Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.26
• j-invariant:
  1
• Trace of Frobenius:
  -137381546011108235394987299651366779
• Discriminant:
  1
• Anomalous:
  false
• Supersingular:
  false
• CM-discriminant:
  6134885641591612255497560766468467084110046420941258648476388160195683

SAGE

F.<x> = GF(2)[]
K = GF(2^233, name="x", modulus= x^233 +  x^74 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf * 0x4)
G = E(K.fetch_int(0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126), K.fetch_int(0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3))

JSON

{
  "name": "K-233",
  "desc": "Koblitz curve.",
  "oid": "1.3.132.0.26",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 233,
    "degree": 233,
    "poly": [
      {
        "coeff": "0x01",
        "power": 233
      },
      {
        "coeff": "0x01",
        "power": 74
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126"
    },
    "y": {
      "raw": "0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3"
    }
  },
  "order": "0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf",
  "cofactor": "0x4",
  "aliases": [
    "secg/sect233k1",
    "wtls/wap-wsg-idm-ecid-wtls10",
    "x963/ansit233k1"
  ],
  "characteristics": {
    "j_invariant": "1",
    "anomalous": false,
    "cm_disc": "6134885641591612255497560766468467084110046420941258648476388160195683",
    "discriminant": "1",
    "supersingular": false,
    "trace_of_frobenius": "-137381546011108235394987299651366779"
  }
}