Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.3
• Seed:
  C469684435DEB378C4B65CA9591E2A5763059A2E
• j-invariant:
  4949518941300124932197833942361144997943533558142111060080
• Trace of Frobenius:
  41351533396743040039645025261
• Discriminant:
  3779502969702448100548644654746965771458990594820505358394
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1046183622564446793972631570527719147114527610058446656003
• CM-discriminant:
  25108406941546723055343157692789314130938891761521654819855
• Conductor:
  1

SAGE

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffc)
b = K(0x22123dc2395a05caa7423daeccc94760a7d462256bd56916)
E = EllipticCurve(K, (a, b))
G = E(0x7d29778100c65a1da1783716588dce2b8b4aee8e228f1896, 0x38a90f22637337334b49dcb66a6dc8f9978aca7648a943b0)
E.set_order(0xffffffffffffffffffffffff7a62d031c83f4294f640ec13 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffc, p)
b = Mod(0x22123dc2395a05caa7423daeccc94760a7d462256bd56916, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffff7a62d031c83f4294f640ec13 * 0x1
G = [Mod(0x7d29778100c65a1da1783716588dce2b8b4aee8e228f1896, p), Mod(0x38a90f22637337334b49dcb66a6dc8f9978aca7648a943b0, p)]

JSON

{
  "name": "prime192v3",
  "desc": "",
  "oid": "1.2.840.10045.3.1.3",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffeffffffffffffffff",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffc"
    },
    "b": {
      "raw": "0x22123dc2395a05caa7423daeccc94760a7d462256bd56916"
    }
  },
  "generator": {
    "x": {
      "raw": "0x7d29778100c65a1da1783716588dce2b8b4aee8e228f1896"
    },
    "y": {
      "raw": "0x38a90f22637337334b49dcb66a6dc8f9978aca7648a943b0"
    }
  },
  "order": "0xffffffffffffffffffffffff7a62d031c83f4294f640ec13",
  "cofactor": "0x1",
  "characteristics": {
    "seed": "C469684435DEB378C4B65CA9591E2A5763059A2E",
    "j_invariant": "4949518941300124932197833942361144997943533558142111060080",
    "anomalous": false,
    "cm_disc": "25108406941546723055343157692789314130938891761521654819855",
    "conductor": "1",
    "discriminant": "3779502969702448100548644654746965771458990594820505358394",
    "embedding_degree": "1046183622564446793972631570527719147114527610058446656003",
    "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
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "41351533396743040039645025261"
  }
}