Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.1
• j-invariant:
  1
• Trace of Frobenius:
  -4845466632539410776804317
• Discriminant:
  1
• Anomalous:
  false
• Supersingular:
  false
• CM-discriminant:
  46768052394588893382517919492387689168400618179549
• Conductor:
  1

SAGE

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^7 +  x^6 +  x^3 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x000000000000000000000000000000000000000001)))
E.set_order(0x04000000000000000000020108a2e0cc0d99f8a5ef * 0x2)
G = E(K.fetch_int(0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8), K.fetch_int(0x0289070fb05d38ff58321f2e800536d538ccdaa3d9))

JSON

{
  "name": "K-163",
  "desc": "Koblitz curve.",
  "oid": "1.3.132.0.1",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 7
      },
      {
        "coeff": "0x01",
        "power": 6
      },
      {
        "coeff": "0x01",
        "power": 3
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8"
    },
    "y": {
      "raw": "0x0289070fb05d38ff58321f2e800536d538ccdaa3d9"
    }
  },
  "order": "0x04000000000000000000020108a2e0cc0d99f8a5ef",
  "cofactor": "0x2",
  "aliases": [
    "secg/sect163k1"
  ],
  "characteristics": {
    "j_invariant": "1",
    "anomalous": false,
    "cm_disc": "46768052394588893382517919492387689168400618179549",
    "conductor": "1",
    "discriminant": "1",
    "supersingular": false,
    "trace_of_frobenius": "-4845466632539410776804317"
  }
}