Defined in IETF in RFC5114

Parameters

Sources

• RFC5114

Characteristics

• j-invariant:
  6234286251230310114240839169629130138801351179850969208331
• Trace of Frobenius:
  31607402316713927207482677199
• Discriminant:
  5525402385154848923235289274741921730185152131202286251655
• Embedding degree:
  627710173538668076383578942317605901376719477318284228408
• CM-discriminant:
  -24109379060336110122544161233113975664949272517896865359515
• 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 * 0x01)

PARI/GP

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
a = Mod(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC, p)
b = Mod(0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831 * 0x01
G = [Mod(0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012, p), Mod(0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811, p)]

JSON

{
  "name": "192-bit Random ECP Group",
  "desc": "Defined in IETF in RFC5114",
  "sources": [
    {
      "name": "RFC5114",
      "url": "https://tools.ietf.org/html/rfc5114"
    }
  ],
  "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": "0x01",
  "characteristics": {
    "cm_disc": "-24109379060336110122544161233113975664949272517896865359515",
    "conductor": "1",
    "discriminant": "5525402385154848923235289274741921730185152131202286251655",
    "j_invariant": "6234286251230310114240839169629130138801351179850969208331",
    "embedding_degree": "627710173538668076383578942317605901376719477318284228408",
    "trace_of_frobenius": "31607402316713927207482677199"
  }
}