Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.

Parameters

Sources

• RELIC: Efficient LIbrary for Cryptography
• Implementing Pairings at the 192-bit Security Level

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  -246288457138303
• Discriminant:
  273728064501339756603462468369185104987958288074891940133644204431064409085893803646700523799946827238917453720697332026264620142876572570876459
• Embedding degree:
  1970307657106440
• CM-discriminant:
  -3
• Conductor:
  604128092931004996153900356638872198640435149234420528912987303159267285

SAGE

p = 0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b
K = GF(p)
a = K(0x00)
b = K(0x04)
E = EllipticCurve(K, (a, b))
G = E(0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD, 0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E)
E.set_order(0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001 * 0x41550AAAC04B3FD5000015AB)

PARI/GP

p = 0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b
a = Mod(0x00, p)
b = Mod(0x04, p)
E = ellinit([a, b])
E[16][1] = 0x57F52EE445CC41781FCD53D13E45F6ACDFE4F9F2A3CD414E71238AFC9FCFC7D38CAEF64F4FF79F90013FFFFFF0000001 * 0x41550AAAC04B3FD5000015AB
G = [Mod(0x15DFD8E4893A408A34B600532B51CC86CAB3AF07103CFCF3EC7B9AF836904CFB60AB0FA8AC91EE6255E5EF6286FA0C24DF9D76EA50599C2E103E40AD, p), Mod(0x0A683957A59B1B488FA657E11B44815056BDE33C09D6AAD392D299F89C7841B91A683BF01B7E70547E48E0FBE1CA9E991983131470F886BA9B6FCE2E, p)]

JSON

{
  "name": "BLS24-477",
  "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"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x167278fac63bd5b007ebb8f693a2ab3dbd9f92cf437c399d928e94bfe9a04a009fda9e8cf9226901de62aea9dcea48bf1a0ebbf8860a5e7ad000152b",
    "bits": 477
  },
  "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"
  }
}