import unittest
import nimcrypto/utils
import ../bncurve/[fields, groups]

# Total size of test vectors is 10_000, but CI is too slow to test it
# in reasonable time, so we will test only 1000 vectors.
const TestsCount = 1000

const
  FRExpected = [
    "0000000000000000000000000000000000000000000000000000000000000001",
    "0000000000000000000000000000000000000000000000000000000000000003",
    "2042def740cbc01bd03583cf0100e59370229adafbd0f5b62d414e62a000000d",
    "1eced988f1c4e0f7f7433f99dc0eb1b89dd2a1b7c00a6e1a5df4900b27c8a6b3",
    "02363a20539db6638514cb4ba7ec49c91b2c5d405b7e5c021d3a0bf834f2ef0a",
    "09889144b32647e7a6a9ec0646bbabe83d9b7d9188c3bdcd3b002c55c9aa80ef",
    "014ced1876c520cc926b880803323cb80b4554f8c2588032f6cb727157371641",
    "179da4e61ae3117b9b12f86f5aa4f14e1fc3b46bf05d1423900f9ce6228b6d40",
    "067140865d6292881384dc2252b9dd20111c942dc2364e8c98f1da3c28da888f",
    "2ca25f36b7b20358489b49421b20f6a10eacf80e7f3d2bfce7593d0777fef418",
    "2bf0a17a3fa0670820f4f2469774a98f9bcd6a5e490e97d6e11f361c914cfe8c",
    "29a228ca3b4b8ed9cf1c2957a826aaf9cc3d1bdccc99996092b42907e8d763d4",
    "296a1aae3b4d8c87257609dba587338419937a3f7a8e37234deca0eb9b761478",
    "05c9dd8d3da17bb45967ad595e6440ba84243707a5b2a45568f22731b7f2055c",
    "2e99a1f1b911be2b5eae798a1bdb87ec8b6b66015af43114d4c4f0c3081808d8",
    "0500c67659a93bcd482ce6e2e198e671bff5e9bf276891b0c7f79200da6dd6b5",
    "020a4cdd4381c2c7e2a1885ac88036bbacc0d6aac38ca1113c10efe9226e5744",
    "29329d9432d2146f11a0d9e2578c09f7f1182b9cb20f988c6bad57bcb614e48f",
    "09507fcafb26bb82d68228ef5f5ed7b71aab295bbe4cdc759df141917d11d79e",
    "00a0ba7dcf0405380408feb28cdeeb784a19d0b9679d1adc005e9f1ab34f251a",
    "067517b1a7f50aa3a3c9dd3db988b0e2e87a8e6b3fb1184b8a06cc3529141132",
    "13e5c7527050b265295b9739cd2f95312932bfb62ce4c159c0ab92a61f0dcdab",
    "2a737c37b6881ca875205b949c313108f54eee116d876d4685a88e77a88a7589",
    "1103f082a016eea4c4dde6b7caf6d5f23d45007920eacd4ac8c952a9ece70d33",
    "12f45350d4c50366dd0c88a77ce35b802cf1e6929210449ff83a73a627ae8a9b",
    "18b04aa529992886a880fbabdcc834a983bf07bfb23cfa7bba660aec0a10a8ae",
    "03820dad30db55157ce87fc6812ec0a4e659e7547b18206d5844a6d1f28399e1",
    "030dfdd27e4e180392ec965b8bf2586d3203fe8931be034c966c37433625fd9a",
    "08a9b73efb3282526bee3e609fb408449503b70f617b3bab42919108852cf44b",
    "184b6a8fd93b49422099e5d75090dce92edf553115452635bbc8e623ce312ad3",
    "030273cc32bbe84b480930f2313491a19c00e2dd39fbd30993603bb8b5495e95",
    "1622dd450399ca70b99e94f60d87490b1078ff0dc3ce82cb32fd7dce0c4a4499",
    "0195e53a05f7b95040d27b2819f7b23b40c0871dbc476e3c102e4cb64904483e",
    "2910b512191aae4c5f27f90aea2f41b3b0e0f2042d57ebc8dc51901d06b10024",
    "2e795bc0783c41c950330abcbd7e92a6d7e558787e7f579b4c2e4aaf9f66630f",
    "0c34e777e38a18cb4edc5e9d3f4f07dbb1b074f38347dd53a015be494f24c0b0",
    "277348139e45c362741e424e4dc10b94df979bbf14f7c4b6dc144a0a0c593e1c",
    "1dff63c029e19454c2360a88baf804cafa60f6a50cbb71a79715c2832cf47408",
    "23e84f6518e9bab5af850cf1f38a873fe8be0c2f786d1d4e1fdaf32d46150500",
    "211b26970071c65390a8c6d822423ab281aae480a12a6fc836b40884a4337e53",
    "296abf4e45cc54ba75225ebac4fe863d5cfe725105cadfc9f9357f791d7ffdd9",
    "22cf34de7b862a2c4874a03b7ce9a9ac8e748e4741a7d01ef7e443430a543b33",
    "2fca5ad500e198625c9d542e0d4aefdcda28d246edf9a83f34c57ac1cfe98a34",
    "2a471ed73102e6918e55b0ef00822a5281ef0e49b4586cce10ab2671ddf95731",
    "2210b49819b69ca317b63ccfe3a4fed4fcc9b9b368dee5d988624487f7cd7d99",
    "0ac117037c41ac977dfac11e614ff3c1f0604fdf1e934addd96ca426a2d56c45",
    "18a0c2a40073a85c4a4cec75dc9e049a18def78960c7429a9c6abc1cde4d1c42",
    "229574d27795392985547b551380cda18972a32c2caf87b910746ebda6615ca8",
    "1c6f0bc008a80d5d36cf483df553e24ac4f969d7a02f45e93181441d79fb72fc",
    "1060b506a53a740169a80954eb5fcfc6b261cfca0c021a8113841bfa2b10d3df",
    "23ecc4f3237f76dc81fbbb8e467d253ebb6b4e99b9f2c607daec1bb599a63108",
    "2350041950c0d7144e6790f939fa4f2f53165b82e6f5c1c730b7129ff1dd6075",
    "179de2653b84e8e5d925b21cf206b9886ffe9df14dd300ef48341707f3a8e43a",
    "16c670be2c945714cf9e5b30cc54b846a86ade34ca2f19e95cb9782cd1a1f4f6",
    "2a6ac3b3bd2a3ca35792323fe39384b7ba44fd70b8788bfb9a28f0397e6c58f2",
    "27c800eb72d3f1ac091747cedb323b02178e9cab5951f1b1c97b70430bc93f49",
    "0acb5953cf1583df3f5be7fc264a01d561642171ed8ad66cb0750ef84637919a",
    "239f76d1622590038d64e710422cda6cb6e3e12d1593b07b08faea2dd71848de",
    "2dab87d5e027c3aa07b95691cf313088176763b92a1a101142b202224c889319",
    "2ebb685e594b7ae133c381606c8fc1c7a07ec46c653b1d5e73734362bc8cc31b",
    "238274a880a47a28cec6660f31ca766e7c024fb458f7e1df5cc8d9f1fa49b364",
    "27c5e092fa1ee06da63928770d5ecc7931845869260b3966d6523ea526db2789",
    "00dcdcb4cc0015ab8b8bfca1d52e335275b6fb39b58d41c2b30367a104dc2fec",
    "22c7f9595340b66a5f0781fc8c6856facc2228ef749ebe8f4e26a3c9ab74465c",
    "2ea0cafc90188c763ae65f132d3d5c873e4bf9a50ceb079874d1c346ab8fb63d",
    "180066c34e34c473953b3e66d98660e733729376074b231198e921d4ae28ac75",
    "0cc81637599da9f5b8285737283752575daedabd7b463e02992933126b59e167",
    "274ced6e1efb4148e7fb778afdb6e7a41a5af073df6c43b7103f291efac8ca76",
    "2dccf0cb2b0c9165392462712673c4075a99d1f1e3118ffb3deadcda415768a6",
    "1d0128b4b0f47f814b2fb6491f03654541725612c465267f02b73ed28074fbc1",
    "264770a08b4fcfe8dcde0161cb4cfe1d851227fa5538adcdef80827636d95f92",
    "08cd18d2188a1b7e7103b95a1b7022cb56f14916b5b5a8b4db2b7305d222fb1c",
    "2b0fa450d5c7dda8eb466723cd25e0b762968e52fb8a558225ad2b0b3c9f15e4",
    "0fb89c9eb27d7e49d4988722e645714fe5be1fd5d1dd7b9f475a10222aef9fb0",
    "2384e79d245f048e6433b04a3c7e527a736c198c67682a23cccc127e0fe341c3",
    "240c04ce80bb543b5b9dc19abacc681c8c58778141349e9e3f492515c54dbfdd",
    "1b2c3e4505b9325d56c1fe596f839bc3bc023ca08485a3f71f575994e61e4e9a",
    "2c341055bdfd39ae1c9012b5456790d9e6bb603a56cd215b8fc7ff5df23babda",
    "2a618fada6222167ec179c0d2d5a3db64b07d04a0d8ce903ffcd878708131fc6",
    "098505eda76826a820e63e004a19ce3c16fbc465d5c294e4710121781e476016",
    "2198b95feb3a29a0bc7439a763caf039448143e464d12c3a5753fa4b4039b97e",
    "23e150228a041db5a598c4955ad4b763b2edb6208b5f4caccf790d0a2d927215",
    "1806b48868d9900275573f4e57ecc9257f0b8787527a2b96d2e24f1cfd4b6ac1",
    "2b7b0225bd8e48a401ab3a10507845bf3110c5959980023d166dc4be0aabdadf",
    "1b5d5b3c9f454b4019116206d223c708bba4ee71138fffb32ed8674943c72486",
    "2a495d1c7fcaa4f27be5914c7c6fed4fb65ee46e6d7974a55141d9bab30b39b4",
    "1fddf00cfacfef6cf8dd5e88e04298fd376934a40938aee523338677258469ca",
    "01fd18b9683b1aac8675185d5d06773aaab0e19112ddc9bb63e2c63bcde49db0",
    "140899d53f48c9b200a48a8618dda9f24ba27a9acdb63dcf633107feae16fe98",
    "0a0a0501eb8fbabf040f420ecad8797db587601e3deab6a01ce4b0d306be7cc6",
    "2fa5a098db8149032e6bb899bc0b97c6b2ffdd6cfcc955d17ea2afe6a3cc3990",
    "26162db3d4a6e6172f0b8d1d7ec1f706f9eeb7c6d3b0c2a510d7d0e04fe4eda6",
    "1fc0dbbbbdea0ffaf2864ccca1b7e937efadd6987ad73881c5fd534ce2ae55ff",
    "00dc4562c8483647fe1d924d50c574fb00b53973333cf3f42b24cb0412d1949c",
    "2fcdf1fcbdfbec79a47715a340effb55d042f522b0b86acbd4c2c286d8afbbc1",
    "0b11546ba7759df51528a4b9656d09ab5c2b7423ea82ed36d7acb01fe96cc8b7",
    "2f3dc23b191c92d0a582a35f19c25831bc60fe3aa228c3e00e70fd371f72e80b",
    "17b160611d7b3fbffd972f516d72b933980f325db9220cb1f953f74d166badfd",
    "17e5ddf96d4c64ebb06179a3544afca2bae78fc1089031906aea8afae5610147",
    "012ae487cf528b8197e4333b56705d7c31c92545607e6edbb0105717f5e33f66",
    "03a07c50c596fe0ebae61d554d46b055a6fb0de2da4a5434e026052292ef06ac",
    "27d9bc26fda4e6554de6d29b88934c53cae2eaee241ae7be961598f41118a7cc",
    "0a772b263180a8fd6c99db42be795b3d2944d4858fd84d307cc438dd82541cd1",
    "1ff90c2b7d3df22a1dd77b407e7f499d7ce6c7d5d3dfe360c485b6c49ccefcad",
    "0253973b5ebdc95b42002fb7695d51aeb1410ba1aeb24d98fac263963e527daf",
    "29912c9332807ec705d49f06c24b30caa6b9cc764dd223510e0fd21faf1aa1e4",
    "2c9482d7500b2eb22073cba5e6793b8bdc684e2b979df3b18e340ac27141b147",
    "25ef1f7f3369c7490da551cdee2eb521d4c058ff26c9ce503174f4b776a62134",
    "2850f791ce002da71a143489ca75f103cdb06faacf0cc1cb42d3f16f007c6ac8",
    "1b2dfc7f783b9a94a2374d632c7f2b9261c64f3384e7879f8777c761a0f38916",
    "1dab259a8cd28a888944dc62f0d71f77fbea3cec30777146eee454d8a38862e3",
    "0ff237bdb85a4d1d59d1771a372d85bc4c929c13bd11dc5ab547efbdac506d72",
    "03ccca3ce8529946b5971cb7b6cee1b7f0603d1a14fdb2399a0b754616881106",
    "0ae33319df196d3e6a9d381c5e9216bef5f269ccdd9bea3228bef871ec64a5ce",
    "29c85de273bf79ddd69170fb339c8935870d452eea31b4814181315098fe04b9",
    "192ee992c2734232d8cbcab87466cb7e4bd75498bf744bf0fca69ae2598170fc",
    "0adf8249950d832031f2c04795d1be24b8e819970b3bcabb6fd36c577c87d171",
    "1b91d0bd5d309d5f45f5df4d86d97c1958157dc4cde3c9328fb649d4c2a2660c",
    "0e4c23d81ec837f232fe6760a9bf81bb664af07b329d66e89e6f91916869c3d2",
    "0c53fc069fc35d46b0c407bab69c9b6e2fb9c5376628f2a01e0d15c33f0594d3",
    "10c10f5778177ea594ccd59c145dd1d6b98d79f29ee7df7cf350250629ea3749",
    "0591aff9a9a7aab76de4b8daaae1c7d99ed89fde5cdef42b7e043f537bc06cbc",
    "2ba5d15ac6497c83a9febd0295a25541876fd36f81d09b0042cb7237d73ab5f2",
    "1fb87964fdc64b2daacc9dae6e72c02785f508eef8b768518f3454e330dc2165",
    "0aec2e9eeb137a1c543d268adecf786041461fdc60744b2f22578e631caab5b7",
    "24646eb97864a13313b58b69196a7a12b9d050b193367f130eb8c10a49a186ad",
    "1dec3036641c822b85e64b8de5bc408c76c6838d0a3014a6e27e1272b9bb9483",
    "18c693429e6f97f4e5c28f4919fccedc3a1bcd5ccfee44aa43016d433900b84c",
    "09a1de0b073437aa7865181f666739ec4c8d44d97f68d2d7d5e5df25076f327f",
    "05db3ad1ab9e2a28de04383ea7b230236123ac43f1bf7eac680dae9172008971",
    "07414b2883fd13eb65025bdc1f9009cac40a35573dd165ee02cff68131ac324f",
    "1a6d9d6e44d0fbc16e3e6dbf6c3155f2da235c111c4a0db70658caf85321918c",
    "1e2762f9794b2c378e80cd7dafb47e5de60f1c592ed17bd50ac8d893a1ab8f42",
    "12ddaeb6d3f21d798299054a866e82a2c687fbca1cb831d6505e0cd7c1f641da",
    "0a4ca4d5033ad947d714f58dbef044e956c1df7061805da40d075e0626a50650",
    "194cb0367525c19f645870790da4347d1bc8376103b185744a1fd253fb5df988",
    "13612ad38e3f776ae2952123eb8a366f969b168789c313c3b59bce858d1048e6",
    "2a9f4b659f496117b4a61752f4eb5f8c75e529a576c975843481b308c6192da1",
    "286367a78683c1f6b8d510f301d47d2773830687f0fdaaa8b263914564c527d9",
    "2c86680ddd0725e9b2af495ee35323448857e92d6400d84dfe3eb6cbff09d982",
    "20580670c6aee21bf2939ab1e75f321bc770326571151ee1b971461b1a485d34",
    "19d278981137c795751250ada37ff5f6967df47c1924fd0c01eaf73f3755dee2",
    "284d344ac35e17eda12715cab736a7bf80985220618e1982d0ba87f483e29548",
    "10d804047e9456a88e30ce550825ec9de169a8c8c294b8ad7d7d9c9de862d959",
    "1f28bad964382258926d40448c4a52bb012b79baca651fe9caa46dcddb4c692e",
    "2afa3d3af4f7c010b53158e9c33ae7d274450321825074e7b4ec99fc4e17824a",
    "05ff0dcb51139aeb4ce592da202d0a8b376db0eadfdf41c67759bf6395c23bbc",
    "2334361a2ae3090202f63bbc1a5d0606f80c3817997f4686479ac95067e0ddbd",
    "17e7f62ebb033222a16bd649f8e18aa4c39f4579c9fe8849fb496bf3d24e68bf",
    "042ed895ea559f87e450c9ee9112d42c2b06375c8a1c80b9741a422417a439e5",
    "09a3922bd7af67ce23774e3e0019bc2791ee66c1afed7e64486e1be75cf62d87",
    "2f8fb6382868931fd4388be0a53ff48b9e1c425f9a2cee2994b95c8d8994fd2f",
    "25ada41ba5758d9af61c25918dbe508e8fddbe0dd5c96f543652756da1b7861b",
    "2d6d129a127b15041afea320ae1d534e410f831455019ddc27f7a88e7a50a419",
    "20d9b00b819f4ac9ad506c906c0a60aa3ef01baf0c026fc25f190b3c7eb8acd2",
    "1b0e79aa01e76b5b44def6bab00a6927429dbd964f9181e0f4c8faeff4e4b358",
    "1e388c3af19982c482b5734946c797c300086348b735454a0b6032759e1e1d85",
    "03bf169e108954db8b98a81ccf96f539212e4491cd1fc0b448209bd3a4e4b8b5",
    "27db16d43236c7ae051c875115fac377cd35ea29edb5bdd66754fbb0bd852da0",
    "2fe844d1c5e84734e37507c6a1f16f21025d3391e6dc19af44c31ad380ecf62a",
    "0a1891a91e9b999ade247f5c3203d62b63e1dcf30a5136dc58f133f9f3efa784",
    "155db434a5865c14d355be34288558a623221248ed4ccf2ddacbab53d43ff026",
    "12f30e1c34e90f41e8fb0cd725ecd21b8d4d0d0e13e0536678545d15ad31d75b",
    "0c9c5d97733b08e0ce12673389b0a988a900c73894b1bf32d6df821b5cd06923",
    "2c5e1f0ed5ae2ccd6fa362c8595493fb8733ee03ccc703276a2e7e261150e3ce",
    "0a4fe0e235edbd52fe49122b81784a1ad9e05c20edabbe9c3195c7437fe60b99",
    "1a4d1b1876001e8c4a4e8ec80e3276b98fcbb4b4d7e0bbac913f3ec6388c50de",
    "025ef23c4826f24abc515b6576c8814c86b0f58c19e470425822972dfee15a17",
    "2454d98e12169f0fb10ffa355c51354f19dbd7337fe77805517153a4569c8e09",
    "1e0a1b4d5976b1d7754aa48866827435a40dc118c71db2561ba14fd20ad458c5",
    "2a8f3dcb8bbb6b163eb3184b6c57e66fd0b635358e94711f65669c9230ef291a",
    "1f615c784a4963cbca0069b3ee7ca910dd6ebf41613baf47192001f0d810ab1a",
    "021771f686c9674fe64b16af8b9ff43eb6862552ed38540f360f5e04be5324aa",
    "041dc8286b7b9c7201d210ea989c7b73ba4cb547e895baf626b3c59e94ecb3bb",
    "122170c888db5b0158b6dd659aeb3f1be0a96618df56602569647f05006815e4",
    "2c4d161863b06f59bf2bb9e5df4773d8a6e7219caec224d3e087beac96ce2e50",
    "169500eb9d3fa165fabee918ed964f824016c1058ad9300ace91f93785651cbf",
    "06aac3da9360797dbf12c3eeb049fd5bbff42600a70f0c14bee8c4f851353b3f",
    "12857dc1b3ac209e5ac7fb6cd2db0076f8e440e63df0a0e1ac11791a91ea83f9",
    "1fce21960f7025f81c5ff3e6c2b92cf57b94e505efb53ca7ff9c70362859e189",
    "2ad4af7fe20895c1f1bcf7657d2f3aa39c77bd28f3725b40b90ab1e79e222c8e",
    "117cbf377aad859d93bbc6e9263c7b06c54c4731c5342b82df62be9653ed45b0",
    "2f0ab8f73fb9cd1971bdf31b252c332541db0a7bc441c956a62041e5c10ac106",
    "2e1a343d58eb4486b721f6be8fe57b80be2950a0d1f8953ddb2f1a443ebb6670",
    "046428e7bc1a0d6050c6bea075594ae5d8516d6c09f794832a2ed44869fd34a3",
    "2d8177c39f6f24e77301c55b1628f7ef5959d99d270c4efa1362820e5cc76fd9",
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    "14889763041484601e85d4ff8159336a8793f18d5edb865974538ad5b58db01a",
    "0d454faa86f40794dd02f256c1a338c22f3c814c847b4e205cf20082ff1a5827",
    "287e7a4cea0baa17d1c3132536df29f057d03abf655feda515cee4bd45001de8",
    "1658219d6a2fddc4251f3432bbc8b9e49684fcd79aae97a0e78df0104d060ff0",
    "15cb0566bc07a7ff76ce7fb625640816c32716f2fcc031844aafb2f09b3266eb",
    "251fba7c2bccc579147461d7caed44ffc4d7aba749f7c480a143fcc52ff6d0d4",
    "0f88bd8cbf293e53bd7ea661309647621bf243b07c3010867a71e81d56daa32e",
    "2e50739ded1d40ef1faffa7247fb35f3f3d8738bb300053009720f464b245b4a",
    "08a860efa3e963177cd69cd935fd4ce61812deb1ef476eba5c18b53a1825f73d",
    "02ef0b5bfd2869670ddc1dde1c9a29ac9a93a28633dd55cd543dd93d031a3776",
    "00ad678ff09f4f1d62f3eb67a93e95202c4002b4435a3930b2e97fc8a437c860",
    "2c53a9ac608631a119e7f57ed5cb0498134671e6f517757546b3ff61dc24ea9d",
    "0b262e363290fd3157aa34482f7d3b63e7293e766a34c528fcaeac7b78c669ab",
    "2c729367130f7492d6c7fa81d933e572ceb2cae48abff54290364f7ffd98bbe2",
    "0c52b752688f7c1231a81213da5d399f0de08127a0410ab6cec26224520a7302",
    "015ed07c528f1f75c39013233daae79023c9a10051e272b2a0a5596745b50def",
    "054c68de3da880b3efd04d6dd592070402cd24056b7c170657335e9ccfb45ed9",
    "0653a2625249ca142027b136af44aa3bea7ce98801ab7964102b20385ed3e38f",
    "128265fbcf4f8dc26f44e5de2ccbd57ac858b7a1a3d955a1cafe98de79d239ef",
    "290a90817d105423426ab71c2b097df309086c3cc0b83ccb1bf90486cbce4114",
    "0ec81adacd88f9f1401c42ceb56348bbf36181a0c03f2512e34fdef39f23859b",
    "0059843dff350356ce8db94fc588542dcd43c7621d326a56c7de9126548a84ef",
    "05f1d7d0fc3a5e6bfc55ce75e7688236e879a7f60cb52f138f52069b048f05a9",
    "2dadc5fa46bbc50df63dadfc9b4fa72bd344e26e93f0fbc184f03bf4a76b51e1",
    "1bf5f44265a2400afe65e220ed0c8b49306770e192cfcbe06c8c28206a42cd78",
    "0f484d2249c289e95f4c1b2fa0330572037b157ae41187aebf92468d617dacd5",
    "1a4dd8999a4847cb26d5cc32ac2b94ff7f5e4e6a37263e34cb18dd53d8be1b75",
    "2fbf545602120abfff0a56316d9143d152d43816ef782a67780e1b8f9252a4ff",
    "1835d89422d3d824fad14501a3f3c8a6ae474df2b5a29011b5c36030c2b8bdfe",
    "18c215d302d89a958d8d9cdad60b5010024e91b510bcab7ffbb384cd21b625da",
    "0179533ed710624344ced7dd685ab4dbce139efd5ea097e8adbd02c32aaac947",
    "07b91c56dd39dd5d5de474540858aa9b5cd0d91cad2099bd14befb060f4f3b96",
    "2a79af347cb1fa3996755c7f68ad83f86b86ba81bd2b9fa98948cfcef63cce23",
    "0c38e0161d3e3d317108e518dc74150f8205fb74083fd47b3b88aafc9d0130cf",
    "0d65129efa0b7fe99f91e540166753bbbff12cdaa9b5777208f26ba72a87b52a",
    "065923e0aa248690099aa247581f481061d9243cedec15a538c6f3dabc54ed3f",
    "209749a7661b281882cd713683824ed6122820968a9552ed27f208a45c2837ec",
    "0567e0493586c14d0ef128252f9a20c74602ec56626b5c2f3644fc79a7983a16",
    "2a3746ab2d1fd023c90559abcb8c36d3273b3685b7da3332b3162e894a6cbcea",
    "2fe83a4aa399397b998bc1bf32a322b69e58244d60ccfb546c013ec9818e1355",
    "2cba41b38555075f0caa9773c8f358d018620c4fec64c15142e33bae27ff07be",
    "262d890f3c3d9ebe6eb150754a0677d94a64f645ddc813eb87f82418160376bc",
    "184043dc9ed8d23817f34010c7689116620fb892ebe7b92e7afeb2dff8203bb0",
    "16150e6cd627f1aab252d573c715c3e132d63d714e232c200a86db5279dc24f9",
    "1aa1be02875b4dd93beaa0841dc74dd43b2f69accd3c3625cd28e720fc3077be",
    "0870eb40106c6c25725f4e303741257e730098d7d4f7c07155bc89c805f3e573",
    "2c174e5eaedc48a0f83b0638038d79d5ce719a7ba41a974f68dc307a4d7df27e",
    "1c5f8c2978c5db3c6483e6c59ecfa4b4591f81c346f882166fe1395f09067c01",
    "25a5229df981407d38b35494facd5d3be74835427a084bc796046ee533804256",
    "14198c56049b0bafe24c1e58227a15dfdc1730f7570a0425cc3f5175078d3b46",
    "06f649866a0de8a7127623c9a87e528dea9d7df9a761fd1bbce65bc1dccc06aa",
    "1164c0172f7edcf878d89bec7c593dbac32f366f7c26136c219c9ff79fb4ba8f",
    "1d57c7d112c7559eef860394ffa55686dc4addc269e1f4763a3a329d85b9203c",
    "29c8787c8830fac709c646dbfda04db6ecf9f508e056fb42d9a7efd3bb0a0360",
    "23ef9d9c4a48657f835f302dd6f6efa94f21f7d65fd188fe53c540bc7fbb48f2",
    "259ff75fdd8a23943f9d9e91e335395223a11bde135182fc543af4763a9c491b",
    "1b14061e2f2c468feb62b9ce08729d60a700aad2f37e7aefdcd977243a50f02f",
    "2a79870f9070251178edd6c30596db17a75375b7bc163d39cfa97f42bea1e487",
    "2920015344e43aa0e279bb8bbd180ad00f80a2d88d7ee3d75f794ea94f788c5c",
    "262f785087e1fb1873a803e55d7f1b6e1d31ae6ce6c25ad0a1ce39f3dc870765",
    "2f34183f18efd7f36cf92ef3310ea2b5fcbdc68a08ec1246f86ec7821bdd3593",
    "24976ddc28c17b43f06aff004f5237fdf5216bcc98656c4cbfd80d2ceb28f5b4",
    "1c75ba32a127cae227f83616357be97ccf95559f4e10a202f6f073f6615708a2",
    "29a2d25cbda9f5b67fa860e6d42bd3408a8538b9c6879851db68d2a6bcafc02d",
    "0aa84212e380e99137636932c0aadb021c2ecd448bfde7f9bba46dbfae9847c5",
    "21f78689e3e2585bd2fa23848df576d8ca6a20c1e22ad912ba5e9bd9317f072c",
    "293a1159d1c02a6429adbb0da020a819a687ee7047679c3c60d58c3ff98ae3ea",
    "1a7d485f430c376e12fc7d1b3613a511822193599e15e0b30d214cb989edd72d",
    "148f89c16be581d1dde28de8b229a14509505effd37e672e3f47a90515f0767d",
    "03c2411a03c742bb60b08116a2fd8ea86e1cbaa1f6f82b45951801caab0a6448",
    "05b054684c6e494317541efe51da10ca76fb31a10452b442e4993814a08b6bf1",
    "1ca534bb0ce1f2ae8149ababf167c5491f00edb4b144f6ea92a7d7918b6d4cd3",
    "1c2740412825060b5f2a80d387fd83d5023d1be26ba6eb2b0a5d8e90ecf98f44",
    "15832c8f5667b380e31a84435232af18e685d784d201faf7b9bbae68c20aca82",
    "14d6fefe0a848db15e0baddc508b71614642dc5dca6e267a4c082eedb7f22f3e",
    "0c0a1384c660a036ad581bcce6af24ca06f7b647be7fea648cef6355901fadb1",
    "24d5243e9dfd338ac19c7a01a6edb2ddfafb256e6b84964d3c50cb3fd8dca48e",
    "0a4d7c32d85fe6458c9b48597aa03087ff6ad9a766ae6e3db65e2b23b6d7dd52",
    "1db213ff1511c1dbd7f764afcafb3d1ac5811e7a5795fe61f00ab8abad903bdd",
    "1665a557b4a74548ceec6f598ab5684f32bcaa867c12e8d1abdd6acee1285792",
    "2fd5d39615c3cfbe8ccc5e362e635cfe06c588e9bc0cb1d95c1df71dad1c0b7d",
    "100e6f9483e9c38ce0a7fe26cfd8bd1d915a967ef85e9c3126b6f97b8c67ab0f",
    "02f04bc9ea7e55f3901d844e427bc348f934f48551eb0b60051f9ee756a6aa3c",
    "18bf6a3dc3320590adae58baf410b4367785d21d0a38e1fd8ad0b5ac73ecf609"
  ]

  G1Expected = [
    "0400000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000002",
    "040e97c669de7c670d734ca98a3bc5176c8f82aa5e44f9a8780998c22dfa5fb5ea19305ad020d76d8529f57dbdc43f7e77a637f17b2d5db5b06a2554c1151b1255",
    "04070eef7bbfe7c9fa76338ed6d6a12b84f61a1a1b5b4d54c009b3993e2262c5fb1f4118919fac6678cb671ccfe5a3ab7ffc42dae56e8f4382ea3e6582ea7fdd15",
    "041ce66de558c33edf36b637bd39478e2f317f674e0559025d1e428f37dda84c342e916be0e1e8ab1ba6a9ef642a2f1de44c1f6f91aca23991cb636dbb997cbc01",
    "042e8d7e2ab119b53b2e2e5f8ddda2116aa821949ae0bd00a6ee6ebbe130397c0709e07974bfeae5c973c098c6dff65e864ee6ee05e9ccd1d61c8ca72e0c49232a",
    "040460253e7e4e9804bdc30e1d76f98d7f7fcb4a6845fd6f9df0f06a18e1a2ebb3066fddd38227281acd80b6b6253f5d89e401918586254edad1a56fbb8544dbbd",
    "04130f5f5f20846ffcd6dbfded402bebb7bb07e0a4cb2024bc84262de67498dd7e18dfc445b80fd0a1843d6ddb5ffc16cb8872c373b7adb9fd1b98ccc922318966",
    "042849878760819716f11108e902836a72f4bba88eadbe26b5b9f53e75c1f8714f0732eeeaacbbde8dce07be752d413d58538fc11f82a1c434afac5c27760e8688",
    "041846eb3215c26d8be94d8cb688f19f59db6c771bc8155d1fff826440bdaf8ce720553790d70aeccfb178e6c33f4331b8cc24e02c8ae8b5a0bb9b57a9c1132001",
    "0421f8b0a60f933351788799a7271fce8eb3349b98b1e0dae6a1de4eebba06daed2f966958654ace4bad972296bfd8d3f1568954bec25b665c0fc8f64f1a0c9856",
    "04163ddafd9f4677caa2b8feb510a6b0ef09191a00adfd9f09ae3e59d687af8ccb1a47d8362079b22c9064718f02948da7832a8e123b8c6e3730a9e7e137f84da7",
    "041ac98fe325a2faf01816da51b3733edb8a13935dc0b82a6fc2667773d09461ce258861533cd79b9ca801a366e40dbf61431296ca6431b51e61adb41e389328ea",
    "040dfcd832e70b1ebfc5f07d66ef71e88f1903eb69e25a43e17fcb119305f936a101f6022efdd7bb49bb2f9882d1edb54a618117ac9a213776ee09661dc813cb90",
    "041c11d08dd28ed037fb7800988bf9ed0ffe5dea2ee321ba36725bbc2fbda12df82151ba8776a883a4d2fdb5daefb681aed75636db330956b36a795031b238494a",
    "0407592e35e3444f61a5cd4bd3b62765ab5d67ff57b88aa781bfc0a14017746f9f2ff61c2caf223a33ea998503491389ec7b5ef2797f9d7bf5b63640cff086bc11",
    "040a5e52f3b28b3d8a4eae2332ddcfaeb3300432f9c11409c4388607dfe2a0dd171781fd5e8fffab898a916ee4436f487b7ff9a0a7ffdae2e0f98d6fc1075f60fe",
    "042db55c23fcdffc4000befcc40b612d1bc38d8e34ba4c1eb68f7a1446f851630d200c8cc5cf724a332ac366160836f91c086df5c8e023e0131eac51f1c18431c3",
    "04283f5279f2bc83c2c0829d1814f066d1828c267c95edc39ad4853c5cb35c02dd1f0f1bfd04a340863a34d8638c0b7c254473da29ec0c0a95fae6a7ccde78c740",
    "0401cf54e2dd9c2c97a96b809781114b82aee7d0b9f648d91fe01533062f99fe590037123d18acef099417572bdb041f77ef044b9c3fbef0ef0f9894f9a4061313",
    "040b0115940193b2c17fb561c317ed88d5b5bac173f4eacd887fc8de03b9915ce62be17e169ae45579e2f0982b686a611309a8435d1e2f0de9a49c97f72679c795",
    "04194e71fb26deed74c5681a0e616ed67135add9f3eb97fba96202539876fe0a642b27a2f7a125e849eca00af763e532d5c86ab650bcded04d47d26d8c6c62c139",
    "04001082425143d275f44e16040d7f8922ccdcd77892cd80796a86051f4ff5b2de272e4a7dbfccbd7ef79cae19d0de3a0697adc6cc44d99f014187a99b6c26d7cc",
    "041e6b87d81c1af93bacf529258f36145b434b84e843e0963674c529133b7ccbdc09384b95b6c343d8012f4a8b3a1bd6f34142d7688963df85c38369638b1c3117",
    "041e34c8d7c0ba039b67537c75939a14fd61598babc9a448cd103601253b93692c1eb61a4444ac063eb1ae75e77df30f69cda5dadc08912727ce2426276fca10ad",
    "041cd5b925c2174a380cf78f14a57388711b91c90010c55c0bea173cf77443869f1f7fdb3f0414e61d12589a46d8ae49f95ef9b1bece46a85d2d14d2deed1cbdaa",
    "042826a17e76e78d1883003a32e8cabf44ea62087a2ec95ef68d72ed31f0dc0eab11d1fcb397c18539c7ed620a502fba6f4ee19adc17aaf9501b801e72a21c7b9d",
    "0425b7a1770cc9e63055969af6b201dc7b6b5c8ac819b6ef82f39d3dec427a41c914b4f4c56c3fd44b34430f2a5cb7ae272c1a6fbcd86a22255db728fcc91d14b3",
    "04150f39cb53bcf80d39c77a2a2d52ed7f3e0ce5b576a89981b9d9d6aee05110131ad181c717291b23eb881845ba88903859be7f65fc6e795507574452a03d4e25",
    "041555ccb4555301cd5e3beaa6d0b8778a4505b72135567322f9a5a540e3b8a4fa127f16e181d7e3a75a2d944091c78caf9849eb6c3f3b24242c514e42fd30c0b3",
    "042349519b9c99cf376534801d42d098b2541903f5fd07e0fa81d71ea68c806f89086bad59e91f4341cef634582513b9359c751e3640c0fa9a205a6bde1fdaf697",
    "041033e55052e5ad95302c5dbd98a7be3387d605956d0eec74576a4251eb58f4da2534b51e49ce5768a4bef802e159fe1ffa37dba8437669d4c31292a2ecd24e4d",
    "04070ca0593d04d87f769bb59c63b76cc1478fcb5eb5528b2d32ec6294eaa155351aea25fbfd40948c8fd8d202e31c4a1374869cc9eabd991ac2e00f5b2baf4e78",
    "041d61b6c3dfba531cea1f35f652f6f94dbdbd1f62c43396dc378f70b6b0990e5b23b161cbce3acc6673a44939abc55b4a86f683e1e8ad4e0aec9e0e991c4ffd09",
    "04131d5925f21a50af1da2367abadf38f2dfd9e7257523dc4662d0bacbc0808f130dbf763b7934a0a6224c34de1b4d5a791d88729df242434e0145bb713a38288f",
    "042bfe71e528ee56f4c1c6f1c1de11864fe3d67e56b87dfb97cf608a83c4c2f18a2c2383632ed6378da76655cf8a5e151fc692ef5e07bfceb339c3d9504555a47f",
    "04058210b550fc16609877b5fc0fb3722a44e77de300ea96de918d913e952f0c401a03daecc90ce916f495fac309acf7c33694a2f77bbbc770384460c2c98fd13c",
    "0428ae164d26d0987c3c875e691d78b346d8c32a0aeb6fefe1510e5528e7fe05232a52f102a41d3dda80ec1eac66c6f759b405257bb836eec514b298747129b6ca",
    "0422b56318bed36b21b46827b3d39a6a63fd327d84ad09efdd6fd9b7d5bd71c22505fc11eb76fd14c4b5b692723e28c454f7db0a36eace914b2f2c87f9b81e52ff",
    "042a3e5a4c98a171667d6caaa396b0ccd03aee91724c0f3349214523861e5fcfa81ff385ef6803e70830ded0e23c2e76fa4d94ec16043290b16ac805dc2ca51153",
    "0420be7bffa5976e062a75eae9a4dca83c27207152d8e7301c92bf990e2eddec35166a2963ed3c15a5350c685cf5f9c6580b9b96de49afcd5842344350a9d4d03f",
    "0422e11534dc3c78583b6be6a70f21bd3f91b2d65f0776b88e871be1444c5323c21fb10a5e7f3f001a0476a99ed6eef5988d8899916f2e89c1d813a59d19bbdfcc",
    "040da396124abe233d7227258003fabf15f50e21fea5c48fd98c805104240a084113368c4132a31a97f20762b7c0fcdda013936649d410ed33575d9fd727fdd22e",
    "04278100c505a2dcdb395665dce5b91afb7d458deb9b2e148f63671f8bad4f67910271a00bb8db2441412cbe445219773f4be7b7d628a2123d667f2fca8a05055e",
    "042ccfdef921ed73c7c5bfc7e77f630048631e0e1d9dac267a2cc55fd15d9648ed30380375c926c49823159426aaa804e7aae72012d0a10373466c6c09c27ee0dc",
    "04016b16f7158ea78ed57cddf9eefee37f652faf139225b23fbbe72fdbeaaa1c5900deae79748f9742b576cfc8936fb1b24c86401e5756457791925764e4088fc3",
    "042e27be22937dac068c73fd21b5d70df22a95a7c5fc1902f28ee36f1c1211c46421657c8e8d11664c0dc1d0ea02dc0126e0430448cf415e1d7d2449dca37a06a6",
    "040d3b6892d20ddf0eb053e3fb40b71461a35f89212d25b8e6ff4c7b3e4272d5a61e8bb4cce229d8035ca37cf6a9fabf103299ce19b05a2cef38cb0948dee5b799",
    "0411d389c11fdc323af24c9e3488abb5064b1b0b312f641c2041572777922525ef26f06bda6216d6310b1d2d9997b1d721b34f8b13c5c9c06fa19badf43da68e72",
    "0425f96f8440bbe27602bcbec4ef5ae8d1bddcf2933a915438320c8d652823c9902508cabfce8c45cf54c9598cdf75371b7d55dc73cabf16e0199e83b5d06d203c",
    "040d6229b56cc2c4005612bb667790d1e5ef7d7737ed62c31b97b84d6af2e160ec03190f4f4bb3fcb136b89a99f82f4941b1c54a2b3d7224e56e04f9273c0b8d79",
    "042fcc98351a49c7137bbcf3644b6961e6b40adc959207dfa5894705da09d3b898028570506c9076b553b9399a488060c7b80c8279fc461ae9e150fcf55d4a42f0",
    "0400662d7bf0d66e45ce36e706f3c762933ed4ab09e664a58c557c3323e1eaab67118a6509dfc87dd195a650ab7781c410ebe0fbcaf1f462ab4f7966cfc705463d",
    "0413aa3bc49295213ae2369d60baacce80e2468b482a5e2a36233d9cac99c2d3f00a22280c564152ef48f9310f91a58658b39624b5d0f44b77f2d7388ed63392a9",
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  ]

when isMainModule:
  suite "Test vectors suite":
    test "[FR] operations and serialization vectors":
      var acc = FR.one()
      for i in 0..<10000:
        var num: FR
        var buffer: array[32, byte]
        check acc.toBytes(buffer) == true
        var chk = buffer.toHex(true)
        check:
          FRExpected[i] == chk
          num.fromHexString(FRExpected[i]) == true
          num == acc
        acc = acc * acc + acc + acc.inverse().get()

    test "[FR] invalid representation vectors":
      var num: FR
      check:
        num.fromHexString("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000") == true
        num.fromHexString("30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001") == false
        num.fromHexString("f0644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001") == false
        num.fromHexString("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000") == false

    test "[G1] serialization edge case vectors":
      var num0: Point[G1]
      var num1: Point[G1]
      check:
        # zero point
        num0.fromHexString("00") == true
        num0 == G1.zero()
        num1.fromHexString("23") == false
        # point is not on curve
        num1.fromHexString("04177cedb64589bde7a64ad24f89bbb8c9f05535810865aaea8fbf8184ff9e120313500226b2422d2068614d1c8c7146c806a97743e78d9901748a9ded08ea9e5f") == false

    test "[G2] serialization edge case vectors":
      var num0: Point[G2]
      var num1: Point[G2]
      check:
        # zero point
        num0.fromHexString("00") == true
        num0 == G2.zero()
        num1.fromHexString("23") == false
        # point is not on curve
        num1.fromHexString("0404d4bf3239f77cee7b47c7245e9280b3e9c1182d6381a87bbf81f9f2a6254b731df569cda95e060bee91ba69b3f2d103658a7aea6b10e5bdc761e5715e7ee4bb01b4c328f0cbdb4aada63b3d09100d792376b94d07a6004e46054eeec849e8de9835158a11d28483dd8db236ea49f3630edc9e41944e494c5aacfc36af3b66e7") == false
        # out of bounds
        num1.fromHexString("04ffd6a64a62b843a22c6250eda2354d603e74c30ed0b1435951c3f7dd541538beb8a43915823125c6bb89aece89125664ce78ca69b81cdb8164b40eb2833560b606e11258ce33c4076eff0d5824f210466b588d324b60ccd5a2b7f180f9a7cd7f1ab564ddb03b1b684ff4315acc6eef5229d99fe107afaea83a5c72f2b4c33aca") == false

    test "[G1] operations and serialization vectors":
      var acc = G1.one()
      var by = FR.fromString("23938123")
      for i in 0..<10000:
        var point: Point[G1]
        var buffer: array[64 + 1, byte]
        check acc.toBytes(buffer) == true
        var chk = buffer.toHex(true)
        check:
          G1Expected[i] == chk
          point.fromHexString(G1Expected[i]) == true
          point == acc
        acc = acc * by + acc

    test "[G2] operations and serialization vectors":
      var acc = G2.one()
      var by = FR.fromString("23938123")     
      for i in 0..<10000:
        var point: Point[G2]
        var buffer: array[128 + 1, byte]
        check acc.toBytes(buffer) == true
        var chk = buffer.toHex(true)
        check:
          G2Expected[i] == chk
          point.fromHexString(G2Expected[i]) == true
          point == acc
        acc = acc * by + acc