Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.1
• Seed:
  3045AE6FC8422F64ED579528D38120EAE12196D5
• j-invariant:
  6234286251230310114240839169629130138801351179850969208331
• Trace of Frobenius:
  31607402316713927207482677199
• Discriminant:
  5525402385154848923235289274741921730185152131202286251655
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  627710173538668076383578942317605901376719477318284228408
• CM-discriminant:
  25108406941546723055343157692799058262018920874353817167917
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1)
E = EllipticCurve(K, (a, b))
G = E(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811)
E.set_order(0xffffffffffffffffffffffff99def836146bc9b1b4d22831 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffc, p)
b = Mod(0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 * 0x1
G = [Mod(0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, p), Mod(0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811, p)]

JSON

{
  "name": "prime192v1",
  "desc": "",
  "oid": "1.2.840.10045.3.1.1",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
    },
    "b": {
      "raw": "0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1"
    }
  },
  "generator": {
    "x": {
      "raw": "0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012"
    },
    "y": {
      "raw": "0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"
    }
  },
  "order": "0xffffffffffffffffffffffff99def836146bc9b1b4d22831",
  "cofactor": "0x1",
  "aliases": [
    "secg/secp192r1",
    "nist/P-192"
  ],
  "characteristics": {
    "seed": "3045AE6FC8422F64ED579528D38120EAE12196D5",
    "j_invariant": "6234286251230310114240839169629130138801351179850969208331",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692799058262018920874353817167917",
    "conductor": "1",
    "discriminant": "5525402385154848923235289274741921730185152131202286251655",
    "embedding_degree": "627710173538668076383578942317605901376719477318284228408",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 20,
        "least": 4,
        "r": 5
      },
      {
        "full": 48,
        "least": 48,
        "r": 7
      },
      {
        "full": 55,
        "least": 5,
        "r": 11
      },
      {
        "full": 12,
        "least": 4,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "31607402316713927207482677199"
  }
}