Parameters

Sources

• ANSI X9.63

Characteristics

• OID:
  1.3.132.0.27
• j-invariant:
  4307676474001897771242333711874131057278497100044075715856582737706846
• Trace of Frobenius:
  -206777407530349254000433718821372333
• Discriminant:
  2760497980029204187078845502377898520307707256259003964398570147123373

SAGE

F.<x> = GF(2)[]
K = GF(2^233, name="x", modulus=u^233 +  u^74 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x000000000000000000000000000000000000000000000000000000000001), 0, 0, K.from_integer(0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad)))
E.set_order(0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 * 0x2)
G = E(K.from_integer(0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b), K.from_integer(0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052))

JSON

{
  "name": "ansit233r1",
  "desc": "",
  "oid": "1.3.132.0.27",
  "sources": [
    {
      "name": "ANSI X9.63",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9632011r2017"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "poly": [
      {
        "power": 233,
        "coeff": "0x01"
      },
      {
        "power": 74,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "bits": 233,
    "degree": 233,
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad"
    }
  },
  "generator": {
    "x": {
      "raw": "0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b"
    },
    "y": {
      "raw": "0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052"
    }
  },
  "order": "0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7",
  "cofactor": "0x2",
  "aliases": [
    "wtls/wap-wsg-idm-ecid-wtls11",
    "nist/B-233",
    "secg/sect233r1"
  ],
  "characteristics": {
    "discriminant": "2760497980029204187078845502377898520307707256259003964398570147123373",
    "j_invariant": "4307676474001897771242333711874131057278497100044075715856582737706846",
    "trace_of_frobenius": "-206777407530349254000433718821372333"
  }
}