Signature Verification -- ML-DSA-44
pk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
signature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
message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
rho: 5B003CBFAF3E5166A85F8A45B9C1A4533FF216FB226CFEB83A81A20EE6E97E54
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Proper number of hints provided. Provided: 63, expected: <=80
||z||: 130971, ||z|| check passed
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trCandidate: A9CBDF7C927F677A561B66AB5BCD6E1F267279AFCCA1576595E6BA6E4D1B225C95123962C9523C7276AF324071DFC205F88140E81C44199FE92964744959CE99
muCandidate: BA55E8D45110BBFC1C9A23DDB43B93AC4DC6EB68780D5A1CE0FDF50895E1AB0E9F1EBCD34FE2E952B9C1BB8DE721E892A741C1C055190AB43563BF73479AB937

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NTT(z): [[6959427, 6929453, 6113881, 4981143, 3545954, 6943164, 1647500, 2087619, 7374489, 5817057, 7760820, 6107494, 6733654, 3414907, 3084396, 6976092, 4524195, 1134448, 5455403, 7615404, 5437795, 2388161, 6067566, 8106135, 5149580, 1197549, 715482, 1487487, 816214, 4654614, 4530571, 821539, 2286874, 6215522, 187743, 4607626, 8233428, 4965811, 312425, 4395327, 4126877, 1251027, 8215260, 8099878, 6689499, 3007890, 1351214, 4648513, 8322275, 4701207, 3680576, 579589, 7911362, 5888358, 7470897, 3336213, 3033214, 398788, 2394650, 7097412, 1273943, 6761361, 4471955, 5961848, 1867684, 5678828, 5092966, 2490753, 4030038, 8281514, 1590874, 3539002, 7467865, 7902152, 4568002, 1968104, 167503, 4305271, 882438, 7856953, 512003, 7490931, 2264092, 4685771, 1220359, 7936191, 5501422, 2310695, 4576202, 8211066, 5196061, 1215466, 126890, 2682026, 4055496, 7978979, 7664157, 4733521, 7620692, 2430348, 1824001, 1348423, 757005, 1205861, 2705179, 942779, 1553770, 6779698, 6092485, 5192092, 7511954, 3526928, 5193445, 3341250, 1845434, 5155232, 804251, 3216005, 5592583, 1631689, 102210, 1239036, 5457414, 3773927, 487202, 3023050, 7925802, 4071896, 6759401, 3472389, 5181442, 2528890, 3953392, 7182345, 1498246, 3190030, 4815814, 3543809, 6149794, 2491832, 755633, 263965, 8164688, 110699, 8171467, 1499998, 2479632, 1104838, 8380069, 7603633, 1738053, 1715766, 51128, 333608, 2165322, 7827135, 452579, 1687120, 1161120, 1493909, 8072589, 6419730, 8074608, 6349630, 7419021, 937495, 719739, 585924, 8252699, 4722738, 2131266, 6586423, 4047185, 5072429, 399897, 8073343, 6473068, 5420569, 6091475, 6334801, 585138, 80095, 6183567, 5180643, 2170908, 6380189, 4136323, 1117869, 1513395, 1426697, 7796431, 5691067, 4775042, 3237265, 2549690, 2233088, 7239136, 1476201, 2637861, 3898301, 2728371, 6396647, 73661, 831887, 1788640, 6126136, 69311, 2974319, 1968649, 1821869, 3896956, 1994098, 2678717, 4007338, 5630415, 5422460, 2514601, 7630006, 1538712, 5417019, 2450091, 4794665, 1959170, 7000235, 7260013, 7434864, 2786333, 8029627, 2329946, 399921, 7397779, 228492, 5501356, 6038344, 3695073, 2966569, 1596732, 3620179, 5369560, 4811951, 5028487, 894833, 1148098, 1990919, 5096888, 2902066, 5903058, 2299980, 2536359, 353393, 6160211, 3799526, 2932452, 13889, 4785163, 5719273],
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aHat * NTT(z): [[8205148, 3682531, 6246060, 749942, 3179582, 6639911, 7079666, 4195088, 375904, 7358218, 7510083, 2890955, 2299967, 775515, 1123241, 4864387, 280980, 4284786, 5276268, 6092218, 2368962, 8257738, 7843599, 5429360, 2176683, 2458918, 6176321, 2979301, 326467, 6544070, 4426555, 5565838, 6861970, 6195233, 1082871, 8151208, 2158289, 5250476, 5201485, 6844098, 6126112, 6740678, 1710605, 2176198, 279888, 6912941, 2331073, 5737299, 6110144, 47639, 6244629, 2943723, 1731234, 3634703, 6494858, 4093016, 6975600, 1811896, 6672715, 3285103, 3321945, 1638046, 1853883, 1434631, 3395331, 6807804, 559718, 6285981, 2297818, 7357477, 3394232, 498557, 676323, 1307854, 7675005, 858948, 345405, 4901608, 4788313, 6491567, 2028266, 1140705, 203441, 5616498, 3987329, 8017384, 7786403, 7227827, 1145671, 8341405, 3720052, 1280588, 8180188, 5157924, 3633332, 7550204, 246437, 6685090, 5014940, 1231296, 7076501, 7585961, 3853999, 5705174, 5392746, 7172194, 6821750, 6545972, 5309344, 4377545, 4045993, 1940775, 2864877, 8363328, 4868314, 7241921, 4808661, 4868043, 1379402, 6533329, 8247864, 2906877, 2837650, 497706, 2653477, 5880621, 2957676, 2552364, 2564580, 2257177, 1108697, 2560451, 766181, 6945552, 15106, 4974383, 7615508, 552948, 5607119, 7322344, 3148564, 6899358, 1121988, 415891, 3050142, 4750775, 4959488, 3935466, 3461475, 3901617, 645458, 4630902, 7203359, 1274198, 4612419, 6942362, 4654875, 619745, 2836738, 7679402, 7679176, 7540638, 5269595, 7179282, 4682761, 2972404, 8026033, 335301, 4170618, 4980411, 1668531, 2818108, 7021901, 4660950, 1911829, 4994893, 1121019, 6485553, 3910961, 3587424, 8169754, 96829, 3891217, 5047221, 6703485, 6151051, 7370289, 1107370, 7157358, 3292390, 1039250, 5472165, 7727742, 4293032, 7316198, 6586981, 7800199, 4189193, 6614612, 5194276, 3538879, 4435297, 3714244, 3496842, 4110062, 5517404, 4206484, 7179608, 8173290, 7913226, 1959596, 2832537, 2853043, 7864057, 3434576, 3958180, 3707679, 8107789, 6472597, 5258825, 5446472, 2982864, 5855164, 5572520, 1461433, 7822388, 503843, 473872, 1827910, 1915065, 6602821, 399220, 6498754, 7783536, 205707, 3410635, 8012041, 3593088, 1865824, 2988308, 3075087, 7317604, 8105798, 579384, 116787, 4906619, 2954373, 2192972, 5712935, 3115715, 7727112, 2302792, 1101049, 2989417, 4439262, 1698749],
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NTT(c): [6740534, 4045296, 2602173, 4057786, 3828614, 2205945, 8167143, 6593076, 3152783, 8270939, 5589630, 286975, 2981496, 6078868, 5695322, 4821040, 3400817, 1314165, 6916919, 7557989, 1846599, 4105184, 5776369, 4840805, 7760990, 7747766, 912494, 7667549, 6289738, 5097966, 2067219, 4308073, 5212698, 7306521, 4512398, 3281175, 5818272, 4994761, 5980882, 4218491, 8361027, 6294504, 7452914, 3906401, 375630, 1922874, 1461297, 1400371, 2857978, 3557489, 2019286, 6586919, 7656425, 3132691, 2829832, 6721617, 8046840, 2715316, 7328591, 2873021, 4584642, 7110958, 6529875, 1915054, 8366937, 6813065, 1697637, 7686310, 6760467, 7867530, 7591153, 2456768, 4196834, 3444292, 5335229, 2646134, 3005076, 4166756, 185197, 4267237, 3739858, 5271252, 7881540, 1372338, 4921204, 7485778, 8327496, 8118769, 5377216, 6659216, 5442299, 7921455, 4181906, 4037289, 7903765, 2577029, 1264520, 7646150, 7788316, 431555, 4032549, 3004849, 5584448, 7262803, 8107325, 7148810, 5927230, 3947731, 3637913, 6505681, 5789489, 6233059, 8133424, 7547652, 3807226, 6771971, 5052513, 1126737, 6428787, 6270833, 8347135, 5080926, 5443004, 1554467, 2620784, 4162411, 2677195, 8174155, 8167614, 8083736, 4103884, 6138475, 3868441, 3058591, 3287132, 3554264, 6051153, 4447803, 85723, 7811203, 1880235, 7257594, 1416016, 3643956, 6510808, 5622948, 2312829, 5667263, 6435933, 1460290, 715812, 1110571, 4478725, 2606905, 3308123, 855461, 7736072, 2691346, 1349031, 82963, 1226437, 3636801, 7629644, 4107021, 4662108, 3328979, 1921218, 7597867, 1231090, 2616761, 382219, 6863112, 2658847, 4571491, 1523666, 1145137, 4111354, 4594549, 4892337, 7318873, 4212052, 5245483, 6606989, 5636142, 5258319, 261093, 2462993, 1319192, 8218231, 81833, 1131088, 778267, 6573469, 7790901, 139901, 216918, 3161787, 496529, 317439, 6467255, 1573077, 2978028, 1854261, 4876274, 3929997, 5622067, 6534990, 7610339, 7840598, 7028975, 5470236, 1412610, 3491051, 2609731, 1019356, 3714433, 1692545, 4407518, 7468941, 8128921, 6829928, 6323993, 3439418, 4947990, 747233, 4254147, 4768115, 4953593, 6361340, 1205148, 5524342, 880353, 4969290, 4239383, 4135673, 2451652, 2297363, 4151280, 164558, 3840049, 8091764, 4638140, 3444910, 7491500, 2326591, 4783310, 2552869, 3417953, 5697174, 3354837, 8255872, 2914938, 4159237, 670649, 2634557, 4445631]
NTT(c) * (NTT(t1) * 2^d): [[5324147, 7803716, 2455124, 465449, 6859752, 7840043, 3419480, 72744, 7270387, 7283536, 1228177, 1426655, 7968572, 3683039, 4561167, 4989237, 4266806, 5272268, 5064962, 6263924, 1554062, 128055, 7815981, 495182, 1142496, 7018628, 2435573, 1100683, 923978, 4889791, 988610, 2007092, 4819155, 3263112, 6082486, 2616358, 8254692, 4881619, 2285166, 341216, 4876866, 6426357, 5497339, 4830097, 4511162, 5825553, 3763531, 6531088, 3560476, 7559667, 7399935, 4543706, 5469408, 6795439, 2992864, 7755990, 500576, 4145669, 6647214, 6156225, 8159170, 781240, 1231699, 8108328, 7210092, 2557045, 1147295, 693297, 951676, 6497828, 936923, 4536158, 7647802, 6108887, 5494065, 4013865, 6960094, 4653219, 5370174, 7922250, 5640862, 2049126, 1764666, 4222507, 419970, 2809364, 4011657, 30966, 2064019, 5098129, 7052393, 7394427, 3569758, 2151822, 2363969, 6565422, 8294112, 4481388, 2682138, 3568302, 2938418, 4133413, 297319, 3131123, 4427095, 7713817, 3652501, 7896960, 5929397, 7811578, 247489, 1725019, 6033539, 3999703, 5878239, 4872300, 4768387, 4458328, 8080500, 6685461, 124867, 2903431, 4552757, 6791588, 4026762, 2494463, 6422116, 7017752, 3404371, 5595256, 282947, 4473398, 2869144, 3506727, 3113765, 2953058, 3462897, 1953723, 3418822, 2095396, 2623480, 1634255, 2896338, 4200850, 2793155, 4906561, 923655, 4840381, 808319, 2629524, 2517553, 7792876, 5006863, 4294485, 2393749, 1155145, 4649063, 3876239, 5698122, 5676211, 2465828, 2064269, 1365067, 6129365, 1733194, 3535750, 3401762, 4297852, 3781701, 6739172, 4821706, 3735209, 7048414, 6582452, 7778001, 1467247, 531700, 1810815, 2219695, 2837934, 3930973, 8260162, 2170908, 6325034, 1327682, 121724, 8155888, 7271356, 3117788, 6091466, 7285087, 5959153, 7998312, 756912, 797224, 4703253, 2835707, 1530764, 3721003, 1124667, 7143833, 2529643, 4203189, 4966113, 4314832, 6933633, 3667617, 899584, 5985083, 4612864, 5493013, 6702186, 32018, 1978077, 4237398, 7371799, 923149, 5019909, 3165208, 5780043, 2887367, 531176, 2740610, 7382660, 5651446, 5637605, 2145656, 6834593, 1274789, 6243770, 3244770, 4538484, 4968887, 6421601, 4261510, 4958558, 3338733, 7785155, 2164985, 3711950, 5947657, 6297886, 7845111, 7859908, 7555079, 3414075, 6364779, 6355178, 2066417, 5296287, 2931394, 2837594, 6072273, 3114893, 7856886, 2253998],
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wPrimeApprox: [[7922246, 5265226, 5506507, 4646550, 2602037, 8056124, 4540058, 3683346, 947069, 5492323, 5072451, 2036902, 3275644, 360403, 1342966, 5373180, 7674721, 1297549, 2199143, 6894242, 343750, 2205389, 2116220, 6594064, 1118119, 1295454, 8091477, 4263775, 2523493, 1196616, 3661568, 952793, 6553128, 409094, 5843568, 7588096, 7206890, 1387541, 3910260, 1615866, 3204319, 6008770, 3207733, 2822546, 7390952, 217966, 3013480, 8147607, 377067, 6505514, 4938257, 6747540, 8350324, 241057, 5708389, 1401833, 3154492, 4642862, 1007346, 7096032, 2699631, 7095420, 1032206, 6518894, 2549201, 5311426, 2169241, 3587873, 8190761, 3055915, 2480486, 6320344, 5043359, 1812196, 4076521, 6763189, 3796329, 1151663, 2932163, 5249902, 3389035, 3598376, 1697664, 5135427, 143201, 2097652, 6227765, 3495314, 230338, 6131540, 2965605, 6401148, 5796656, 8011592, 3697362, 4055182, 1652999, 5859724, 4583350, 4118738, 6900549, 1979736, 3749765, 4896511, 2784731, 2974587, 7029353, 4644697, 811913, 529529, 5279632, 7193704, 8200892, 455819, 8084352, 5651871, 2324574, 4435168, 3984154, 7783985, 4083681, 5250368, 7193306, 2835143, 2541641, 7015314, 1496169, 3070010, 4736328, 4094833, 1649735, 8316439, 2107201, 5479837, 5420028, 5331640, 4812159, 2979855, 43743, 3851683, 1003852, 4274128, 4223552, 7053633, 735719, 6475447, 5182951, 6486366, 6291990, 5768144, 4814576, 5074815, 6039719, 8189702, 2552747, 6880843, 4440237, 6054553, 4148682, 3374626, 2351101, 6930949, 6718152, 2038927, 1131767, 5949083, 2712530, 4731930, 4889762, 2646679, 8309083, 1295165, 5096741, 4064525, 5698306, 5552877, 438386, 6662316, 1493238, 2760265, 4669231, 6667396, 348494, 5017208, 2859845, 3121936, 1626834, 8317021, 1376896, 7301378, 3722083, 1454327, 8332394, 6435160, 3463564, 4589233, 1762634, 7107619, 6973980, 567330, 405166, 3340814, 4132934, 5055395, 3052776, 5645452, 1330250, 753174, 162386, 7567049, 5282371, 1490773, 373754, 5518187, 5163937, 7090619, 2025712, 5860195, 2905493, 2939529, 4180014, 5893834, 2867324, 5959307, 7285421, 899898, 1473854, 7100562, 1991199, 4036436, 5760422, 1832317, 2640425, 2626744, 5032742, 7426912, 7427851, 1439988, 6723198, 1421273, 5180931, 6349612, 5179903, 4643329, 3669151, 2546371, 6082638, 2187263, 4253789, 3524114, 6182567, 384197, 5078545, 2991234, 585998, 4359249],
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w1Prime: [[42, 28, 29, 24, 14, 42, 24, 19, 5, 29, 27, 11, 17, 2, 7, 28, 40, 7, 12, 36, 2, 11, 11, 35, 6, 7, 43, 22, 13, 6, 19, 5, 34, 2, 31, 40, 38, 7, 21, 8, 17, 32, 17, 15, 39, 1, 16, 43, 2, 34, 26, 35, 0, 1, 30, 7, 17, 24, 5, 37, 14, 37, 5, 34, 13, 28, 11, 19, 43, 16, 13, 33, 26, 9, 21, 36, 20, 6, 15, 28, 18, 19, 9, 27, 1, 11, 33, 18, 1, 32, 16, 34, 30, 42, 19, 21, 9, 31, 24, 22, 36, 10, 20, 26, 15, 16, 37, 24, 4, 3, 28, 38, 43, 2, 42, 30, 12, 23, 21, 41, 22, 28, 38, 15, 13, 37, 8, 16, 25, 22, 9, 0, 11, 29, 29, 28, 25, 15, 0, 20, 5, 22, 22, 37, 4, 34, 27, 34, 33, 30, 25, 27, 32, 43, 14, 36, 23, 32, 22, 18, 12, 36, 35, 11, 6, 31, 14, 25, 26, 14, 0, 7, 27, 21, 30, 29, 2, 35, 8, 14, 24, 35, 2, 26, 15, 16, 9, 0, 7, 38, 19, 8, 0, 34, 18, 24, 9, 37, 36, 3, 2, 18, 22, 27, 16, 30, 7, 4, 1, 40, 28, 8, 2, 29, 27, 37, 11, 31, 15, 15, 22, 31, 15, 31, 38, 5, 8, 37, 10, 21, 30, 10, 14, 14, 26, 39, 39, 8, 35, 7, 27, 33, 27, 24, 19, 13, 32, 12, 22, 19, 32, 2, 27, 16, 3, 23],
[22, 6, 12, 1, 35, 29, 19, 16, 19, 31, 32, 13, 40, 25, 27, 22, 36, 41, 4, 30, 13, 30, 25, 18, 25, 41, 9, 13, 40, 14, 9, 9, 10, 29, 41, 36, 24, 29, 11, 10, 31, 40, 32, 7, 19, 21, 36, 3, 39, 13, 2, 16, 27, 23, 34, 21, 40, 24, 32, 36, 6, 32, 4, 41, 26, 7, 16, 7, 34, 42, 31, 23, 38, 13, 19, 12, 24, 11, 4, 15, 6, 0, 35, 0, 20, 14, 28, 12, 1, 28, 28, 30, 1, 11, 8, 29, 42, 40, 30, 21, 30, 1, 30, 1, 4, 30, 13, 12, 12, 33, 36, 30, 42, 35, 11, 24, 20, 34, 29, 1, 24, 24, 29, 41, 41, 4, 16, 36, 38, 38, 8, 10, 42, 14, 9, 39, 37, 15, 25, 17, 34, 17, 16, 21, 14, 6, 8, 10, 37, 21, 7, 22, 43, 42, 10, 20, 15, 6, 4, 19, 29, 18, 6, 32, 22, 26, 9, 37, 2, 13, 35, 30, 7, 6, 33, 17, 13, 19, 3, 13, 8, 28, 40, 20, 2, 16, 27, 5, 12, 2, 41, 31, 4, 31, 43, 6, 9, 27, 43, 1, 10, 19, 3, 8, 17, 24, 17, 10, 19, 9, 42, 43, 5, 1, 39, 42, 1, 18, 22, 18, 0, 21, 3, 42, 42, 34, 2, 35, 38, 23, 36, 12, 14, 16, 30, 42, 28, 0, 12, 28, 29, 18, 30, 15, 23, 7, 42, 7, 21, 26, 19, 25, 8, 7, 19, 25],
[28, 17, 19, 1, 1, 8, 41, 31, 43, 3, 18, 10, 21, 23, 17, 43, 32, 42, 8, 42, 9, 22, 27, 37, 21, 0, 42, 26, 0, 34, 9, 42, 22, 36, 18, 38, 23, 32, 35, 19, 21, 9, 13, 23, 7, 27, 16, 21, 31, 36, 8, 14, 16, 14, 15, 17, 28, 28, 15, 22, 23, 8, 0, 10, 6, 8, 37, 28, 20, 36, 16, 2, 2, 23, 15, 10, 7, 12, 33, 18, 16, 17, 24, 8, 18, 31, 15, 18, 6, 5, 26, 5, 35, 11, 20, 7, 10, 0, 13, 6, 26, 39, 43, 42, 36, 33, 6, 26, 24, 41, 29, 17, 36, 41, 22, 8, 8, 17, 17, 3, 8, 42, 6, 31, 7, 17, 30, 38, 32, 25, 5, 18, 7, 31, 28, 12, 35, 21, 29, 29, 42, 30, 25, 14, 41, 35, 20, 29, 42, 29, 43, 22, 7, 25, 9, 25, 40, 21, 16, 7, 39, 24, 35, 41, 16, 0, 3, 11, 33, 34, 4, 7, 0, 25, 36, 41, 42, 3, 34, 27, 2, 24, 37, 17, 40, 13, 33, 27, 15, 25, 18, 1, 29, 41, 17, 3, 9, 31, 33, 31, 17, 8, 36, 7, 20, 26, 33, 28, 30, 0, 2, 16, 24, 29, 1, 15, 40, 8, 33, 17, 22, 36, 30, 6, 33, 8, 21, 38, 43, 9, 1, 6, 34, 34, 9, 13, 36, 15, 28, 35, 41, 19, 9, 23, 20, 38, 18, 10, 4, 17, 22, 10, 14, 41, 9, 19],
[11, 15, 7, 7, 25, 18, 41, 6, 14, 30, 8, 26, 6, 10, 41, 1, 17, 22, 33, 14, 4, 41, 12, 27, 6, 2, 25, 16, 20, 0, 13, 14, 12, 18, 22, 30, 1, 10, 7, 24, 10, 29, 20, 7, 13, 19, 30, 19, 38, 31, 43, 16, 34, 29, 24, 1, 20, 21, 4, 13, 31, 10, 27, 37, 6, 39, 28, 19, 41, 25, 11, 15, 36, 36, 15, 17, 14, 15, 4, 0, 11, 21, 4, 35, 40, 39, 28, 20, 4, 27, 30, 33, 4, 22, 11, 6, 13, 3, 19, 37, 15, 27, 25, 28, 18, 20, 5, 22, 32, 28, 11, 43, 30, 37, 7, 5, 14, 31, 34, 16, 5, 15, 39, 17, 12, 11, 21, 43, 32, 34, 42, 43, 2, 1, 18, 18, 37, 26, 20, 1, 32, 39, 8, 4, 24, 15, 25, 9, 17, 12, 34, 42, 2, 37, 22, 40, 20, 10, 17, 10, 31, 33, 12, 18, 24, 8, 3, 1, 14, 33, 27, 39, 9, 1, 26, 24, 3, 1, 16, 6, 13, 25, 15, 17, 15, 21, 41, 30, 16, 20, 6, 27, 33, 13, 27, 0, 18, 31, 21, 15, 36, 17, 12, 31, 2, 26, 14, 29, 27, 15, 10, 26, 43, 19, 34, 30, 26, 12, 21, 13, 6, 36, 21, 3, 14, 15, 3, 25, 26, 8, 36, 21, 27, 42, 42, 4, 34, 26, 37, 33, 32, 14, 30, 11, 41, 2, 15, 35, 36, 36, 20, 32, 23, 9, 30, 18]]
w1EncodeTemp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
cTilde: E98901A3F79293983D935DCF3A4DC9BA8966F70CB2991E6E1E5942643D37A152
cTildePrime: E98901A3F79293983D935DCF3A4DC9BA8966F70CB2991E6E1E5942643D37A152
cTilde == cTildePrime, signature verified
