Curve used in https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf

Parameters

Sources

• Faster Explicit Formulas for Computing Pairings over Ordinary Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  129607518034317099905336561907183648775
• Discriminant:
  16798108731015832284940804142231733909889187121439069848933715426072753862995
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  129607518034317099886745702645398241283

SAGE

p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
K = GF(p)
a = K(0x00)
b = K(0x02)
E = EllipticCurve(K, (a, b))
G = E(0x2523648240000001ba344d80000000086121000000000013a700000000000012, 0x01)
E.set_order(0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d * 0x01)

PARI/GP

p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
a = Mod(0x00, p)
b = Mod(0x02, p)
E = ellinit([a, b])
E[16][1] = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d * 0x01
G = [Mod(0x2523648240000001ba344d80000000086121000000000013a700000000000012, p), Mod(0x01, p)]

JSON

{
  "name": "Fp254BNb",
  "desc": "Curve used in https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf",
  "sources": [
    {
      "name": "Faster Explicit Formulas for Computing Pairings over Ordinary Curves",
      "url": "https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x2523648240000001ba344d80000000086121000000000013a700000000000013",
    "bits": 254
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x02"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2523648240000001ba344d80000000086121000000000013a700000000000012"
    },
    "y": {
      "raw": "0x01"
    }
  },
  "order": "0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d",
  "cofactor": "0x01",
  "aliases": [
    "bn/bn254"
  ],
  "characteristics": {
    "discriminant": "16798108731015832284940804142231733909889187121439069848933715426072753862995",
    "j_invariant": "0",
    "trace_of_frobenius": "129607518034317099905336561907183648775",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "129607518034317099886745702645398241283"
  }
}