A Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.31
• j-invariant:
  0
• Trace of Frobenius:
  146402144145231529258894028971
• Discriminant:
  6277101735386680763835789423207666416102355444459739537159
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  3138550867693340381917894711530632135978561957600422756038
• CM-discriminant:
  25108406941546723055343157692684263520264190248580064135217
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffeffffee37
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000000003)
E = EllipticCurve(K, (a, b))
G = E(0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d, 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d)
E.set_order(0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffeffffee37
a = Mod(0x000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000000003, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d * 0x1
G = [Mod(0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d, p), Mod(0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d, p)]

JSON

{
  "name": "secp192k1",
  "desc": "A Koblitz curve.",
  "oid": "1.3.132.0.31",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffffffffffeffffee37",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000003"
    }
  },
  "generator": {
    "x": {
      "raw": "0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d"
    },
    "y": {
      "raw": "0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d"
    }
  },
  "order": "0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d",
  "cofactor": "0x1",
  "aliases": [
    "x963/ansip192k1"
  ],
  "characteristics": {
    "j_invariant": "0",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692684263520264190248580064135217",
    "conductor": "1",
    "discriminant": "6277101735386680763835789423207666416102355444459739537159",
    "embedding_degree": "3138550867693340381917894711530632135978561957600422756038",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 24,
        "least": 24,
        "r": 5
      },
      {
        "full": 3,
        "least": 3,
        "r": 7
      },
      {
        "full": 4,
        "least": 4,
        "r": 11
      },
      {
        "full": 12,
        "least": 3,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "146402144145231529258894028971"
  }
}