Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.36
• j-invariant:
  1
• Trace of Frobenius:
  10457288737315625927447685387048320737638796957687575791173829
• Discriminant:
  1
• Anomalous:
  false
• Supersingular:
  false

SAGE

F.<x> = GF(2)[]
K = GF(2^409, name="x", modulus= x^409 +  x^87 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf * 0x4)
G = E(K.fetch_int(0x060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746), K.fetch_int(0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b))

JSON

{
  "name": "K-409",
  "desc": "Koblitz curve.",
  "oid": "1.3.132.0.36",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 409,
    "degree": 409,
    "poly": [
      {
        "coeff": "0x01",
        "power": 409
      },
      {
        "coeff": "0x01",
        "power": 87
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746"
    },
    "y": {
      "raw": "0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b"
    }
  },
  "order": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf",
  "cofactor": "0x4",
  "aliases": [
    "secg/sect409k1",
    "x963/ansit409k1"
  ],
  "characteristics": {
    "j_invariant": "1",
    "anomalous": false,
    "discriminant": "1",
    "supersingular": false,
    "trace_of_frobenius": "10457288737315625927447685387048320737638796957687575791173829"
  }
}