github.com/consensys/gnark-crypto@v0.14.0/internal/generator/config/bls12-381.go (about)

     1  package config
     2  
     3  var BLS12_381 = Curve{
     4  	Name:         "bls12-381",
     5  	CurvePackage: "bls12381",
     6  	EnumID:       "BLS12_381",
     7  	FrModulus:    "52435875175126190479447740508185965837690552500527637822603658699938581184513",
     8  	FpModulus:    "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787",
     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:     -1,
    21  		PointName:        "g2",
    22  		GLV:              true,
    23  		CofactorCleaning: true,
    24  		CRange:           defaultCRange(),
    25  		Projective:       true,
    26  	},
    27  	// 11-isogeny
    28  	HashE1: &HashSuiteSswu{
    29  		A: []string{"0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d"},
    30  		B: []string{"0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0"},
    31  		Z: []int{11},
    32  		Isogeny: &Isogeny{
    33  			XMap: RationalPolynomial{
    34  				Num: [][]string{
    35  					{"0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7"},
    36  					{"0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bb"},
    37  					{"0xd54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0"},
    38  					{"0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861"},
    39  					{"0xe99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9"},
    40  					{"0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983"},
    41  					{"0xd6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84"},
    42  					{"0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88e"},
    43  					{"0x80d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317"},
    44  					{"0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9e"},
    45  					{"0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7b"},
    46  					{"0x6e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229"},
    47  				},
    48  				Den: [][]string{
    49  					{"0x8ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1c"},
    50  					{"0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bff"},
    51  					{"0xb2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19"},
    52  					{"0x3425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8"},
    53  					{"0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21e"},
    54  					{"0xe7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5"},
    55  					{"0x772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3a"},
    56  					{"0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5e"},
    57  					{"0xa10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641"},
    58  					{"0x95fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0a"},
    59  				},
    60  			},
    61  			YMap: RationalPolynomial{
    62  				Num: [][]string{
    63  					{"0x90d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33"},
    64  					{"0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696"},
    65  					{"0xcc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6"},
    66  					{"0x1f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cb"},
    67  					{"0x8cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedb"},
    68  					{"0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0"},
    69  					{"0x4ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2"},
    70  					{"0x987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29"},
    71  					{"0x9fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587"},
    72  					{"0xe1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30"},
    73  					{"0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132"},
    74  					{"0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8e"},
    75  					{"0xb182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8"},
    76  					{"0x245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133"},
    77  					{"0x5c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224b"},
    78  					{"0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604"},
    79  				},
    80  				Den: [][]string{
    81  					{"0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1"},
    82  					{"0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03d"},
    83  					{"0x58df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2"},
    84  					{"0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416"},
    85  					{"0xbe0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001d"},
    86  					{"0x8d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7ac"},
    87  					{"0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775c"},
    88  					{"0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9"},
    89  					{"0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4a"},
    90  					{"0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55"},
    91  					{"0x4d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8"},
    92  					{"0xaccbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092"},
    93  					{"0xad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345cc"},
    94  					{"0x2660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7"},
    95  					{"0xe0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8f"},
    96  				},
    97  			},
    98  		},
    99  	},
   100  
   101  	// 3-isogeny
   102  	HashE2: &HashSuiteSswu{
   103  		A: []string{"0", "240"},     // A = 240 * I
   104  		B: []string{"1012", "1012"}, // B = 1012 * (I+1)
   105  		Z: []int{-2, -1},            // Z = -(2+I)
   106  		Isogeny: &Isogeny{
   107  			XMap: RationalPolynomial{
   108  				Num: [][]string{
   109  					{"0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6", "0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6"},
   110  					{"0x0", "0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71a"},
   111  					{"0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71e", "0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38d"},
   112  					{"0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1", "0x0"},
   113  				},
   114  				Den: [][]string{
   115  					{"0x0", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63"},
   116  					{"0xc", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9f"},
   117  				},
   118  			},
   119  			YMap: RationalPolynomial{
   120  				Num: [][]string{
   121  					{"0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706", "0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706"},
   122  					{"0x0", "0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97be"},
   123  					{"0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71c", "0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38f"},
   124  					{"0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10", "0x0"},
   125  				},
   126  				Den: [][]string{
   127  					{"0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fb"},
   128  					{"0x0", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3"},
   129  					{"0x12", "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99"},
   130  				},
   131  			},
   132  		},
   133  	},
   134  }
   135  
   136  var tBLS12_381 = TwistedEdwardsCurve{
   137  	Name:     BLS12_381.Name,
   138  	Package:  "twistededwards",
   139  	EnumID:   BLS12_381.EnumID,
   140  	A:        "-1",
   141  	D:        "19257038036680949359750312669786877991949435402254120286184196891950884077233",
   142  	Cofactor: "8",
   143  	Order:    "6554484396890773809930967563523245729705921265872317281365359162392183254199",
   144  	BaseX:    "23426137002068529236790192115758361610982344002369094106619281483467893291614",
   145  	BaseY:    "39325435222430376843701388596190331198052476467368316772266670064146548432123",
   146  }
   147  
   148  var bandersnatch = TwistedEdwardsCurve{
   149  	Name:            BLS12_381.Name,
   150  	Package:         "bandersnatch",
   151  	EnumID:          BLS12_381.EnumID,
   152  	A:               "-5",
   153  	D:               "45022363124591815672509500913686876175488063829319466900776701791074614335719",
   154  	Cofactor:        "4",
   155  	Order:           "13108968793781547619861935127046491459309155893440570251786403306729687672801",
   156  	BaseX:           "18886178867200960497001835917649091219057080094937609519140440539760939937304",
   157  	BaseY:           "19188667384257783945677642223292697773471335439753913231509108946878080696678",
   158  	HasEndomorphism: true,
   159  	Endo0:           "37446463827641770816307242315180085052603635617490163568005256780843403514036",
   160  	Endo1:           "49199877423542878313146170939139662862850515542392585932876811575731455068989",
   161  	Lambda:          "8913659658109529928382530854484400854125314752504019737736543920008458395397",
   162  }
   163  
   164  func init() {
   165  	addCurve(&BLS12_381)
   166  	addTwistedEdwardCurve(&tBLS12_381)
   167  	addTwistedEdwardCurve(&bandersnatch)
   168  }