Curve used in: https://eprint.iacr.org/2010/354.pdf

Parameters

Sources

• High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  126611883464401272108868536818127077377
• Discriminant:
  16030569034403128277756688287498649515636838101184337499778392980116222236113
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  126611883464401272127243293666542878721

SAGE

p = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001
K = GF(p)
a = K(0x00)
b = K(0x05)
E = EllipticCurve(K, (a, b))
G = E(0x01, 0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0)
E.set_order(0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001 * 0x01)

PARI/GP

p = 0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001
a = Mod(0x00, p)
b = Mod(0x05, p)
E = ellinit([a, b])
E[16][1] = 0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001 * 0x01
G = [Mod(0x01, p), Mod(0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0, p)]

JSON

{
  "name": "Fp254BNa",
  "desc": "Curve used in: https://eprint.iacr.org/2010/354.pdf",
  "sources": [
    {
      "name": "High-Speed Software Implementation of the Optimal Ate Pairing over Barreto–Naehrig Curves",
      "url": "https://eprint.iacr.org/2010/354"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x2370fb049d410fbe4e761a9886e502417d023f40180000017e80600000000001",
    "bits": 254
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x05"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01"
    },
    "y": {
      "raw": "0xd45589b158faaf6ab0e4ad38d998e9982e7ff63964ee1460342a592677cccb0"
    }
  },
  "order": "0x2370fb049d410fbe4e761a9886e502411dc1af70120000017e80600000000001",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "16030569034403128277756688287498649515636838101184337499778392980116222236113",
    "j_invariant": "0",
    "trace_of_frobenius": "126611883464401272108868536818127077377",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "126611883464401272127243293666542878721"
  }
}