github.com/consensys/gnark-crypto@v0.14.0/internal/generator/config/bls12-377.go (about)

     1  package config
     2  
     3  var BLS12_377 = Curve{
     4  	Name:         "bls12-377",
     5  	CurvePackage: "bls12377",
     6  	EnumID:       "BLS12_377",
     7  	FrModulus:    "8444461749428370424248824938781546531375899335154063827935233455917409239041",
     8  	FpModulus:    "258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177",
     9  	G1: Point{
    10  		CoordType:        "fp.Element",
    11  		CoordExtDegree:   1,
    12  		PointName:        "g1",
    13  		GLV:              true,
    14  		CofactorCleaning: true,
    15  		CRange:           defaultCRange(),
    16  	},
    17  	G2: Point{
    18  		CoordType:        "fptower.E2",
    19  		CoordExtDegree:   2,
    20  		CoordExtRoot:     -5,
    21  		PointName:        "g2",
    22  		GLV:              true,
    23  		CofactorCleaning: true,
    24  		CRange:           defaultCRange(),
    25  		Projective:       true,
    26  	},
    27  	// 2-isogeny
    28  	HashE1: &HashSuiteSswu{
    29  		A: []string{"0x1ae3a4617c510ea34b3c4687866d1616212919cefb9b37e860f40fde03873fc0a0bf847bffffff8b9857ffffffffff2"},
    30  		B: []string{"0x16"},
    31  		Z: []int{5},
    32  		Isogeny: &Isogeny{
    33  			XMap: RationalPolynomial{
    34  				Num: [][]string{
    35  					{"0x142abb491d3ccb00d65810beba93dbb0a661fd85974d6aa82c4bb2e1a3c84ffdd6ef419b80000000000000000000000"},
    36  					{"0x4d9d782ee8a7b7630cd57be9a2ca555e2f689a3cb86f60022910be6480000004284600000000001"},
    37  					{"0x142abb491d3ccb014ac44505178f6ec539a237640b7ceab573689a3cb86f600114885f32400000063c6900000000001"},
    38  				},
    39  				Den: [][]string{
    40  					{"0x13675e0bba29edd8c3355efa68b295578bda268f2e1bd8008a442f99200000010a11800000000004"},
    41  				},
    42  			},
    43  			YMap: RationalPolynomial{
    44  				Num: [][]string{
    45  					{"0x142abb491d3ccb014ac44505178f6ec539a237640b7ceab573689a3cb86f600114885f32400000063c68fffffffffff"},
    46  					{"0x35c748c2f8a21d6af848e30c1b78229a46644922460e73f6faf06c327b438084815848140000010a11800000000002"},
    47  					{"0xd71d230be288756a6446249c205dced645709767bd81c863eb7f8d8e4f15003f5f407b84000000a64af00000000002"},
    48  					{"0x17872fd54cc6ecd6d73a5085f0d2013b6de7eb4a0d6711d3b14f5e9c2c81f001429f19baa0000007467a80000000001"},
    49  				},
    50  				Den: [][]string{
    51  					{"0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508bffffffffff9"},
    52  					{"0x746c34465cfb9314934039de742f800d471ce75b14a710033d991d96c00000063c6900000000000c"},
    53  					{"0x3a361a232e7dc98a49a01cef3a17c006a38e73ad8a5388019ecc8ecb600000031e3480000000000c"},
    54  				},
    55  			},
    56  		},
    57  	},
    58  
    59  	// 23-isogeny
    60  	HashE2: &HashSuiteSswu{
    61  		A: []string{"0x152964189f4c623685ae0423eb10294ce6458c064f093208504005b37d04d5d336dc9d66a97093f84d62e778f8c82be", "0x735c455387ab435839e5a5dbc1a30510070300f4becac797642fe56985064e95f7d6521a1a6e71004047f835c1f957"},
    62  		B: []string{"0x19e38372e0d4bf401d2fa5f2261e1e3fc95d51a3857fc23b1385d51ea9c973a89c22148a93dff96447700bf1c3aebac", "0x1579ddb5c1c595b7c08c3a3cef5626143c25757c6b67d0a2677b22fc0c890d8b2b1a17895d047a98c49047069f725"},
    63  		Z: []int{12, 1},
    64  		Isogeny: &Isogeny{
    65  			XMap: RationalPolynomial{
    66  				Num: [][]string{
    67  					{"0x113b0abb7ba48832ffb7aaaa7ce085078312d4bf0bf8882e8f4a0a6e24d91b535b6c81277ad9369cacc733de5cf86d9",
    68  						"0x11e62d211119d8108bbf13b3b4b79a1aabbe2d6004858109139667b300e5097370015d42782ca1bf7652dba1d4cac3c"},
    69  					{"0x51a19546efd3c582ec16ee049bafb8ccbdd87d98f753e654e0b93ae62a627a6f610b30f76016baa8d18dc4677dc401",
    70  						"0xddc3aac50aa5af86f8c1d31db787f4b6ac0262a8ea40c07d61389c2a70b06c51fb59520394e05c55c72e363b9607a1"},
    71  					{"0x93198927f09c55a596756ab909a06ab3c0127be6538fb275f2b7b5bfaa1ab85b12a45ef345d628d5c6e69effd7e76a",
    72  						"0x2c02fb38b1440c7b2d4fae061763cd734c40b1eddf1ca9552554d2859906f8d6290038a485a655f8178f99b1fe43e1"},
    73  					{"0x19091208a40d61bd9a55359da28b532617da69a58addac35288930ccd5083166d791cc7dd3c6533e01f786000c532f7",
    74  						"0xcf913d369130273a81f982f469bc8fd98a8983af247d28845d76729468a777836e1d3cdf1e1adea6b08566db5b514f"},
    75  					{"0x181a36b975099a83b4773c6e62d93365d5fd3787c2b62d0a315245f6226ab13cd462f731b73a436a598b34dc0ec58d0",
    76  						"0xdeebd58f0234fa272439c69d9f0ed559b955d416256645c2ab1857d988b49109ff460206e2b978d877fc9274fe4840"},
    77  					{"0x10cd4f85b581fa9bbd614f001a2e64839a4635373187b57373f17f77e11ea30ce505e6ebab860ee2aa46c9e6b327add",
    78  						"0xc1f11111a68f3346dfeb807985c61491498efd3439c5c7a0b77e9d819a48be950e43c9f30cd21e5e439815a2ab6a9a"},
    79  					{"0x1813ccf2b39896b88561d57592c5e7d7594146f9eb341852cdbc192e88792058059bd79b248c5b8c415d6149d51130a",
    80  						"0xeb958c5ed40e2b75a170536e42368207df82fcc26518f6f83f40cea65efdd81dcc248290c660107e0a2d650a38d526"},
    81  					{"0xa143ff2d94ba2d2322d63cb3769874b17c00fe76fff4b53fb5fa4744da3114899adaca240bde7d88357aa80b144bb1",
    82  						"0xa25054cd91b2b06cdad439cdf86265929d35738f09e759a56164861f45586602c630ef182e9262f0413374b154dd20"},
    83  					{"0x1f0a897c94b01589c9eb5cdd999c580c284f39c6fa6f2ad0c569c3b219cc245484ed7310b858f980b2917508d94f59",
    84  						"0x5c56eb37beca858c993f39fbf09b73efbd98934b5b1d8de0c21fc75d20075e6d7720601832565b1823339bffc17a6d"},
    85  					{"0x13a21ac110c90240e49de23070e86bcb64b8c500d8f9d792095a0a7f9133f4d8d94c518f9eb1359c8c82926e41d004c",
    86  						"0x18471a982b5d8d7756ff4971fbba3945be37cea5cda74e17674b76cbf527f8ae51a27236a95d815a4f36a2461df5b67"},
    87  					{"0x380e386dce2ad72755e1d21461a3d33ce275b036c2a11a755df7e948161f3318531311b8dfaad26a2b6af699e42f07",
    88  						"0xc86f279fd500d0594160f87a462ff89f4b0db7b7fe6bc809871f11183f13235d343e0a8bae13c9f5791a2821ce8bf"},
    89  					{"0xd73c34c8f904e327cd1fc22e8a90e04bed13e46eb98e3d47d18cde142b9e0f3a03eaac69214acac03042aa9b9b6495",
    90  						"0x76ea3cf6b7185d7d6e3e73ac03a21b645e5aaee7a99dccecc485620fdf64e7486c7b1e4f8b6e069240b7a1e76b0609"},
    91  					{"0xca983f9f6ea728c5b4bb9a6dc72d24ecab7833e1a8242bf1a84140deb996176a8f7c7d6fe34fdb4660afd6dfa5fd74",
    92  						"0x7e4badbdba86487f1b87daccf8d14f62bcb01bca058d8e318ad40ae8343a47d40f6b18af1e0bf9860eeb32db4f02aa"},
    93  					{"0x1552beaa2371b711181b528b4ea3e801e3a71c2bc0bde70a2babef6d5702ff12af4f5f2823599093d5485b94c873d36",
    94  						"0x11783b91dc5ce3d03283278116bb901408dc61ef8bad40991144de2f3509787d83b566820fd315b558ccd76c9debd5d"},
    95  					{"0x175374ccff26ce81965dce12856efd5cb587251e70a588e2e4633110d65bf17f2991df664e727ebc65b42d74a938e4b",
    96  						"0xe75b2e26120b6428e51285251602a89ca9f865d444853ac3527b940d7b218df89806e725ec52e75b92dfcf63616483"},
    97  					{"0xecfa3729a48226a477e72d4067aa372a29fa8943324495f2f39f754bd1d114fc2d9c62453fde06e3272bf09faea06f",
    98  						"0xe95c673c49bda6dacee18f07327cee3902582326fbe658d3e8cb15b40327b8b7c1b04e0160071f1e8c617361754705"},
    99  					{"0x155dd556a15b55b766cc98f3455788f3ca450ac5c613b2e1464b53f0e5412a626e423cf9dd5127edaa6deeaa5638f93",
   100  						"0x15ac434170f220d28273b44c48eca01f2cfaae20e2342429ca6f3668e0825821a3d7f1227db23b1a7a36e7f8abf89e"},
   101  					{"0xe785dde291472723e95d737c7bc0bb72a8125cfbd91b122beedd3f45dedefc1480e9350bbfb6a5ca2fb9ec905573fa",
   102  						"0xe01e2c8ab4ddf439c8d4028ccc68b13de8099e3aa7d5120867366605682a4db4ec308cf07e043cf7256e35c23ecbc7"},
   103  					{"0x4e2c05f403fa31d03e91053fb52a3fc12ae58977575f53cd8a52b53d1067cc61de65daada7c7c1bf5bdb07f3719b14",
   104  						"0x18de34a92f81eba3a57d55a9d4bd5cf7da7b1794a0f9ece37abd537ddcdb29edbb01aa88baef416408d34a227874c33"},
   105  					{"0xe4a28f5d9cdcb181099868140cf3064cd573f892aceb79e3df63546686df19a3164efedc851333bbe232be84e3e627",
   106  						"0xd31f8027ef5f6b916364d998dbc4640196191cf0ca44e2c2c4825bf4babd706351d21f1f6177ee4c3f5d16928d059b"},
   107  					{"0x602985c2bf7472638e59af721dc3e635d08ede15ad23084d54441a493d515ab9d727832a06110b8a5e4cdf978980d1",
   108  						"0x159cb19fac8df89c704efce7423d8965e1477606471d21f77988cd744d0ea0938a85eb4a21d41a34c97d64a409f7314"},
   109  					{"0x12f6020b2f6dc691f96e6a7c5e42a221a861c1b27223e30adbb75022ff42f318e8d96e0a964dfcb9dd0d20fd3a7c247",
   110  						"0x1766ffa6c449787005d03e90251c271190a3c8e6db8383ce2925b91c87ae29c989d503705ed7566fe5c7bfefb6902c6"},
   111  					{"0x471dda72677bf4df7027fff15bb88083362b56b41dbbeb3e3f9afed6c7fd9b8e03a7b66f7dde784cdb94ef12714ed1",
   112  						"0xb95429ba2726547f58f812d8516a9c7545fb43d2080d1b154e4e8aaa689a378141fd28ad946cf12fef100e180c9762"},
   113  					{"0x1ac99df3bf98db5235d2892b0f00a86db204cc8f367535d37ff878fd945bcd6f4991d08e3d7598788e2f860c950d110",
   114  						"0x0"},
   115  				},
   116  				Den: [][]string{
   117  					{"0x146e50faa64a7651c3b0b61836501a66805927dcb051b32662d0d261c3b5458776918917726e7ab20050fb3f1e9d32c",
   118  						"0xb1ea777f7008d8bcafa4799bac2e33475d6b287b6c831af5c06bb778507412d8aa8d347a14ea074b7983518d668616"},
   119  					{"0x79f0dba8c34b89c8d1fd2363421e1f97f7f12579ab42f520b86c9e7b44e822fadf62f6e98bfebed3065ef7e6d873e2",
   120  						"0x40dd9ff7e21f5f6802ef1e47c240880f84fbe0232f659145f22f9c842736890572e9a0018ff427005b45140ad2597d"},
   121  					{"0xde82c1e45e55039d5d8ae4684e278f230e94285b4bc97eae01f84acf258e9be8888a96dd0fdccde825922ec5517ec5",
   122  						"0x101b161db02dadd38c1b219d253f01728d2b3ba65e3dc05ebf102ff9fab2f2ef1cc95047570148228b4915820b0301d"},
   123  					{"0x19c6b7b7a90b244a9cc8e9cf77c1fc40ffeae17efe57efaad45c6b85105effe955b8aec25cd5a33b5fe1b403099cc87",
   124  						"0x1658235a28d3dcd62a783eb6e135a65f19ee1ded96bf717f26fb9e81763b6d1d0d32ef686998776504a5c6426ba2ddc"},
   125  					{"0x1374e714d24649d3de48ea7e809ed20ba8de79a7a95b59e26babe22856e57c5f9e6667da8107e27b1215afe2846471",
   126  						"0x9fa434f0a714ff9b2bb5ea51856efce45659377666fe4377774d04ca63a1ae957c5cc11376defad113c94ae6ce4652"},
   127  					{"0x11796b770f7504fb0a25336ae91aca083bb600d5523a27885e44f3bedff57966411346d44cce4bbaf50770a210445b7",
   128  						"0xa5dc732bb3f95325df484711467e89dc69a7986d2439a692fb9667c22512d87f968d452c1a7a4af94629d6fbfab126"},
   129  					{"0x36fc8fd543e00229e3e56ca9655db01cb161ad493c35d5225acea1924f2673890b0981feb9170a2b73e1ed5852276a",
   130  						"0x11e47853a548367d9473b4251c2641a1a05ded1721fb74dfd4455bb41894cd35ffa77ac1a1dda4171e8e3c598cc0cf"},
   131  					{"0xec3aecb4916b2621d73c22adf37fd2bd067cfcd09f38cfa7060c1dc08573f6e6da62ae459d00c719b153b23eb30380",
   132  						"0x33b7e5c5174d637291e17246bd01864eaf2b12d27ab74b84e029ed82c9cf3551faa44b79bdbb079a9f57f598e8c35"},
   133  					{"0x14d8b5c3fe739ff9bca51db2433814bd39a0ba8f082801125801599b81682fe51896aeed82936cfc3d7850d2f9622a3",
   134  						"0x7adf53096d8b637caa65a6703d654842a9b7d4d82a1ebd6ae4eb4cf7df07912638d359dbfe6f8443fcae492cb150c5"},
   135  					{"0x16e8eda7dfd1927fe1dc22dacaa78237dfa0714315f535e804649326acfe5c67a86dcbee4d78a5d662ff122b8580245",
   136  						"0x40de374242af4c470b0952cc13dae780d77d43729e9598ba3173ac586624ebe305c8c9e6e5e7245f98a970af1ee60d"},
   137  					{"0x16c94723b3eacaa13fef87169f4eca0959eecf2184d6a7468da9d8f32acb6a36c5254bf31d733f5b1c053dd88e54282",
   138  						"0x19c508401f6e0cdcf9e2b694c12550eba4247c85c52b8aba5991f9aeecbefee61355271663b842b0b23c0de66bcb8f1"},
   139  					{"0xf3ffd87f27eee739719fa368e3d9bebdb8f06a192b5ae980b629ad78421034b2f919d658fbcd1490fc7692e1e916ce",
   140  						"0x1468f37ed6477c421170d67235b0370aa3388db7e4c0cb3dbcf1fef55b2c7cd6989451199b411d7aaf8a5b24436f6e3"},
   141  					{"0x1035e4ec93dc6bc358f961e7dc4c82087605cbe2bfdbe713fa5e7b21d75c1ad45088bdbc6daaa2e12d1f0bcfb4b84f7",
   142  						"0x11e842bd544d0bbee76808f0a1ba264be31aedda57ceb64330b587d5a89d03598cdb8d2b528fe56a02dbfd48e8aaa83"},
   143  					{"0xe57bf7b799080766c07fa8b997f65da74043a005d785b60215c0875d8d80a2a55de8c81dc081ee75cafdcb6d9f5bab",
   144  						"0x4f2c024aca0ee3f8be88ed1450ac2448d3bd8b540d7cb9b5d93d68eedc20119213d260c02c7dbaa180aa008407b0dc"},
   145  					{"0xe0b435cad88cfd17508b5b3da274b76521f715b9129c3141f70a3c7dd22e14c3fe58a5db7c168f47c673d91a05c02f",
   146  						"0x16ba8b632d08a5abe396f990cfc790f6d29725220c89e7dacb3be59699757c6245bc0793bfeb5b2f917508cdd949a79"},
   147  					{"0x17c5e37674a25c3385908a02be0a23c1623eb710deb01632301277cb968ae2bccd3e5b38e144e424a9da459c4b8600a",
   148  						"0x503556d7e47b59d5888f787cb7cec46d917d02f8118e01a63ffc3b01398260d7c722dc26c7cd03d7c05e1a996e5471"},
   149  					{"0x890e4e58ded34996cf252dc184d7aec1c1866ad2da0b50ffc208a1ef31dd9e277b3f5e2fd1f3cf9422b81c526bbd0d",
   150  						"0x108938787e3377815ba98065f7c57b955fb7bc2247a21fd516fcad09652e92819c4bd34cf9be483e261639e540ce577"},
   151  					{"0x665b1acc1e271d15bf9416f014ae1ddc76838a60230be0cd17cc7505d6b5f7cb01037545fd2c3b9997b0745ad8ad9c",
   152  						"0x1ae0fc9e185ac85323228f01780e30ba86767c59cc90d2d05ddbba8d6cf35bbd737b7fcd09b3850af513ebb6fc3ced9"},
   153  					{"0x16db2dd779c2cc1699abf727df65339443007994b70c43a8d9767e265dfe45809093cc631ba5b79f1280236ac93fddf",
   154  						"0x43671e62ee377b90bbd80c91a3dc1eb53ed37ea8ae6ccc0154e2f1cf498198acc92b2ce3c07e292b2b5f038c6c04c9"},
   155  					{"0x93b2b87c160c52f6b056e4c085930add9aeb706709ee013eb54ca60bc820b0da42fbca8e9c9a579585bdb8af77acbe",
   156  						"0xcb5381cf50932ff1dd7fed460732ae9311b24ab543d98304b80963cf706598ef147c2b047d6c2e49357f5704e568ba"},
   157  					{"0x731b19b58014b17a0be1915dfee088ceb8ca7964deed74d985adfbe0e9aa99cac1453ae4210abf949afc9c7425f2b6",
   158  						"0x3f906b21602c1254dc293fbddc3974f24bef13d0291760083c7a125c8ad5c49ed9ba755743e9344387d1e712d7ede2"},
   159  					{"0xbee29453de653858b3b37cd3b85e7941177c94de27ab781cb8ea619a1b9668a0b0ddd01318b6699bc582051c23dd8a",
   160  						"0x1793e129728346d60828550ad395de628b4f4ab2952bd0e95003c382bebd49daa486d981fb51dee163ded1fb204d09f"},
   161  				},
   162  			},
   163  			YMap: RationalPolynomial{
   164  				Num: [][]string{
   165  					{"0x19474819a519191689e0816c7f84b2a58a6a5aaf5adfd7fb0204d8623f67c19e9a64d522ce4c963e32de8edfd367284",
   166  						"0x100e238102de877617418a44564d9379372b6f69c721b205c60af2e298bfa546a7c7a39883e433f947601b24266a306"},
   167  					{"0xb58b352e8f9bc6162e40b4ab27f066cb71ed844e9b5e376cdef8e8be14e38d2f13392f19da19ca1faa758bbb083dc6",
   168  						"0x3293cacae9e6251abad8ac4d8263754f1301062d54ff721d183d201f9133db07341cd48c721d8b9ec40e41d4bd0db0"},
   169  					{"0xdfec4d8ecb1cb0adbe13f68ccb2e070bcbf5ee3ee8328cb6613a63a543c252ef4ecb525fbf65ca12f33b425da04d5",
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   232  						"0x0"},
   233  				},
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   291  					{"0x6dabe74a1d15321e50aabfd662991b784c84a9b72e3340eee8efe520e68624376814038f2d1d683df0cc4f81c37a3",
   292  						"0x130be04e20fed0aabac1be1a13614e262414e7492e8701816e89b9982a435e2cf80b11474358c9bf758393f8fe05022"},
   293  					{"0x83889427d535bd6411a28c2a0ac1d40396ee0e686f0052f0bf59abb62bd3004f1ff3a76bf93b70926638b5c05f0a3c",
   294  						"0x131b916656d906aeda904a98d7664ed693a9a793a051a824c4ed8c815835eed2bcf1d686414c859af676f850e3dfd71"},
   295  					{"0x160c9ea53e9e85745773c4faccea8a4bc12d558b01068c2f3d88ca4d43b6f5e338a0ab7230fb044757ec2666f769dbb",
   296  						"0xb40e44b0581a642829ebdc74a3579c83018737cb432db5f3d692411082f2139753f6122e53566737d4ef53ac06ad1"},
   297  					{"0x186657fc77b2f47a24d4ce9ff9978c8b856ebb1d23e75468ac95d73168cdd6f7ae9ed767ad52bc9a3ea835a37c34aa3",
   298  						"0xa216aa737f6a614825bc46fbbcd767235927731a2c14c71ac6e2a38da8479785028a30559d92f544c2cf5d24b542fd"},
   299  					{"0x11e53de7dcd97d4850d8d3b3d948db5e1a33adf4d3b81342b155f926729619cf1094cb81ca5119e69a84307aa35cc4f",
   300  						"0x15ebff8d6d9c62eada64518cd85683baffe02073d8191ce5006a93c64dd1aec73e6f5c2178face4ded883af8b0738ee"},
   301  				},
   302  			},
   303  		},
   304  	},
   305  }
   306  
   307  var tBLS12_77 = TwistedEdwardsCurve{
   308  	Name:     BLS12_377.Name,
   309  	Package:  "twistededwards",
   310  	EnumID:   BLS12_377.EnumID,
   311  	A:        "-1",
   312  	D:        "3021",
   313  	Cofactor: "4",
   314  	Order:    "2111115437357092606062206234695386632838870926408408195193685246394721360383",
   315  	BaseX:    "717051916204163000937139483451426116831771857428389560441264442629694842243",
   316  	BaseY:    "882565546457454111605105352482086902132191855952243170543452705048019814192",
   317  }
   318  
   319  func init() {
   320  	addCurve(&BLS12_377)
   321  	addTwistedEdwardCurve(&tBLS12_77)
   322  }