Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.16
• j-invariant:
  1
• Trace of Frobenius:
  7777244870872830999287791970962823977569917
• Discriminant:
  1
• Anomalous:
  false
• Supersingular:
  false
• CM-discriminant:
  62165404551223330269422781018352605012557011072423593807226997823852966163742694371715
• Conductor:
  1

SAGE

F.<x> = GF(2)[]
K = GF(2^283, name="x", modulus= x^283 +  x^12 +  x^7 +  x^5 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 * 0x4)
G = E(K.fetch_int(0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836), K.fetch_int(0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259))

JSON

{
  "name": "K-283",
  "desc": "Koblitz curve.",
  "oid": "1.3.132.0.16",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 283,
    "degree": 283,
    "poly": [
      {
        "coeff": "0x01",
        "power": 283
      },
      {
        "coeff": "0x01",
        "power": 12
      },
      {
        "coeff": "0x01",
        "power": 7
      },
      {
        "coeff": "0x01",
        "power": 5
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x00000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x00000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836"
    },
    "y": {
      "raw": "0x1ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259"
    }
  },
  "order": "0x1ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61",
  "cofactor": "0x4",
  "aliases": [
    "secg/sect283k1",
    "x963/ansit283k1"
  ],
  "characteristics": {
    "j_invariant": "1",
    "anomalous": false,
    "cm_disc": "62165404551223330269422781018352605012557011072423593807226997823852966163742694371715",
    "conductor": "1",
    "discriminant": "1",
    "supersingular": false,
    "trace_of_frobenius": "7777244870872830999287791970962823977569917"
  }
}