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

Parameters

Sources

• Pairing-Friendly Curves
• Secure and Efficient Pairing at 256-Bit Security Level

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  -5368710016
• Discriminant:
  4576545538729420598762745822889397370509838601207708465545582186285824315458656151272834027217178198654229063318759931344008864619718319130560845441720114764111976549023321979
• Embedding degree:
  42949680144
• CM-discriminant:
  -3
• Conductor:
  2470234952045228861226479692223628411074049366373861109485273675792210673668036995939286

SAGE

p = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b
K = GF(p)
a = K(0x00)
b = K(0x01)
E = EllipticCurve(K, (a, b))
G = E(0x02af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640, 0x0cefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70)
E.set_order(0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01 * 0x85555841aaaec4ac)

PARI/GP

p = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b
a = Mod(0x00, p)
b = Mod(0x01, p)
E = ellinit([a, b])
E[16][1] = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01 * 0x85555841aaaec4ac
G = [Mod(0x02af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640, p), Mod(0x0cefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70, p)]

JSON

{
  "name": "BLS48-581-G1",
  "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"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b",
    "bits": 581
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x02af59b7ac340f2baf2b73df1e93f860de3f257e0e86868cf61abdbaedffb9f7544550546a9df6f9645847665d859236ebdbc57db368b11786cb74da5d3a1e6d8c3bce8732315af640"
    },
    "y": {
      "raw": "0x0cefda44f6531f91f86b3a2d1fb398a488a553c9efeb8a52e991279dd41b720ef7bb7beffb98aee53e80f678584c3ef22f487f77c2876d1b2e35f37aef7b926b576dbb5de3e2587a70"
    }
  },
  "order": "0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01",
  "cofactor": "0x85555841aaaec4ac",
  "characteristics": {
    "cm_disc": "-3",
    "conductor": "2470234952045228861226479692223628411074049366373861109485273675792210673668036995939286",
    "discriminant": "4576545538729420598762745822889397370509838601207708465545582186285824315458656151272834027217178198654229063318759931344008864619718319130560845441720114764111976549023321979",
    "j_invariant": "0",
    "embedding_degree": "42949680144",
    "trace_of_frobenius": "-5368710016"
  }
}