7761130, 4987117, 7903294, 4867071, 1835433, 1202809, 7827136, 3809059, 1867093, 1405503, 4748091, 192410, 2236245, 4469273, 6371849, 9000, 6450797, 637714, 2226263, 2194286, 245901, 4838381, 5383015, 7053864, 7212387, 469359, 1299197, 5481911, 1934165, 8204820, 1886399, 4482493, 7100018, 3790136, 8222512, 2735141, 1055554, 6696326, 4073299, 1855494, 5230127, 7539718, 3450311, 6043137, 2479912, 3379061, 5568654, 8350447, 7017046, 2960387, 1368758, 5033258, 4274834, 4722768, 514652, 2138907, 3335856, 6460563, 5711458, 5130436, 4041780, 6374381, 8118926, 6620680, 4794823, 3732926, 1541850, 6321160, 5960349, 2389128, 304966, 7685913, 5390282, 6614147, 3567881, 2359284, 4042383, 6742777, 7097351, 3331485, 4160548, 2296016, 871313, 764148, 7649489, 6620606, 1911616, 2168461, 686787, 4506565, 1166064, 4429880, 1273926, 1902954, 1986103, 1501688, 4079071, 293800, 6639059, 4142270, 5394062, 157287, 8158977, 6678748, 6410626, 7246992, 6005168, 3389693, 6609025, 7019943, 4503360, 1791885, 3431554, 1815826, 6083919, 1795930, 6629347, 4766500, 7849685, 5763989, 7396105, 2537326, 6773887, 806389, 7377076, 8295050, 523136],
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w1Encode: 51920D5D626A5513024E1718613995C97A595721A0A36610299200AB18985664414FA16857A67200E579DA167A4EE92C68B805DA15481DC70CE3473D1CA00E4818608FDA9066915ED5220E26F70C42F6082A0A0A0191840C08666A381649795567AAA59A62A49472640173858038304C9071A5291C9DB22A5849AD8E3156CA864A60237540091D9A950D8B247A5B15AE634621E1D70828374E4C359691C514043A2A0B8119D7A12848258C1617ACA36882D2586289A480C998A5DED990C4090C51559A17740ADD236E97434E903565594A1A295791DFC038CDA334CB622DE888558BD935D2C4199FA64AD5A6702BC96D19954807C57C24D62CD379586745464F2609A59A7C490994A63AA01C9975E08811DE3869C7585DA7EA44CF18A289364EA2783943354C57887C297A6AA1173C889819C1743E26A85923B72A135976E2386A4E37344332405E3436DD47284F3AA82586520D111106851967504E9E989854192048B73815F58417926E5A587E8C15A598095DE8D1555B921A95D118612A3210049505B65581194863021C9D925C85A411D1681645513D64306AE638710606A913772D1D93284750684B09101BD78C4F04486036965E107544D690686A9127106C01C38C9D953E5C264189293A02B410A667A560555D1FD2592843600F5264AAA27401D2648D604D9B595452C600C302401E1614D245A6A1488E8AF85599194242275A232719CE567956E1A424D3756652A8C9189CD629559C5302A2778DAA91A5CF9431536A34C41A8D4F7552259334877546A45A9C2995149F06669EA484C3325827E98D868A1C80B1420EAA8D4D934CC9185485940C81155E418931E57A798EC15D965A885463AD20A50801179EC364350D888196881A1555310DD86167BA6828DA900F5A04A5A8111CA27A41B852CB550A98B66D19D26C5B99620701985136441B3A509A2054C8022D53683465610E922181D77652DBE474C0DA2DC6469A02772E12A209CF399C170396843429CB10A68DC474A7B46E593821271605606532097A828F43229C2392D81359C6756ED4985AA5B0A8C5499198027A00F199

cTilde: 6E7A396AD957637BEA3AB6D8BAF6CF363FF45829990B947C35890A827B9F8C76
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95195, ||r0|| too large
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[4144274, 3882210, 6189089, 2800333, 7170079, 1955717, 2067521, 6335262, 3712617, 3998888, 6100077, 4572472, 1409300, 7600513, 2539865, 7696729, 7168397, 4059264, 1483606, 1202122, 7497155, 5306702, 8108071, 5084950, 2451769, 6850864, 825665, 2706020, 337052, 8085330, 8071026, 686285, 5128845, 7834920, 3786674, 5786834, 886303, 4349147, 6403963, 7738178, 8043410, 664146, 2224473, 3785684, 5453763, 7410122, 6576050, 4888548, 7204709, 1050302, 3890917, 2689953, 1023061, 8319709, 4721202, 7386291, 5379876, 2194838, 1297802, 675432, 3735745, 3523094, 4865252, 3471405, 5727577, 7174662, 4897457, 5057175, 1876580, 7432031, 3924620, 1701595, 649297, 1857091, 323528, 3165593, 2681704, 6047248, 3965532, 7814313, 2119878, 8067580, 4000374, 4554383, 6403311, 5948918, 3685423, 1908012, 420264, 5349926, 4654511, 3221351, 7681492, 3981112, 6388845, 3904716, 4797659, 4518555, 6706259, 564103, 6112714, 4361351, 5984502, 2272797, 4740989, 11816, 143248, 7463577, 347639, 6679251, 6705835, 6845785, 4054627, 6614122, 795643, 5774979, 4200013, 8078417, 1464582, 1441055, 298495, 3941806, 7202076, 1185948, 5540222, 4457463, 8132816, 6387087, 3492343, 3625822, 501026, 7976862, 4361016, 7427868, 3105685, 867213, 131258, 2905951, 6210916, 3101158, 763342, 8176843, 4032839, 5591695, 5314452, 6533064, 5579623, 4920002, 3933866, 5583038, 350131, 4389643, 8279051, 4437228, 6803463, 696486, 771147, 8311848, 1236218, 7099074, 7671952, 2779216, 5722795, 4182132, 7396608, 7972044, 8218885, 1088582, 5107062, 683038, 110671, 7822081, 1506962, 7239329, 6738873, 6300221, 341687, 1207159, 5115690, 6285552, 7140798, 7908220, 6844030, 3462309, 427478, 8220817, 7812996, 3017072, 8075507, 5014500, 5293767, 5196505, 330973, 277826, 5782650, 4815922, 603819, 8095184, 5815112, 3890090, 3599719, 6947198, 5529166, 5403879, 5967639, 1827159, 449565, 3226207, 7096242, 3148589, 288262, 4637948, 3903066, 1966570, 7544432, 1266919, 1871975, 2814281, 4832984, 7587970, 6539739, 3078897, 5852852, 5615308, 2280117, 1046783, 6464821, 1765079, 1102385, 6747240, 8308562, 4496111, 3375685, 2923931, 2633909, 158531, 6378761, 8118144, 8092436, 6889707, 7173652, 6524258, 2527895, 5395555, 5041932, 7972812, 4069069, 188182, 3275869, 790387, 485455, 6812533, 996658, 939364, 2552181, 1907716],
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w = NTTInverse(aHat * NTT(y)): [[5240747, 5672693, 3227538, 5608643, 7376451, 6268395, 7842310, 742097, 1523549, 832881, 501924, 8067281, 6329495, 5504776, 3971888, 3801791, 4117407, 6478341, 2044156, 4245917, 6845811, 5187328, 7202402, 132576, 2973864, 3083763, 302412, 1720639, 7057094, 2524533, 5042064, 3599604, 6848856, 2731174, 7342942, 6450165, 1980970, 5897922, 4130069, 7389301, 7300570, 4744648, 2426563, 3852275, 3488525, 2280443, 7124268, 7590420, 2647237, 7998436, 5393177, 5633010, 6830940, 4848716, 4394142, 2495788, 6551700, 1688296, 548462, 3988400, 6527720, 4933464, 7665692, 1326029, 1516316, 3770183, 7816033, 5773859, 5063489, 8331669, 249865, 2543470, 4343337, 3966017, 1354714, 7497374, 757590, 8350046, 5989356, 1766692, 3196249, 3257950, 1102775, 6794739, 6709857, 7652958, 4962759, 4217553, 279543, 3996828, 5422508, 996570, 4230292, 1848464, 4362788, 5392107, 5452405, 5070186, 4205000, 5815772, 2596502, 784391, 4842747, 750757, 735549, 1580091, 7884651, 7809786, 1830210, 7939330, 7195384, 5256472, 4187312, 8089158, 2473883, 371460, 8367488, 1553296, 8135784, 31569, 929530, 3904674, 3604817, 3641032, 5216924, 1999566, 3020352, 230736, 6684437, 131984, 7940540, 3017812, 3704888, 7936164, 6134995, 3451266, 5394412, 193176, 6421784, 4609355, 2581791, 6067133, 2566648, 3216610, 166624, 2000942, 5056112, 8323814, 3908194, 8004673, 2632282, 2754041, 6884513, 2991808, 864632, 3663442, 4878602, 1016755, 4680101, 8213279, 1551614, 7035006, 4825567, 6221821, 460349, 4390147, 6216168, 4067523, 5040720, 3454257, 6810282, 4250322, 4437033, 8182814, 5415801, 6751259, 3754036, 5740963, 1658612, 3221233, 2787967, 7245169, 2938437, 6782459, 7376991, 3686538, 415207, 7442012, 5599946, 803012, 2662455, 4225029, 1532350, 839362, 4384986, 2927226, 4545225, 8052407, 2750653, 6448225, 5601627, 3556228, 5844593, 1394193, 5775775, 3999132, 2465249, 7126096, 5045765, 7056753, 5456519, 7031953, 8251598, 7902156, 2794665, 1770555, 5712115, 1588768, 2397968, 5079326, 831379, 5482259, 463048, 6307231, 5288168, 626211, 2831874, 1998765, 7987835, 5145889, 1892307, 3756507, 6304023, 8113079, 2862649, 705318, 3296139, 7281485, 7935359, 7029680, 1031804, 5814077, 1065813, 5413058, 5261434, 7031552, 524666, 5598565, 3519255, 7258729, 6343450, 5852651, 7410679, 6370965, 5275666, 2377834],
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w1Encode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

cTilde: 46BAEB4009DF2B220F63EA24CA5D78B6DBE55E79A43FD7C75E388A7D452FB673
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95134, ||r0|| check passed
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[890294, 2651520, 2688558, 387763, 2565296, 5517659, 523118, 6761937, 2699953, 6032617, 8351690, 7867921, 393475, 568812, 1446196, 5126390, 6988889, 5957197, 5855493, 5147597, 8166286, 3340190, 7321532, 403956, 3414109, 6191583, 2170064, 5895694, 4323695, 6769409, 2842479, 7423236, 1947672, 755642, 2623763, 7319359, 7283103, 4426245, 6115135, 6299944, 6344921, 3868329, 7849104, 7229146, 5986891, 5711199, 1208591, 2047997, 2633294, 7269318, 2592383, 2027824, 3734050, 3048838, 5484766, 2514494, 8030737, 7830600, 1446477, 5952047, 1071680, 383222, 5868099, 5871466, 960369, 714096, 5668986, 2013601, 2278618, 6778793, 3481509, 3297387, 1466487, 3558549, 1377572, 4031239, 3219136, 2847821, 1732277, 6710881, 832688, 3434098, 280725, 2828707, 8118553, 5042136, 7508725, 4518935, 1362531, 7195134, 6907737, 6033398, 1922437, 1837756, 6409319, 96986, 4771972, 4535942, 6194379, 7271698, 6029738, 594235, 8277108, 5638964, 7041126, 1523334, 1023926, 1638459, 6800518, 4318786, 7967306, 5677239, 2854982, 5406599, 1298997, 3964146, 2582515, 4061381, 2656381, 6806615, 2623706, 6252147, 2108757, 1712897, 1524211, 4664514, 4191526, 5604560, 7541555, 4313027, 2832422, 5543053, 1117871, 6134538, 852813, 2916525, 3479985, 5597661, 172981, 5346328, 7375386, 2647410, 1284525, 2340499, 5868367, 3444933, 4035072, 4168098, 6012657, 1990704, 804991, 7647327, 2324897, 6483554, 2360032, 2237996, 6111322, 342921, 4583467, 1047388, 5808981, 830471, 3293096, 6130438, 2791695, 4666794, 6213476, 5700024, 3195401, 1626564, 5000794, 6608156, 1697562, 7619996, 1092916, 5059756, 6033575, 7320364, 6380138, 1237120, 6758769, 8231223, 1081584, 3593918, 7217392, 8157915, 3879657, 6692399, 3203197, 2973059, 2152783, 1325226, 1524163, 1747596, 4937355, 1543934, 6787929, 7977554, 6802240, 6281156, 4722904, 3817259, 4865951, 2798518, 609140, 4923137, 7475480, 3637557, 2917269, 6693645, 7126995, 862322, 5611775, 3624547, 3972090, 2678014, 2667504, 307573, 3502753, 2552501, 1792377, 1171165, 6680757, 2335828, 1268549, 7194055, 8170340, 4764767, 94084, 198721, 4914224, 2297696, 8355441, 7346458, 47210, 2703528, 3069564, 1787844, 8029397, 7275989, 3181284, 4660125, 2318191, 2158331, 5236544, 7040114, 6319317, 1797415, 3782036, 4403737, 1170407, 726178, 573260, 6800791, 2136897, 7985912],
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w = NTTInverse(aHat * NTT(y)): [[7624703, 240004, 2962974, 4152364, 6463756, 2415566, 3786264, 6154666, 3889519, 1100982, 7580840, 4326198, 4924153, 2874925, 7907723, 5555767, 6391451, 4049873, 8074931, 1893800, 950453, 2959143, 8019761, 4148133, 3883490, 3708927, 5271804, 7515854, 1051073, 7247763, 1518251, 408661, 5334341, 55737, 2018703, 5144345, 6612492, 7651462, 5931065, 8192531, 7758789, 2536827, 684454, 7236206, 4487486, 7831429, 7990553, 709177, 2987503, 751576, 2729366, 7972189, 2747989, 2522381, 4416254, 240891, 7576318, 7917005, 3022012, 3097114, 7206265, 5725099, 745443, 3752366, 3465657, 4814055, 6974705, 7666570, 3728792, 5220210, 5663196, 5871436, 583085, 6968732, 2416160, 4663658, 5193451, 6765677, 811614, 7963349, 3969626, 5799839, 7549898, 7902910, 6730593, 7387568, 8084618, 200118, 6497554, 1801143, 4562267, 1277537, 2661944, 2623191, 2033609, 8185038, 701178, 3928782, 8059066, 7938559, 5021973, 4757037, 1053131, 1156675, 2105683, 7212892, 6869130, 5409001, 5929304, 8346957, 4989430, 7363630, 2144236, 5532431, 5270856, 3738502, 2612255, 85507, 5909215, 145407, 1717007, 5712300, 5751460, 5887573, 1460586, 792283, 849969, 7643752, 7705537, 6321600, 163323, 7592530, 1428631, 1732255, 6705417, 1198038, 1719272, 1416901, 563851, 3191560, 6454580, 683784, 3049884, 3633252, 6140333, 4696610, 6526693, 6379638, 1034000, 3794140, 1030894, 5418727, 8340105, 3976177, 6141946, 5588294, 7528683, 6786432, 802743, 2646789, 8060558, 7768921, 7447134, 5587228, 6381403, 7394543, 4384605, 749440, 1602782, 6708673, 1241371, 436991, 4817036, 7911228, 4660309, 3695823, 1982806, 4475766, 7667611, 152376, 1005616, 8139280, 3862468, 2644328, 784232, 2261513, 1599481, 7408718, 1093615, 5067180, 5304027, 4080504, 3830757, 2672714, 249847, 2681896, 4020508, 1388114, 3064553, 2532220, 1252292, 2096422, 6283428, 6593878, 4521977, 4994046, 919551, 2667672, 2419080, 5287667, 1945394, 7206577, 3595768, 6313912, 6896908, 7363857, 6547309, 7430755, 7167386, 6687182, 2726835, 4750409, 3087703, 4664321, 3767946, 4493683, 6277434, 856225, 7383241, 7025367, 1526268, 1273430, 7129566, 7801230, 4723349, 3269582, 3896577, 1681312, 8305875, 3291839, 1663673, 206881, 8238073, 8249897, 258576, 4083472, 6336002, 2937834, 3966306, 2354150, 1907072, 2842675, 2290177, 2544452, 6202865, 1879107],
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w1Encode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

cTilde: AD259CA6B31AF6C5932C3F672E3C5842F6BBCF530A9926AE0A733A08B67164D3
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95149, ||r0|| check passed
Need new candidate round. ||z|| too large or ||r0|| too large.

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aHat * NTT(y): [[328045, 4651046, 8207998, 398219, 1575939, 1224829, 6212378, 3091497, 161251, 532798, 2379498, 7450219, 3318485, 766241, 5920353, 1067651, 3200679, 7559325, 7710382, 3100021, 5892180, 3181805, 2385350, 462378, 1901399, 3627680, 480145, 91026, 689996, 7661746, 3594749, 4651390, 3416785, 7322146, 7372404, 2139715, 1351446, 2040859, 8159918, 2050230, 1607379, 6815058, 2682735, 6449057, 5427178, 1783289, 291987, 3829816, 53503, 59536, 4079875, 546162, 5753643, 2125114, 1348388, 4223405, 2207224, 3099968, 6835296, 7901157, 5729257, 6637005, 3043786, 617353, 5623668, 20881, 5171888, 3730385, 4728793, 7121754, 7932005, 2548428, 5262412, 1922241, 1296221, 1068520, 958705, 6531467, 1129871, 3314492, 5891765, 1228574, 4344938, 70083, 3458995, 3192681, 3933429, 8272769, 4580055, 3784423, 7015086, 6024757, 2483967, 4636992, 6099497, 4626335, 179470, 4722867, 6026489, 6635068, 1811781, 8244393, 4408277, 2628093, 7675603, 2812331, 8126035, 4271631, 4281260, 1742604, 5611707, 5809721, 7920454, 2874945, 3667977, 6936197, 8071199, 6136755, 4490147, 3026111, 8076429, 3518853, 7141297, 689665, 4811296, 3718147, 7923866, 5856300, 7934379, 1075813, 645446, 498940, 7452840, 49988, 8235221, 719087, 6241272, 4318742, 6295964, 6419844, 5670640, 4119276, 7179633, 1365020, 6636685, 7130126, 3794633, 3199491, 7253697, 2469505, 5116320, 7890224, 3017692, 1424390, 3226919, 2593279, 8109268, 4375045, 6350287, 4467294, 7658658, 8227658, 7048095, 7208166, 5315901, 8177317, 6502372, 2966247, 1618236, 2827076, 722675, 7648815, 8373780, 7318606, 8034246, 1352238, 3776847, 8249957, 750062, 548563, 2058987, 99140, 6795936, 3917453, 1823513, 598456, 1243526, 7007669, 1082411, 1098938, 5164443, 2561390, 32598, 2270429, 430474, 1568532, 348774, 5067425, 7027250, 6951505, 3271134, 7127820, 3742884, 236875, 5769554, 7724347, 1093052, 1395552, 2450542, 4507976, 2585414, 1487152, 5497449, 5494631, 7973376, 7197661, 3109390, 3178976, 5818549, 2663439, 1225682, 5636066, 7449409, 3624910, 5847996, 6692969, 5417547, 8379132, 6743486, 5301805, 185139, 8287890, 5705608, 103265, 4239931, 6998701, 2070720, 2470064, 5584042, 1785299, 4452002, 1332443, 1954644, 2744128, 3431789, 6122989, 7274603, 5012114, 4930350, 3032981, 5332426, 4287192, 7314728, 4299849, 4206291, 7596894],
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w = NTTInverse(aHat * NTT(y)): [[2914167, 7412710, 2516425, 5105571, 7653783, 5981531, 4720398, 5955779, 1632128, 3840053, 373831, 324036, 157512, 5578275, 7626230, 6579438, 5943553, 1170107, 1441779, 7269464, 3183179, 3574906, 3259883, 6086023, 1700055, 1942326, 8232690, 2896121, 6640707, 8161679, 3981478, 7852625, 8211569, 6743609, 3144731, 2071760, 5817433, 2527603, 2737149, 3548727, 1551088, 3456340, 534070, 4838785, 1963603, 8041274, 1068901, 1858667, 247192, 3924202, 373543, 5504466, 4485326, 1030581, 7125755, 6402242, 2527137, 7093859, 1474778, 6850523, 7934427, 2951053, 7242525, 2127112, 4789995, 1125680, 5355564, 829814, 5989152, 6965957, 5418497, 2454949, 4162481, 3533497, 6436173, 2120982, 399220, 5635447, 7148398, 5555980, 7306578, 2221290, 853887, 6163597, 6722104, 922798, 8179041, 565681, 7938467, 5187911, 3267885, 5535546, 4975445, 1447127, 3004757, 6855982, 7415057, 3502053, 826857, 5290859, 135584, 4334497, 6682018, 7568569, 3201825, 411330, 2067326, 2319054, 3125636, 5363770, 6122634, 1364271, 3076517, 4361845, 2150695, 3002902, 4974636, 156527, 1893824, 7168514, 6231279, 3706706, 3309057, 51484, 3755217, 1949025, 7920037, 3921138, 4720567, 5153154, 4164629, 4923096, 7040477, 5963637, 7188229, 5175240, 3917880, 2250351, 1627834, 2231045, 1290471, 728365, 2163955, 7716835, 6971971, 770738, 7785303, 2669491, 6971638, 714250, 673426, 2813389, 7222281, 2339984, 8224998, 1119976, 1283003, 5695544, 2553923, 83431, 7847940, 6065108, 6256129, 7102546, 5878002, 5980630, 3731596, 5657340, 4311498, 7426206, 2170348, 4503339, 4770566, 536216, 8317875, 3281052, 1430660, 6648496, 6784083, 3450666, 7065877, 643171, 6479721, 5920022, 5945975, 1036452, 5288663, 371311, 4900447, 3882412, 1398523, 6210154, 5781818, 5475239, 8073881, 5900808, 4370773, 3977402, 5754706, 4377952, 4819061, 6556576, 3578911, 873369, 3211315, 4636676, 6048813, 4121618, 1558561, 5777254, 7094946, 6674304, 7706422, 345284, 6332340, 6593524, 6147601, 4599304, 858498, 4931335, 6789890, 7678258, 6326718, 6340837, 6742375, 7621580, 5507587, 1055211, 5756440, 493306, 672063, 490753, 5368326, 6329957, 1818349, 407554, 4603551, 5414927, 2967857, 4476888, 7701170, 7856747, 1014362, 5622866, 5420390, 7405500, 5251110, 578247, 3253807, 2063851, 6905173, 1789719, 52263, 3954017, 1248277, 7981534],
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w1: [[15, 39, 13, 27, 40, 31, 25, 31, 9, 20, 2, 2, 1, 29, 40, 35, 31, 6, 8, 38, 17, 19, 17, 32, 9, 10, 43, 15, 35, 43, 21, 41, 43, 35, 17, 11, 31, 13, 14, 19, 8, 18, 3, 25, 10, 42, 6, 10, 1, 21, 2, 29, 24, 5, 37, 34, 13, 37, 8, 36, 42, 15, 38, 11, 25, 6, 28, 4, 31, 37, 28, 13, 22, 19, 34, 11, 2, 30, 38, 29, 38, 12, 4, 32, 35, 5, 43, 3, 42, 27, 17, 29, 26, 8, 16, 36, 39, 18, 4, 28, 1, 23, 35, 40, 17, 2, 11, 12, 16, 28, 32, 7, 16, 23, 11, 16, 26, 1, 10, 38, 33, 19, 17, 0, 20, 10, 42, 21, 25, 27, 22, 26, 37, 31, 38, 27, 21, 12, 9, 12, 7, 4, 11, 41, 37, 4, 41, 14, 37, 4, 4, 15, 38, 12, 43, 6, 7, 30, 13, 0, 41, 32, 33, 37, 31, 31, 20, 30, 23, 39, 11, 24, 25, 3, 0, 17, 8, 35, 36, 18, 37, 3, 34, 31, 31, 5, 28, 2, 26, 20, 7, 33, 30, 29, 42, 31, 23, 21, 30, 23, 25, 34, 19, 5, 17, 24, 32, 22, 8, 30, 37, 35, 40, 2, 33, 35, 32, 24, 5, 26, 36, 40, 33, 33, 35, 40, 29, 6, 30, 3, 4, 3, 28, 33, 10, 2, 24, 28, 16, 24, 40, 41, 5, 30, 28, 39, 28, 3, 17, 11, 36, 9, 0, 21, 7, 42],
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[35, 10, 21, 0, 12, 22, 22, 29, 29, 5, 24, 8, 19, 43, 12, 11, 30, 3, 43, 12, 31, 22, 37, 20, 16, 41, 5, 12, 1, 11, 4, 41, 37, 23, 4, 24, 12, 0, 42, 36, 31, 35, 2, 43, 33, 8, 0, 7, 7, 13, 43, 9, 42, 40, 0, 31, 14, 34, 28, 38, 43, 41, 17, 12, 12, 42, 40, 19, 18, 17, 37, 32, 26, 29, 11, 22, 18, 27, 3, 29, 42, 8, 6, 28, 30, 27, 3, 13, 22, 17, 29, 7, 32, 27, 6, 1, 7, 27, 8, 11, 41, 19, 30, 18, 27, 6, 24, 26, 19, 6, 8, 31, 12, 29, 32, 20, 14, 22, 21, 24, 29, 2, 1, 22, 9, 25, 42, 11, 7, 8, 17, 9, 23, 4, 42, 9, 1, 37, 40, 39, 42, 5, 3, 20, 21, 32, 0, 3, 9, 27, 20, 34, 23, 26, 9, 42, 41, 39, 21, 29, 35, 19, 5, 24, 34, 1, 35, 41, 36, 40, 41, 39, 18, 7, 8, 15, 9, 10, 13, 42, 37, 30, 35, 35, 38, 2, 16, 14, 10, 13, 26, 22, 30, 7, 5, 7, 27, 4, 1, 25, 3, 34, 24, 7, 22, 30, 34, 10, 26, 6, 35, 7, 2, 38, 11, 42, 34, 39, 28, 9, 4, 31, 20, 11, 7, 34, 28, 20, 17, 14, 34, 29, 30, 11, 26, 12, 37, 31, 30, 14, 10, 4, 5, 11, 5, 0, 1, 0, 0, 41, 3, 12, 20, 15, 15, 12]]
w1Encode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

cTilde: 809AE94EE60181B39FF0495A0F2D956F90BF26840547C60DC054F343C3EC669F
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||94893, ||r0|| check passed
Need new candidate round. ||z|| too large or ||r0|| too large.

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NTT(y): [[3035491, 2809772, 6725498, 567655, 5447090, 6430497, 588219, 6597274, 7259775, 1642189, 5313552, 2601666, 2944974, 6295297, 3581905, 6874192, 210561, 5960622, 8253565, 1195910, 881601, 4493663, 2179253, 4108348, 2194037, 3996638, 1092261, 6030678, 7838006, 7178403, 7282500, 584553, 1196877, 6707165, 3199084, 341095, 2044660, 7260281, 7420712, 3935267, 5121238, 5061590, 4626576, 6810977, 4897094, 4376922, 2750335, 2672078, 4726553, 3835189, 7154356, 6007954, 348031, 8134029, 1086976, 1982084, 7887771, 7603668, 1137358, 2661850, 7083102, 5369091, 5136523, 2967271, 1090697, 1184083, 854006, 3047869, 4419322, 7632282, 1167593, 1602068, 5018103, 4849750, 1454288, 2691760, 1839621, 3047899, 6110858, 2913054, 1579439, 5043108, 2139766, 3158238, 875297, 4132116, 866980, 6627278, 4157724, 5458883, 2927175, 599965, 5480327, 1909569, 3517404, 1026413, 6227609, 4232653, 2602036, 6395209, 3269477, 3530197, 4957058, 1966457, 2010565, 8082568, 8356231, 5794772, 211493, 3943577, 3005661, 2208475, 2128484, 7280590, 4006397, 945258, 4386251, 4270003, 4562849, 4419605, 4085646, 1669095, 5338362, 6956914, 8088896, 2570387, 5809058, 3752494, 1528102, 8106951, 5281806, 1355547, 5718434, 647305, 3174723, 6294224, 6933676, 1820988, 5246163, 2993621, 7329355, 7635290, 4674588, 6794689, 1558704, 13104, 4121732, 70093, 3501674, 1710767, 904290, 5208425, 2010454, 4145847, 2139346, 3989361, 4896166, 5247669, 4844193, 4114924, 5978018, 2410798, 1287242, 1207752, 5599430, 1089814, 1328558, 2940340, 1825295, 6570469, 6499124, 4467027, 2388572, 1411007, 6084438, 4491391, 5830304, 1062451, 8160682, 5678304, 1537916, 6474149, 4327172, 2051369, 6153936, 3901731, 2262951, 4390798, 2300164, 1383317, 7253257, 2623464, 2264376, 3077163, 8031165, 213399, 7916711, 7842821, 4759366, 1218096, 3085194, 7688597, 2187444, 5973181, 426078, 4729405, 8226232, 7314396, 6955759, 3279731, 1027695, 812647, 8082499, 4609741, 6331955, 3230751, 1167788, 3865767, 563670, 3659339, 3426433, 2023447, 935587, 4310876, 3726513, 5038520, 598057, 3073178, 4581131, 6079904, 1641703, 8243976, 5950162, 2792072, 3029808, 5979230, 3124170, 680394, 6496266, 6795290, 8212648, 4230877, 7439539, 6670916, 7370223, 6232007, 81198, 7359779, 497921, 914519, 8230522, 2866914, 5483100, 2743711, 4173558, 1558382],
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aHat * NTT(y): [[6144420, 4965121, 7555555, 3905658, 6043149, 7189003, 8075652, 2203037, 2783350, 3674236, 2430017, 5393384, 4941164, 4296081, 6148283, 7660585, 2308491, 1400256, 5671721, 3907686, 5929147, 1265500, 3022283, 1128849, 15574, 1164226, 7675964, 7558208, 3796492, 1639674, 6566290, 314927, 4898735, 581906, 7454937, 3852529, 3924068, 348752, 4848573, 3055577, 7606360, 5403547, 300170, 4424597, 6359459, 5663745, 4166932, 7643757, 2658231, 7396270, 3515068, 6668595, 6816951, 1341650, 4326698, 5564663, 1551431, 540782, 7485380, 4301755, 7992433, 1982296, 5421315, 4601611, 1833982, 1233808, 451588, 6988939, 2623962, 725611, 1854355, 2299692, 8157936, 4660457, 1970445, 4882334, 1443783, 3442510, 5224830, 5740279, 2946669, 4274368, 1147247, 6032402, 344604, 6479211, 6386428, 6248897, 1114601, 1819988, 6627179, 7751680, 3368594, 3215054, 2934481, 8152614, 2127743, 6144216, 99341, 628249, 8185372, 4886275, 796140, 5659210, 7415036, 2166062, 6183401, 7168789, 1359981, 4034680, 3106993, 2687128, 4003063, 2830728, 2350180, 571473, 8076459, 7748540, 7779703, 4991982, 3704813, 4850252, 4730293, 2369138, 2195049, 3209146, 855317, 2293644, 1338310, 7730177, 5464760, 7470852, 6016224, 7824305, 8366169, 6185769, 2722279, 4360138, 3451312, 3121272, 1268389, 5342663, 7216470, 6790051, 5017975, 2871315, 486414, 3953334, 3338544, 380084, 881141, 1851686, 4299945, 2134416, 3936945, 2503968, 6908224, 1663979, 1675835, 7517557, 6186323, 565056, 4401910, 2164127, 393499, 4404266, 7991691, 4656990, 1120793, 7509848, 4117686, 271242, 1180957, 7773347, 4448666, 4650398, 8309537, 7543726, 7829590, 3909950, 5371264, 7541323, 3986488, 5523577, 7213719, 741439, 5468872, 5309732, 8039561, 448734, 2777779, 5602961, 3737664, 1512454, 157720, 8295211, 405669, 3071257, 650, 7329231, 7954557, 5088275, 8032917, 4428814, 2085589, 2088772, 6167589, 825826, 7315436, 6584515, 7778454, 6768870, 5115996, 4782261, 3478380, 2784376, 1299269, 5001761, 8371846, 2777149, 2884961, 824294, 204593, 5179108, 3273007, 1261457, 7006787, 7575163, 14721, 7531729, 859014, 2436426, 2605367, 980875, 71276, 557077, 120143, 6055730, 3055587, 1793017, 2909122, 6325769, 2611222, 3649877, 2495215, 3770115, 6269765, 3606572, 8207745, 8138614, 8063635, 5091973, 2111348, 7874593, 7039022, 6481524],
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w = NTTInverse(aHat * NTT(y)): [[4968407, 4718179, 462388, 1119871, 7817329, 3820487, 6327751, 947481, 6639094, 4489022, 8186388, 1912045, 4956263, 7739800, 7404478, 8379826, 6526201, 7074363, 147018, 6952946, 3810768, 902435, 2775266, 8296885, 8051764, 3503130, 5595609, 6009587, 5926137, 4615793, 1905308, 7592716, 3334031, 2416622, 3332599, 6060453, 2063166, 4166850, 7668372, 8279294, 4129102, 2637835, 4581014, 2641700, 4802458, 6272159, 7471382, 1331727, 7108704, 896577, 8144022, 1637019, 6049888, 5089185, 7135655, 6202969, 6642720, 7096641, 6949927, 4687866, 4885849, 205023, 2397822, 3773483, 6111363, 6802280, 7348888, 4460760, 109243, 3411852, 3890924, 2509281, 3441374, 6262583, 2222397, 2289879, 2075549, 1068443, 4816229, 884304, 2750057, 8127817, 4331398, 7959205, 4598115, 6521412, 7951783, 5153698, 7702003, 1185204, 8293833, 6757742, 5016210, 3526979, 2234260, 2757883, 4335009, 736029, 5229885, 6576540, 3778864, 6555783, 2588363, 27210, 7556893, 1316724, 5398479, 6786820, 5230203, 1126613, 8001284, 4382863, 744569, 5163386, 1971936, 807725, 1485084, 2918309, 3900433, 5996273, 1708259, 7456238, 5598718, 2190102, 6309214, 2442543, 2677703, 2729639, 379218, 488601, 2602470, 2504541, 8024695, 6578005, 415191, 7767667, 6168890, 7277026, 5630201, 6681978, 5813748, 5757346, 2291932, 6661532, 794880, 3078399, 121392, 6534939, 2918276, 441979, 3305227, 279035, 4535496, 6579245, 15012, 7428585, 7857467, 478553, 7630954, 4951768, 7436814, 7352666, 2788218, 507218, 3683945, 2257427, 39409, 2043676, 1652461, 4980483, 6269058, 4864680, 7684174, 5956878, 6745341, 7101225, 2356962, 5965385, 3499547, 3793402, 6779465, 5642537, 4772159, 5557066, 568502, 6249119, 407401, 7422643, 7296053, 2649263, 4894235, 5091122, 8241978, 2447280, 3659063, 2327933, 7017258, 3390164, 3554977, 5046435, 7855288, 2716298, 7470131, 8008490, 5971511, 3326059, 6615790, 6674938, 3971260, 2014564, 4457632, 6131577, 7567201, 2605656, 190061, 7420735, 3082400, 2204091, 7861956, 7179538, 5237500, 5034335, 5932748, 327340, 7214685, 1756388, 16316, 700202, 3071802, 4442605, 5333405, 2181761, 23180, 2749222, 4096557, 2656849, 4543861, 1336518, 4808334, 987034, 5117638, 6094840, 7172274, 6111208, 765447, 6263622, 879114, 113155, 144961, 2726877, 5166020, 5132711, 5782039, 7523653, 1503501, 4256400],
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w1Encode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

cTilde: 3202542EF1E239D32BE1BCE5AE4AC8052D578899D653E368E11BC11C5480BA06
c1Tilde: 0000000000000000000000000000000000000000000000000000000000000000
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||r0||95002, ||r0|| check passed
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||h||: 62, Hint check passed
||ct0||: 46263, ||ct0|| check passed

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