Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.13
• Seed:
  9E076F4D696E676875615175E11E9FDD77F92041
• j-invariant:
  163209249997698657452423175699333947802164771662603222395942569544074736
• Trace of Frobenius:
  1688252296967058035833017058395749899
• Discriminant:
  735577866927481491361633396386400994201974151971503584221245012969397568

SAGE

F.<x> = GF(2)[]
K = GF(2^239, name="x", modulus=u^239 +  u^36 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x01238774666a67766d6676f778e676b66999176666e687666d8766c66a9f), 0, 0, K.from_integer(0x6a941977ba9f6a435199acfc51067ed587f519c5ecb541b8e44111de1d40)))
E.set_order(0x0cccccccccccccccccccccccccccccac4912d2d9df903ef9888b8a0e4cff * 0x0a)
G = E(K.from_integer(0x70f6e9d04d289c4e89913ce3530bfde903977d42b146d539bf1bde4e9c92), K.from_integer(0x2e5a0eaf6e5e1305b9004dce5c0ed7fe59a35608f33837c816d80b79f461))

JSON

{
  "name": "c2tnb239v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.13",
  "sources": [
    {
      "name": "ANSI X9.62",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 239,
    "degree": 239,
    "poly": [
      {
        "power": 239,
        "coeff": "0x01"
      },
      {
        "power": 36,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x01238774666a67766d6676f778e676b66999176666e687666d8766c66a9f"
    },
    "b": {
      "raw": "0x6a941977ba9f6a435199acfc51067ed587f519c5ecb541b8e44111de1d40"
    }
  },
  "generator": {
    "x": {
      "raw": "0x70f6e9d04d289c4e89913ce3530bfde903977d42b146d539bf1bde4e9c92"
    },
    "y": {
      "raw": "0x2e5a0eaf6e5e1305b9004dce5c0ed7fe59a35608f33837c816d80b79f461"
    }
  },
  "order": "0x0cccccccccccccccccccccccccccccac4912d2d9df903ef9888b8a0e4cff",
  "cofactor": "0x0a",
  "characteristics": {
    "seed": "9E076F4D696E676875615175E11E9FDD77F92041",
    "discriminant": "735577866927481491361633396386400994201974151971503584221245012969397568",
    "j_invariant": "163209249997698657452423175699333947802164771662603222395942569544074736",
    "trace_of_frobenius": "1688252296967058035833017058395749899"
  }
}