Parameters

Sources

• ANSI X9.63

Characteristics

• OID:
  1.3.132.0.3
• j-invariant:
  1
• Trace of Frobenius:
  -1879124296849029916489117776215138963
• Discriminant:
  1

SAGE

F.<x> = GF(2)[]
K = GF(2^239, name="x", modulus=u^239 +  u^158 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x000000000000000000000000000000000000000000000000000000000000), 0, 0, K.from_integer(0x000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5 * 0x4)
G = E(K.from_integer(0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc), K.from_integer(0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca))

JSON

{
  "name": "ansit239k1",
  "desc": "",
  "oid": "1.3.132.0.3",
  "sources": [
    {
      "name": "ANSI X9.63",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9632011r2017"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 239,
    "degree": 239,
    "poly": [
      {
        "power": 239,
        "coeff": "0x01"
      },
      {
        "power": 158,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc"
    },
    "y": {
      "raw": "0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca"
    }
  },
  "order": "0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5",
  "cofactor": "0x4",
  "aliases": [
    "secg/sect239k1"
  ],
  "characteristics": {
    "discriminant": "1",
    "j_invariant": "1",
    "trace_of_frobenius": "-1879124296849029916489117776215138963"
  }
}