Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  10109980000181489923001201093401906549415298505746886291297633566727
• Discriminant:
  102211695604069718983520304652693874995639508460729604902280098199792736381528662976886082950231100101353700265360419596271313310490295
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  10109980000181489923001201093401911741712157040574514822068840693771

SAGE

p = 0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000067
K = GF(p)
a = K(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101)
E = EllipticCurve(K, (a, b))
G = E(0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000066, 0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010)
E.set_order(0x2400000000000000002400000002D00000000D800000021C00000017A0000000870000000AD400000054C000000156000000126000000061 * 0x01)

PARI/GP

p = 0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000067
a = Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101, p)
E = ellinit([a, b])
E[16][1] = 0x2400000000000000002400000002D00000000D800000021C00000017A0000000870000000AD400000054C000000156000000126000000061 * 0x01
G = [Mod(0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000066, p), Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010, p)]

JSON

{
  "name": "bn446",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000067",
    "bits": 446
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2400000000000000002400000002D00000000D800000021C0000001800000000870000000B0400000057C00000015C000000132000000066"
    },
    "y": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010"
    }
  },
  "order": "0x2400000000000000002400000002D00000000D800000021C00000017A0000000870000000AD400000054C000000156000000126000000061",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "102211695604069718983520304652693874995639508460729604902280098199792736381528662976886082950231100101353700265360419596271313310490295",
    "j_invariant": "0",
    "trace_of_frobenius": "10109980000181489923001201093401906549415298505746886291297633566727",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "10109980000181489923001201093401911741712157040574514822068840693771"
  }
}