Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  29710571568175507457408237575
• Discriminant:
  882718062907666288196217719514349254081211436024346574435
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  29710571568175225982381195267

SAGE

p = 0x240001B0000948001E60004134005F10005DC0003A800013
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000001001)
E = EllipticCurve(K, (a, b))
G = E(0x240001B0000948001E60004134005F10005DC0003A800012, 0x000000000000000000000000000000000000000000000040)
E.set_order(0x240001B0000948001E600040D4005CD0005760003180000D * 0x01)

PARI/GP

p = 0x240001B0000948001E60004134005F10005DC0003A800013
a = Mod(0x000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000001001, p)
E = ellinit([a, b])
E[16][1] = 0x240001B0000948001E600040D4005CD0005760003180000D * 0x01
G = [Mod(0x240001B0000948001E60004134005F10005DC0003A800012, p), Mod(0x000000000000000000000000000000000000000000000040, p)]

JSON

{
  "name": "bn190",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x240001B0000948001E60004134005F10005DC0003A800013",
    "bits": 190
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000001001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x240001B0000948001E60004134005F10005DC0003A800012"
    },
    "y": {
      "raw": "0x000000000000000000000000000000000000000000000040"
    }
  },
  "order": "0x240001B0000948001E600040D4005CD0005760003180000D",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "882718062907666288196217719514349254081211436024346574435",
    "j_invariant": "0",
    "trace_of_frobenius": "29710571568175507457408237575",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "29710571568175225982381195267"
  }
}