Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  662567649291894123450065105820326672097321614256273183056335502227537927
• Discriminant:
  438995889888186407347652991425301965681188858026820794321677547168174289793337316790981018819616267513532082540968716717668009346359904036714835
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  662567649291894123450065105820326670768093618471357310296643630025146371

SAGE

p = 0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900013
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002)
E = EllipticCurve(K, (a, b))
G = E(0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900012, 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)
E.set_order(0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D2807F442328002888F9872944D7E0578112F7FD780062FFF07001F7FFDF0000D * 0x01)

PARI/GP

p = 0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900013
a = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002, p)
E = ellinit([a, b])
E[16][1] = 0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D2807F442328002888F9872944D7E0578112F7FD780062FFF07001F7FFDF0000D * 0x01
G = [Mod(0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900012, p), Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001, p)]

JSON

{
  "name": "bn478",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900013",
    "bits": 478
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002"
    }
  },
  "generator": {
    "x": {
      "raw": "0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D28085442328002888F96F2944D7DED781430FFD780065FFF010020FFFD900012"
    },
    "y": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "order": "0x23FFFFFFFFFFFFFEDFFFFFFFEE0001B3600000006BFFF5DB835FFF5D2807F442328002888F9872944D7E0578112F7FD780062FFF07001F7FFDF0000D",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "438995889888186407347652991425301965681188858026820794321677547168174289793337316790981018819616267513532082540968716717668009346359904036714835",
    "j_invariant": "0",
    "trace_of_frobenius": "662567649291894123450065105820326672097321614256273183056335502227537927",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "662567649291894123450065105820326670768093618471357310296643630025146371"
  }
}