Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  8366863340207706741299716820480866394308615
• Discriminant:
  70004402153711663438486789763681164697717379781714415888917198592851957854802452412755
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  8366863340207706741294993301075392630620163

SAGE

p = 0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000013
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000000000000000000000000000000002)
E = EllipticCurve(K, (a, b))
G = E(0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000012, 0x000000000000000000000000000000000000000000000000000000000000000000000001)
E.set_order(0x240900D8991B25B0E2CB51DDA534A205391831FC099FC0FC0007F081080010800000000D * 0x01)

PARI/GP

p = 0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000013
a = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000002, p)
E = ellinit([a, b])
E[16][1] = 0x240900D8991B25B0E2CB51DDA534A205391831FC099FC0FC0007F081080010800000000D * 0x01
G = [Mod(0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000012, p), Mod(0x000000000000000000000000000000000000000000000000000000000000000000000001, p)]

JSON

{
  "name": "bn286",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000013",
    "bits": 286
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000002"
    }
  },
  "generator": {
    "x": {
      "raw": "0x240900D8991B25B0E2CB51DDA534A205391892080A008108000853813800138000000012"
    },
    "y": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "order": "0x240900D8991B25B0E2CB51DDA534A205391831FC099FC0FC0007F081080010800000000D",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "70004402153711663438486789763681164697717379781714415888917198592851957854802452412755",
    "j_invariant": "0",
    "trace_of_frobenius": "8366863340207706741299716820480866394308615",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "8366863340207706741294993301075392630620163"
  }
}