A Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.32
• j-invariant:
  0
• Trace of Frobenius:
  -9672873182660579502067895643393161
• Discriminant:
  26959946667150639794667015087019630673637144422540572481099315264317
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  4493324444525106632444502514503273391085054513853345758165826444713
• CM-discriminant:
  107839786668602559178668060348078532367421760350741791992292904493629
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
K = GF(p)
a = K(0x00000000000000000000000000000000000000000000000000000000)
b = K(0x00000000000000000000000000000000000000000000000000000005)
E = EllipticCurve(K, (a, b))
G = E(0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c, 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5)
E.set_order(0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 * 0x01)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
a = Mod(0x00000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x00000000000000000000000000000000000000000000000000000005, p)
E = ellinit([a, b])
E[16][1] = 0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 * 0x01
G = [Mod(0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c, p), Mod(0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5, p)]

JSON

{
  "name": "secp224k1",
  "desc": "A Koblitz curve.",
  "oid": "1.3.132.0.32",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0x00000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x00000000000000000000000000000000000000000000000000000005"
    }
  },
  "generator": {
    "x": {
      "raw": "0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c"
    },
    "y": {
      "raw": "0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5"
    }
  },
  "order": "0x10000000000000000000000000001dce8d2ec6184caf0a971769fb1f7",
  "cofactor": "0x01",
  "aliases": [
    "x963/ansip224k1"
  ],
  "characteristics": {
    "j_invariant": "0",
    "anomalous": false,
    "cm_disc": "107839786668602559178668060348078532367421760350741791992292904493629",
    "conductor": "1",
    "discriminant": "26959946667150639794667015087019630673637144422540572481099315264317",
    "embedding_degree": "4493324444525106632444502514503273391085054513853345758165826444713",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 2,
        "least": 2,
        "r": 3
      },
      {
        "full": 24,
        "least": 24,
        "r": 5
      },
      {
        "full": 3,
        "least": 3,
        "r": 7
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "-9672873182660579502067895643393161"
  }
}