Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  454233058419889982668807
• Discriminant:
  206327671360737302491015800744139033450590902371
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  454233058418789397299203

SAGE

p = 0x24240D8241D5445106C8442084001384E0000013
K = GF(p)
a = K(0x0000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000011)
E = EllipticCurve(K, (a, b))
G = E(0x24240D8241D5445106C8442084001384E0000012, 0x0000000000000000000000000000000000000004)
E.set_order(0x24240D8241D5445106C7E3F07E0010842000000D * 0x01)

PARI/GP

p = 0x24240D8241D5445106C8442084001384E0000013
a = Mod(0x0000000000000000000000000000000000000000, p)
b = Mod(0x0000000000000000000000000000000000000011, p)
E = ellinit([a, b])
E[16][1] = 0x24240D8241D5445106C7E3F07E0010842000000D * 0x01
G = [Mod(0x24240D8241D5445106C8442084001384E0000012, p), Mod(0x0000000000000000000000000000000000000004, p)]

JSON

{
  "name": "bn158",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x24240D8241D5445106C8442084001384E0000013",
    "bits": 158
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000011"
    }
  },
  "generator": {
    "x": {
      "raw": "0x24240D8241D5445106C8442084001384E0000012"
    },
    "y": {
      "raw": "0x0000000000000000000000000000000000000004"
    }
  },
  "order": "0x24240D8241D5445106C7E3F07E0010842000000D",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "206327671360737302491015800744139033450590902371",
    "j_invariant": "0",
    "trace_of_frobenius": "454233058419889982668807",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "454233058418789397299203"
  }
}