A Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.9
• j-invariant:
  0
• Trace of Frobenius:
  -2082454586705745521609279
• Discriminant:
  1461501637330902918203684832716283019651637533123
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  730750818665451459101843457585434862698579581785
• CM-discriminant:
  5846006549323611672814741413319718784352071826443
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffac73
K = GF(p)
a = K(0x0000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000007)
E = EllipticCurve(K, (a, b))
G = E(0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb, 0x938cf935318fdced6bc28286531733c3f03c4fee)
E.set_order(0x0100000000000000000001b8fa16dfab9aca16b6b3 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffac73
a = Mod(0x0000000000000000000000000000000000000000, p)
b = Mod(0x0000000000000000000000000000000000000007, p)
E = ellinit([a, b])
E[16][1] = 0x0100000000000000000001b8fa16dfab9aca16b6b3 * 0x1
G = [Mod(0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb, p), Mod(0x938cf935318fdced6bc28286531733c3f03c4fee, p)]

JSON

{
  "name": "secp160k1",
  "desc": "A Koblitz curve.",
  "oid": "1.3.132.0.9",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffac73",
    "bits": 160
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000007"
    }
  },
  "generator": {
    "x": {
      "raw": "0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb"
    },
    "y": {
      "raw": "0x938cf935318fdced6bc28286531733c3f03c4fee"
    }
  },
  "order": "0x0100000000000000000001b8fa16dfab9aca16b6b3",
  "cofactor": "0x1",
  "aliases": [
    "x963/ansip160k1"
  ],
  "characteristics": {
    "j_invariant": "0",
    "anomalous": false,
    "cm_disc": "5846006549323611672814741413319718784352071826443",
    "conductor": "1",
    "discriminant": "1461501637330902918203684832716283019651637533123",
    "embedding_degree": "730750818665451459101843457585434862698579581785",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 6,
        "least": 6,
        "r": 5
      },
      {
        "full": 2,
        "least": 2,
        "r": 7
      },
      {
        "full": 15,
        "least": 15,
        "r": 11
      },
      {
        "full": 6,
        "least": 2,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "-2082454586705745521609279"
  }
}