Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.2
• Seed:
  31A92EE2029FD10D901B113E990710F0D21AC6B6
• j-invariant:
  2188073006583539552141688552564683396860111048461359479401
• Trace of Frobenius:
  128840479891808162805939905231
• Discriminant:
  3136318742261921876063208570368096687049382158828912127687
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1569275433846670190958947355769706484048025134396096264012
• CM-discriminant:
  25108406941546723055343157692701825184443826638755359939885
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953)
E = EllipticCurve(K, (a, b))
G = E(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, 0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15)
E.set_order(0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffc, p)
b = Mod(0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31 * 0x1
G = [Mod(0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a, p), Mod(0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15, p)]

JSON

{
  "name": "prime192v2",
  "desc": "",
  "oid": "1.2.840.10045.3.1.2",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
    },
    "b": {
      "raw": "0xcc22d6dfb95c6b25e49c0d6364a4e5980c393aa21668d953"
    }
  },
  "generator": {
    "x": {
      "raw": "0xeea2bae7e1497842f2de7769cfe9c989c072ad696f48034a"
    },
    "y": {
      "raw": "0x6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15"
    }
  },
  "order": "0xfffffffffffffffffffffffe5fb1a724dc80418648d8dd31",
  "cofactor": "0x1",
  "characteristics": {
    "seed": "31A92EE2029FD10D901B113E990710F0D21AC6B6",
    "j_invariant": "2188073006583539552141688552564683396860111048461359479401",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692701825184443826638755359939885",
    "conductor": "1",
    "discriminant": "3136318742261921876063208570368096687049382158828912127687",
    "embedding_degree": "1569275433846670190958947355769706484048025134396096264012",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 20,
        "least": 4,
        "r": 5
      },
      {
        "full": 6,
        "least": 2,
        "r": 7
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "128840479891808162805939905231"
  }
}