{
  "name": "Barreto-Lynn-Scott",
  "desc": "BLS curves. A family of pairing friendly curves, with embedding degree = 12 or 24.",
  "curves": [
    {
      "name": "BLS12-377",
      "category": "bls",
      "desc": "Curve from Zexe paper: https://eprint.iacr.org/2018/962, params taken from: https://eips.ethereum.org/EIPS/eip-2539 where they are explicitly listed.",
      "sources": [
        {
          "name": "Zexe: Enabling Decentralized Private Computation",
          "url": "https://eprint.iacr.org/2018/962"
        },
        {
          "name": "EIP-2539",
          "url": "https://eips.ethereum.org/EIPS/eip-2539"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x01ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001",
        "bits": 377
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x01"
        }
      },
      "generator": {
        "x": {
          "raw": "0x008848defe740a67c8fc6225bf87ff5485951e2caa9d41bb188282c8bd37cb5cd5481512ffcd394eeab9b16eb21be9ef"
        },
        "y": {
          "raw": "0x01914a69c5102eff1f674f5d30afeec4bd7fb348ca3e52d96d182ad44fb82305c2fe3d3634a9591afd82de55559c8ea6"
        }
      },
      "order": "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001",
      "cofactor": "0x170b5d44300000000000000000000000",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "587269870971281361444171168277668240640243801025419411456",
        "discriminant": "258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321457745",
        "j_invariant": "0",
        "embedding_degree": "9586122913090633728",
        "trace_of_frobenius": "9586122913090633730"
      }
    },
    {
      "name": "BLS12-381",
      "category": "bls",
      "desc": "Curve from https://electriccoin.co/blog/new-snark-curve/. As used in ZCash Sapling.",
      "sources": [
        {
          "name": "New zk-SNARK Curve",
          "url": "https://electriccoin.co/blog/new-snark-curve/"
        },
        {
          "name": "ZCash Protocol Specification",
          "url": "https://zips.z.cash/protocol/protocol.pdf"
        },
        {
          "name": "EIP-2537",
          "url": "https://eips.ethereum.org/EIPS/eip-2537"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab",
        "bits": 381
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x04"
        }
      },
      "generator": {
        "x": {
          "raw": "0x17F1D3A73197D7942695638C4FA9AC0FC3688C4F9774B905A14E3A3F171BAC586C55E83FF97A1AEFFB3AF00ADB22C6BB"
        },
        "y": {
          "raw": "0x08B3F481E3AAA0F1A09E30ED741D8AE4FCF5E095D5D00AF600DB18CB2C04B3EDD03CC744A2888AE40CAA232946C5E7E1"
        }
      },
      "order": "0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001",
      "cofactor": "0x396C8C005555E1568C00AAAB0000AAAB",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "2310096550715768212670172227226928237551693238409523516757",
        "discriminant": "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272552875",
        "j_invariant": "0",
        "embedding_degree": "60529504891766571012",
        "trace_of_frobenius": "-15132376222941642751"
      }
    },
    {
      "name": "BLS12-446",
      "category": "bls",
      "desc": "Curve from https://github.com/relic-toolkit/relic.",
      "sources": [
        {
          "name": "RELIC: Efficient LIbrary for Cryptography",
          "url": "https://github.com/relic-toolkit/relic"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x3cdee0fb28c5e535200fc34965aad6400095a4b78a02fe320f75a64bbac71602824e6dc3e23acdee56ee4528c573b5cc311c0026aab0aaab",
        "bits": 446
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x01"
        }
      },
      "generator": {
        "x": {
          "raw": "0x297792B2D03DE39D64FACA6D49FCF7A8850144CA24FC5D815C082A3AA87D1A16929E56228C136123BA51421AE89CACD5B4789A38CE39035A"
        },
        "y": {
          "raw": "0xDC40DDCBAB2823A7870B5C688AA04FEE40369D913E4F2F0947A152FE1C27A79B7F787E9C35B869C3846FAC4F12A70D0FE22D2E244268CC"
        }
      },
      "order": "0x511b70539f27995b34995830fa4d04c98ccc4c050bc7bb9b0e8d8ca34610428001400040001",
      "cofactor": "0xC02082602B0055D560AB0AD5AAAAC0002AAAC"
    },
    {
      "name": "BLS12-455",
      "category": "bls",
      "desc": "Curve from https://github.com/relic-toolkit/relic.",
      "sources": [
        {
          "name": "RELIC: Efficient LIbrary for Cryptography",
          "url": "https://github.com/relic-toolkit/relic"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x55555955557955572aa00e0f95b49203003f665e3a5b1d56234bd93954fcb314b8b3db9994ace86d1ba6c589556b2aa956aaa00001800002ab",
        "bits": 455
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x0a"
        }
      },
      "generator": {
        "x": {
          "raw": "0x03018DF4C2336D178E6EA61540353ABA01923E3890B3295848906DFC90E0C43008E4751FFC913DC1FF3DF33D11DB57BADA7A9297195ACFB2FA"
        },
        "y": {
          "raw": "0x19A8A9C4C3AC2FFB4C6B380D17B8282E029615052EAA6416C16C8F36F251D87C272657F0702CC58C4E072628D7BAD3C0E9B3A8AEBFC6B2357C"
        }
      },
      "order": "0x10000080000380002E0000F10004F00025E000750001D1000A00000400001C00007FFFFC00001",
      "cofactor": "0x555556AAAAB15555B54AAB6A9557FFAABFFAAB",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "287572867293678436974519977531226436303080379672880577582937484382891",
        "discriminant": "62023615502630691959947542088993379461260029989578145286594463370037455903184790399094337933920614809072869582259708675651604292655077867",
        "j_invariant": "0",
        "embedding_degree": "100743830310820967527764",
        "trace_of_frobenius": "75557872733115725645825"
      }
    },
    {
      "name": "BLS12-638",
      "category": "bls",
      "desc": "Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.",
      "sources": [
        {
          "name": "RELIC: Efficient LIbrary for Cryptography",
          "url": "https://github.com/relic-toolkit/relic"
        },
        {
          "name": "Implementing Pairings at the 192-bit Security Level",
          "url": "https://eprint.iacr.org/2012/232"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000b",
        "bits": 638
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x04"
        }
      },
      "generator": {
        "x": {
          "raw": "0x160F63A3A3B297F113075ED79466138E85B025F7FE724B78E32D7AFC4D734BDD54F871092B8D1966D491C0F45A48A8BBA5586095DFFCC1410B7E26ED16BAF98C1117959134C24A17A7BE31E1AFBF844F"
        },
        "y": {
          "raw": "0x2D340B33877480A9785E86ED2EDCAFC170B82568CB21B708B79FC6DA3748461FCD80697E486695F3CAE76FCB1781E784F6812F57BE05DFC850426650DED8B40A464B00A35718228EC8E02B52B59D876E"
        }
      },
      "order": "0x50F94035FF4000FFFFFFFFFFF9406BFDC0040000000000000035FB801DFFBFFFFFFFFFFFFFFF401BFF80000000000000000000FFC01",
      "cofactor": "0xBFF8001555555555555555554D957EAAAAAAAAAAAAAAAAAAAABEB",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "1201199398395787546723127300641679086142518436131015165481254517460567318887250290819436851298997",
        "discriminant": "1082159996029801447407061915918058655017421337462511263853382495313523741057008334847967336392717312405560092419564537672318099867365585979660877534008398116971703340756992868556828633685746955",
        "j_invariant": "0",
        "embedding_degree": "486738216406382958005937258889092",
        "trace_of_frobenius": "-121684554101595739501484314722271"
      }
    },
    {
      "name": "BLS24-477",
      "category": "bls",
      "desc": "Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.",
      "sources": [
        {
          "name": "RELIC: Efficient LIbrary for Cryptography",
          "url": "https://github.com/relic-toolkit/relic"
        },
        {
          "name": "Implementing Pairings at the 192-bit Security Level",
          "url": "https://eprint.iacr.org/2012/232"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b",
        "bits": 477
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x04"
        }
      },
      "generator": {
        "x": {
          "raw": "0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD"
        },
        "y": {
          "raw": "0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E"
        }
      },
      "order": "0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001",
      "cofactor": "0x41550AAAC04B3FD5000015AB",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "604128092931004996153900356638872198640435149234420528912987303159267285",
        "discriminant": "273728064501339756603462468369185104987958288074891940133644204431064409085893803646700523799946827238917453720697332026264620142876572570876459",
        "j_invariant": "0",
        "embedding_degree": "1970307657106440",
        "trace_of_frobenius": "-246288457138303"
      }
    },
    {
      "name": "Bandersnatch",
      "category": "bls",
      "desc": "Curve from https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957",
      "sources": [
        {
          "name": "Introducing Bandersnatch, a fast elliptic curve built over the BLS12-381 scalar field",
          "url": "https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001",
        "bits": 255
      },
      "form": "TwistedEdwards",
      "params": {
        "a": {
          "raw": "-0x05"
        },
        "d": {
          "raw": "0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7"
        }
      },
      "order": "0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1",
      "cofactor": "0x04",
      "characteristics": {
        "discriminant": "-8",
        "j_invariant": "8000"
      }
    },
    {
      "name": "BLS48-581-G1",
      "category": "bls",
      "desc": "Curve (G1) from https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/ in section 4.3 and https://doi.org/10.1007/978-3-319-61204-1_4",
      "sources": [
        {
          "name": "Pairing-Friendly Curves",
          "url": "https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/"
        },
        {
          "name": "Secure and Efficient Pairing at 256-Bit Security Level",
          "url": "https://doi.org/10.1007/978-3-319-61204-1_4"
        }
      ],
      "field": {
        "type": "Prime",
        "p": "0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b",
        "bits": 581
      },
      "form": "Weierstrass",
      "params": {
        "a": {
          "raw": "0x00"
        },
        "b": {
          "raw": "0x01"
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      },
      "generator": {
        "x": {
          "raw": "0x02af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640"
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        "y": {
          "raw": "0x0cefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70"
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      },
      "order": "0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01",
      "cofactor": "0x85555841aaaec4ac",
      "characteristics": {
        "cm_disc": "-3",
        "conductor": "2470234952045228861226479692223628411074049366373861109485273675792210673668036995939286",
        "discriminant": "4576545538729420598762745822889397370509838601207708465545582186285824315458656151272834027217178198654229063318759931344008864619718319130560845441720114764111976549023321979",
        "j_invariant": "0",
        "embedding_degree": "42949680144",
        "trace_of_frobenius": "-5368710016"
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    },
    {
      "name": "BLS48-581-G2",
      "category": "bls",
      "desc": "Curve (G2) from https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/ in section 4.3 and https://doi.org/10.1007/978-3-319-61204-1_4",
      "sources": [
        {
          "name": "Pairing-Friendly Curves",
          "url": "https://datatracker.ietf.org/doc/draft-irtf-cfrg-pairing-friendly-curves/"
        },
        {
          "name": "Secure and Efficient Pairing at 256-Bit Security Level",
          "url": "https://doi.org/10.1007/978-3-319-61204-1_4"
        }
      ],
      "field": {
        "type": "Tower",
        "degree": 2,
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          {
            "power": 2,
            "coeff": [
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                "power": 0,
                "coeff": [
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          {
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        ],
        "base": {
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            {
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                {
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          ],
          "base": {
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                "coeff": "0x01"
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              {
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            ],
            "base": {
              "type": "Prime",
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              "bits": 581
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      },
      "form": "Weierstrass",
      "params": {
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        "b": {
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      "generator": {
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