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bitcoin-bips/bip-0324/ellswift_decode_test_vectors.csv
Pieter Wuille cc177ab7bc BIP324 updates
Includes:
* Simpler (but equivalent) ElligatorSwift encoding function & spec
* Improved test vectors
* Test vector generation code
* Code for converting test vectors for libsecp256k1 code.
* Code for running test vectors against SwiftEC paper authors' code.
* Miscellaneous reference code improvements (style, comments).
2023-01-11 17:39:56 -05:00

17 KiB

1ellswiftxcomment
200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0cu%p=0;t%p=0;valid_x(x2)
3000000000000000000000000000000000000000000000000000000000000000001d3475bf7655b0fb2d852921035b2ef607f49069b97454e6795251062741771b5da00b73cd6560520e7c364086e7cd23a34bf60d0e707be9fc34d4cd5fdfa2cu%p=0;valid_x(x1)
4000000000000000000000000000000000000000000000000000000000000000082277c4a71f9d22e66ece523f8fa08741a7c0912c66a69ce68514bfd3515b49ff482f2e241753ad0fb89150d8491dc1e34ff0b8acfbb442cfe999e2e5e6fd1d2u%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
500000000000000000000000000000000000000000000000000000000000000008421cc930e77c9f514b6915c3dbe2a94c6d8f690b5b739864ba6789fb8a55dd09f59c40275f5085a006f05dae77eb98c6fd0db1ab4a72ac47eae90a4fc9e57e0u%p=0;valid_x(x2)
60000000000000000000000000000000000000000000000000000000000000000bde70df51939b94c9c24979fa7dd04ebd9b3572da7802290438af2a681895441aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa9fffffd6bu%p=0;(u'^3-t'^2+7)%p=0;valid_x(x3)
70000000000000000000000000000000000000000000000000000000000000000d19c182d2759cd99824228d94799f8c6557c38a1c0d6779b9d4b729c6f1ccc4270720db7e238d04121f5b1afd8cc5ad9d18944c6bdc94881f502b7a3af3aecffu%p=0;valid_x(x3)
80000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fedd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0cu%p=0;t%p=0;valid_x(x2);t>=p
90000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2664bbd550873db31badcc71890e4f67753a65757f97aaa7dd5f1e82b753ace32219064bu%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
100000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff7028de7d1eea9cc59cfcf2fa151ac6c274eea4110feb4f7b68c5965732e9992e976ef68eu%p=0;valid_x(x2);t>=p
110000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbcfb7e712303941aedc208880735b1f1795c8e55be520ea93e103357b5d2adb7ed59b8eu%p=0;valid_x(x1);t>=p
120000000000000000000000000000000000000000000000000000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffff3113ad97eed6b70e7b0767c7d7feac04e57aa2a12fef5e0f48f878fcbb88b3b6b5e0783u%p=0;valid_x(x3);t>=p
130a2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f8530000000000000000000000000000000000000000000000000000000000000000532167c11200b08c0e84a354e74dcc40f8b25f4fe686e30869526366278a0688t%p=0;(u'^3+t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
140a2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f853fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f532167c11200b08c0e84a354e74dcc40f8b25f4fe686e30869526366278a0688t%p=0;(u'^3+t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
150ffde9ca81d751e9cdaffc1a50779245320b28996dbaf32f822f20117c22fbd6c74d99efceaa550f1ad1c0f43f46e7ff1ee3bd0162b7bf55f2965da9c345064674e880b3ffd18fe3cddf7902522551ddf97fa4a35a3cfda8197f947081a57b8fvalid_x(x3)
160ffde9ca81d751e9cdaffc1a50779245320b28996dbaf32f822f20117c22fbd6ffffffffffffffffffffffffffffffffffffffffffffffffffffffff156ca896377b643fce2271f64e5c8101566107c1be4980745091783804f654781ac9217cvalid_x(x2);t>=p
17123658444f32be8f02ea2034afa7ef4bbe8adc918ceb49b12773b625f490b368ffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dc5fe11ed16d65cf3a9538fcb2c139f1ecbc143ee14827120cbc2659e667256800b8142(u'^3-t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
18146f92464d15d36e35382bd3ca5b0f976c95cb08acdcf2d5b3570617990839d7ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3145e93b0d5cd840427f941f65193079ab8e2e83024ef2ee7ca558d88879ffd879fb6657(u'^3+t'^2+7)%p=0;valid_x(x3);t>=p
1915fdf5cf09c90759add2272d574d2bb5fe1429f9f3c14c65e3194bf61b82aa73ffffffffffffffffffffffffffffffffffffffffffffffffffffffff04cfd90616d0e43946aec93f62d57eb8cde68951af136cf4b307938dd1447411e07bffe1(u'^3+t'^2+7)%p=0;valid_x(x2);t>=p
201f67edf779a8a649d6def60035f2fa22d022dd359079a1a144073d84f19b92d50000000000000000000000000000000000000000000000000000000000000000025661f9aba9d15c3118456bbe980e3e1b8ba2e047c737a4eb48a040bb566f6ct%p=0;valid_x(x2)
211f67edf779a8a649d6def60035f2fa22d022dd359079a1a144073d84f19b92d5fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f025661f9aba9d15c3118456bbe980e3e1b8ba2e047c737a4eb48a040bb566f6ct%p=0;valid_x(x2);t>=p
221fe1e5ef3fceb5c135ab7741333ce5a6e80d68167653f6b2b24bcbcfaaaff507fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f98bec3b2a351fa96cfd191c1778351931b9e9ba9ad1149f6d9eadca80981b801t%p=0;(u'^3-t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
234056a34a210eec7892e8820675c860099f857b26aad85470ee6d3cf1304a9dcf375e70374271f20b13c9986ed7d3c17799698cfc435dbed3a9f34b38c823c2b4868aac2003b29dbcad1a3e803855e078a89d16543ac64392d122417298cec76e(u'^3-t'^2+7)%p=0;valid_x(x3)
244197ec3723c654cfdd32ab075506648b2ff5070362d01a4fff14b336b78f963fffffffffffffffffffffffffffffffffffffffffffffffffffffffffb3ab1e95ba5a6314502a8952b8f456e085928105f665377a8ce27726a5b0eb7ec1ac0286(u'^3+t'^2+7)%p=0;valid_x(x1);t>=p
2547eb3e208fedcdf8234c9421e9cd9a7ae873bfbdbc393723d1ba1e1e6a8e6b24ffffffffffffffffffffffffffffffffffffffffffffffffffffffff7cd12cb1d192d52007e541c9807006ed0468df77fd214af0a795fe119359666fdcf08f7c(u'^3+t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
265eb9696a2336fe2c3c666b02c755db4c0cfd62825c7b589a7b7bb442e141c1d693413f0052d49e64abec6d5831d66c43612830a17df1fe4383db896468100221ef6e1da6d6c7627e80f7a7234cb08a022c1ee1cf29e4d0f9642ae924cef9eb38(u'^3+t'^2+7)%p=0;valid_x(x1)
277bf96b7b6da15d3476a2b195934b690a3a3de3e8ab8474856863b0de3af90b0e000000000000000000000000000000000000000000000000000000000000000050851dfc9f418c314a437295b24feeea27af3d0cd2308348fda6e21c463e46fft%p=0;valid_x(x1)
287bf96b7b6da15d3476a2b195934b690a3a3de3e8ab8474856863b0de3af90b0efffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f50851dfc9f418c314a437295b24feeea27af3d0cd2308348fda6e21c463e46fft%p=0;valid_x(x1);t>=p
29851b1ca94549371c4f1f7187321d39bf51c6b7fb61f7cbf027c9da62021b7a65fc54c96837fb22b362eda63ec52ec83d81bedd160c11b22d965d9f4a6d64d2513e731051e12d33237eb324f2aa5b16bb868eb49a1aa1fadc19b6e8761b5a5f7b(u'^3+t'^2+7)%p=0;valid_x(x2)
30943c2f775108b737fe65a9531e19f2fc2a197f5603e3a2881d1d83e4008f91250000000000000000000000000000000000000000000000000000000000000000311c61f0ab2f32b7b1f0223fa72f0a78752b8146e46107f8876dd9c4f92b2942t%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
31943c2f775108b737fe65a9531e19f2fc2a197f5603e3a2881d1d83e4008f9125fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f311c61f0ab2f32b7b1f0223fa72f0a78752b8146e46107f8876dd9c4f92b2942t%p=0;valid_x(x3);valid_x(x2);valid_x(x1);t>=p
32a0f18492183e61e8063e573606591421b06bc3513631578a73a39c1c3306239f2f32904f0d2a33ecca8a5451705bb537d3bf44e071226025cdbfd249fe0f7ad697a09cf1a2eae7c494df3c6f8a9445bfb8c09d60832f9b0b9d5eabe25fbd14b9valid_x(x1)
33a1ed0a0bd79d8a23cfe4ec5fef5ba5cccfd844e4ff5cb4b0f2e71627341f1c5b17c499249e0ac08d5d11ea1c2c8ca7001616559a7994eadec9ca10fb4b8516dc65a89640744192cdac64b2d21ddf989cdac7500725b645bef8e2200ae39691f2valid_x(x2)
34ba94594a432721aa3580b84c161d0d134bc354b690404d7cd4ec57c16d3fbe98ffffffffffffffffffffffffffffffffffffffffffffffffffffffffea507dd75e0d76564aae92cb347e01a62afd389a9aa401c76c8dd227543dc9cd0efe685avalid_x(x1);t>=p
35bcaf7219f2f6fbf55fe5e062dce0e48c18f68103f10b8198e974c184750e1be3932016cbf69c4471bd1f656c6a107f1973de4af7086db897277060e25677f19a2d97f96cac882dfe73dc44db6ce0f1d31d6241358dd5d74eb3d3b50003d24c2bvalid_x(x3);valid_x(x2);valid_x(x1)
36bcaf7219f2f6fbf55fe5e062dce0e48c18f68103f10b8198e974c184750e1be3ffffffffffffffffffffffffffffffffffffffffffffffffffffffff6507d09ae7008afe6e8cbd5055df120bd748757c686dadb41cce75e4addcc5e02ec02b44valid_x(x3);valid_x(x2);valid_x(x1);t>=p
37c5981bae27fd84401c72a155e5707fbb811b2b620645d1028ea270cbe0ee225d4b62aa4dca6506c1acdbecc0552569b4b21436a5692e25d90d3bc2eb7ce24078948b40e7181713bc018ec1702d3d054d15746c59a7020730dd13ecf985a010d7(u'^3+t'^2+7)%p=0;valid_x(x3)
38c894ce48bfec433014b931a6ad4226d7dbd8eaa7b6e3faa8d0ef94052bcf8cff336eeb3919e2b4efb746c7f71bbca7e9383230fbbc48ffafe77e8bcc69542471f1c91acdc2525330f9b53158434a4d43a1c547cff29f15506f5da4eb4fe8fa5a(u'^3-t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
39cbb0deab125754f1fdb2038b0434ed9cb3fb53ab735391129994a535d925f6730000000000000000000000000000000000000000000000000000000000000000872d81ed8831d9998b67cb7105243edbf86c10edfebb786c110b02d07b2e67cdt%p=0;(u'^3-t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
40d917b786dac35670c330c9c5ae5971dfb495c8ae523ed97ee2420117b171f41effffffffffffffffffffffffffffffffffffffffffffffffffffffff2001f6f6e45b71e110b831f2bdad8651994526e58393fde4328b1ec04d59897142584691valid_x(x3);t>=p
41e28bd8f5929b467eb70e04332374ffb7e7180218ad16eaa46b7161aa679eb426000000000000000000000000000000000000000000000000000000000000000066b8c980a75c72e598d383a35a62879f844242ad1e73ff12edaa59f4e58632b5t%p=0;valid_x(x3)
42e28bd8f5929b467eb70e04332374ffb7e7180218ad16eaa46b7161aa679eb426fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f66b8c980a75c72e598d383a35a62879f844242ad1e73ff12edaa59f4e58632b5t%p=0;valid_x(x3);t>=p
43e7ee5814c1706bf8a89396a9b032bc014c2cac9c121127dbf6c99278f8bb53d1dfd04dbcda8e352466b6fcd5f2dea3e17d5e133115886eda20db8a12b54de71be842c6e3529b234270a5e97744edc34a04d7ba94e44b6d2523c9cf0195730a50(u'^3+t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1)
44f292e46825f9225ad23dc057c1d91c4f57fcb1386f29ef10481cb1d22518593fffffffffffffffffffffffffffffffffffffffffffffffffffffffff7011c9893cea2c53b8b0170166ac7da67194694adacc84d56389225e330134dab85a4d55(u'^3-t'^2+7)%p=0;valid_x(x3);t>=p
45fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f0000000000000000000000000000000000000000000000000000000000000000edd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0cu%p=0;t%p=0;valid_x(x2);u>=p
46fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f01d3475bf7655b0fb2d852921035b2ef607f49069b97454e6795251062741771b5da00b73cd6560520e7c364086e7cd23a34bf60d0e707be9fc34d4cd5fdfa2cu%p=0;valid_x(x1);u>=p
47fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f4218f20ae6c646b363db68605822fb14264ca8d2587fdd6fbc750d587e76a7eeaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa9fffffd6bu%p=0;(u'^3-t'^2+7)%p=0;valid_x(x3);u>=p
48fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f82277c4a71f9d22e66ece523f8fa08741a7c0912c66a69ce68514bfd3515b49ff482f2e241753ad0fb89150d8491dc1e34ff0b8acfbb442cfe999e2e5e6fd1d2u%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p
49fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f8421cc930e77c9f514b6915c3dbe2a94c6d8f690b5b739864ba6789fb8a55dd09f59c40275f5085a006f05dae77eb98c6fd0db1ab4a72ac47eae90a4fc9e57e0u%p=0;valid_x(x2);u>=p
50fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fd19c182d2759cd99824228d94799f8c6557c38a1c0d6779b9d4b729c6f1ccc4270720db7e238d04121f5b1afd8cc5ad9d18944c6bdc94881f502b7a3af3aecffu%p=0;valid_x(x3);u>=p
51fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2ffffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fedd1fd3e327ce90cc7a3542614289aee9682003e9cf7dcc9cf2ca9743be5aa0cu%p=0;t%p=0;valid_x(x2);u>=p;t>=p
52fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffff2664bbd550873db31badcc71890e4f67753a65757f97aaa7dd5f1e82b753ace32219064bu%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p;t>=p
53fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffff7028de7d1eea9cc59cfcf2fa151ac6c274eea4110feb4f7b68c5965732e9992e976ef68eu%p=0;valid_x(x2);u>=p;t>=p
54fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fffffffffffffffffffffffffffffffffffffffffffffffffffffffffcbcfb7e712303941aedc208880735b1f1795c8e55be520ea93e103357b5d2adb7ed59b8eu%p=0;valid_x(x1);u>=p;t>=p
55fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff3113ad97eed6b70e7b0767c7d7feac04e57aa2a12fef5e0f48f878fcbb88b3b6b5e0783u%p=0;valid_x(x3);u>=p;t>=p
56ffffffffffffffffffffffffffffffffffffffffffffffffffffffff13cea4a70000000000000000000000000000000000000000000000000000000000000000649984435b62b4a25d40c6133e8d9ab8c53d4b059ee8a154a3be0fcf4e892edbt%p=0;valid_x(x1);u>=p
57ffffffffffffffffffffffffffffffffffffffffffffffffffffffff13cea4a7fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f649984435b62b4a25d40c6133e8d9ab8c53d4b059ee8a154a3be0fcf4e892edbt%p=0;valid_x(x1);u>=p;t>=p
58ffffffffffffffffffffffffffffffffffffffffffffffffffffffff15028c590063f64d5a7f1c14915cd61eac886ab295bebd91992504cf77edb028bdd6267f3fde5713f8282eead7d39d4201f44a7c85a5ac8a0681f35e54085c6b69543374(u'^3+t'^2+7)%p=0;valid_x(x2);u>=p
59ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2715de8600000000000000000000000000000000000000000000000000000000000000003524f77fa3a6eb4389c3cb5d27f1f91462086429cd6c0cb0df43ea8f1e7b3fb4t%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p
60ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2715de86fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f3524f77fa3a6eb4389c3cb5d27f1f91462086429cd6c0cb0df43ea8f1e7b3fb4t%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p;t>=p
61ffffffffffffffffffffffffffffffffffffffffffffffffffffffff2c2c5709e7156c417717f2feab147141ec3da19fb759575cc6e37b2ea5ac9309f26f0f66d2469ab3e04acbb21c65a1809f39caafe7a77c13d10f9dd38f391c01dc499c52(u'^3-t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p
62ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3a08cc1efffffffffffffffffffffffffffffffffffffffffffffffffffffffff760e9f038e2a5ce6a93e795e16d2c398bc99f0369202ce21e8f09d56777b40fc512bcccvalid_x(x3);u>=p;t>=p
63ffffffffffffffffffffffffffffffffffffffffffffffffffffffff3e91257d932016cbf69c4471bd1f656c6a107f1973de4af7086db897277060e25677f19a864b3dc902c376709c10a93ad4bbe29fce0012f3dc8672c6286bba28d7d6d6fcvalid_x(x3);u>=p
64ffffffffffffffffffffffffffffffffffffffffffffffffffffffff795d6c1c322cadf599dbb86481522b3cc55f15a67932db2afa0111d9ed6981bcd124bf44766dfe4a700d9bee288b903ad58870e3d4fe2f0ef780bcac5c823f320d9a9bef(u'^3+t'^2+7)%p=0;valid_x(x1);u>=p
65ffffffffffffffffffffffffffffffffffffffffffffffffffffffff8e426f0392389078c12b1a89e9542f0593bc96b6bfde8224f8654ef5d5cda935a3582194faec7bc1987b63233fbc5f956edbf37d54404e7461c58ab8631bc68e451a0478valid_x(x1);u>=p
66ffffffffffffffffffffffffffffffffffffffffffffffffffffffff91192139ffffffffffffffffffffffffffffffffffffffffffffffffffffffff45f0f1ebec29a50bae138dbf7d8e24825006bb5fc1a2cc1243ba335bc6116fb9e498ec1fvalid_x(x2);u>=p;t>=p
67ffffffffffffffffffffffffffffffffffffffffffffffffffffffff98eb9ab76e84499c483b3bf06214abfe065dddf43b8601de596d63b9e45a166a580541fe1e0ff2dee9b09b136292a9e910f0d6ac3e552a644bba39e64e9dd3e3bbd3d4d4(u'^3-t'^2+7)%p=0;valid_x(x3);u>=p
68ffffffffffffffffffffffffffffffffffffffffffffffffffffffff9b77b7f2c74d99efceaa550f1ad1c0f43f46e7ff1ee3bd0162b7bf55f2965da9c34506468b7dd5c3edba9ee97b70eff438f22dca9849c8254a2f3345a0a572ffeaae0928valid_x(x2);u>=p
69ffffffffffffffffffffffffffffffffffffffffffffffffffffffff9b77b7f2ffffffffffffffffffffffffffffffffffffffffffffffffffffffff156ca8960881950c8f51d6b9a6387465d5f12609ef1bb25412a08a74cb2dfb200c74bfbfvalid_x(x3);valid_x(x2);valid_x(x1);u>=p;t>=p
70ffffffffffffffffffffffffffffffffffffffffffffffffffffffffa2f5cd838816c16c4fe8a1661d606fdb13cf9af04b979a2e159a09409ebc8645d58fde022f083207b9fd9b550063c31cd62b8746bd543bdc5bbf10e3a35563e927f440c8(u'^3+t'^2+7)%p=0;valid_x(x3);valid_x(x2);valid_x(x1);u>=p
71ffffffffffffffffffffffffffffffffffffffffffffffffffffffffb13f75c000000000000000000000000000000000000000000000000000000000000000004f51e0be078e0cddab2742156adba7e7a148e73157072fd618cd60942b146bd0t%p=0;valid_x(x3);u>=p
72ffffffffffffffffffffffffffffffffffffffffffffffffffffffffb13f75c0fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f4f51e0be078e0cddab2742156adba7e7a148e73157072fd618cd60942b146bd0t%p=0;valid_x(x3);u>=p;t>=p
73ffffffffffffffffffffffffffffffffffffffffffffffffffffffffe7bc1f8d000000000000000000000000000000000000000000000000000000000000000016c2ccb54352ff4bd794f6efd613c72197ab7082da5b563bdf9cb3edaafe74c2t%p=0;valid_x(x2);u>=p
74ffffffffffffffffffffffffffffffffffffffffffffffffffffffffe7bc1f8dfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f16c2ccb54352ff4bd794f6efd613c72197ab7082da5b563bdf9cb3edaafe74c2t%p=0;valid_x(x2);u>=p;t>=p
75ffffffffffffffffffffffffffffffffffffffffffffffffffffffffef64d162750546ce42b0431361e52d4f5242d8f24f33e6b1f99b591647cbc808f462af51d41244d11ca4f65240687759f95ca9efbab767ededb38fd18c36e18cd3b6f6a9(u'^3+t'^2+7)%p=0;valid_x(x3);u>=p
76fffffffffffffffffffffffffffffffffffffffffffffffffffffffff0e5be52372dd6e894b2a326fc3605a6e8f3c69c710bf27d630dfe2004988b78eb6eab3664bf84dd5e03670fdb24c0f5d3c2c365736f51db6c92d95010716ad2d36134c8valid_x(x3);valid_x(x2);valid_x(x1);u>=p
77fffffffffffffffffffffffffffffffffffffffffffffffffffffffffefbb982fffffffffffffffffffffffffffffffffffffffffffffffffffffffff6d6db1f1c92ccdfcf4ac550c28db57cff0c8515cb26936c786584a70114008d6c33a34bvalid_x(x1);u>=p;t>=p