A randomly generated curve, using the SECG/X9.62 method. 'However for historical reasons the method used to generate E from S differs slightly from the method described in ANSI X9.62 X9.62. Specifically the coefficient b produced from S is the reverse of the coefficient that would have been produced by the method described in ANSI X9.62.'

Parameters

Characteristics

• OID:
  1.3.132.0.2
• Seed:
  24B7B137C8A14D696E6768756151756FD0DA2E5C
• j-invariant:
  6799963281606188757260601154353010573009354190197
• Trace of Frobenius:
  1731532666194638619521227
• Discriminant:
  10341149448350347985759700389662805134872097107929
• Anomalous:
  false
• Supersingular:
  false
• CM-discriminant:
  46768052394588893382517912915388390434351221854005
• Conductor:
  1

SAGE

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^7 +  x^6 +  x^3 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x07b6882caaefa84f9554ff8428bd88e246d2782ae2), 0, 0, K.fetch_int(0x0713612dcddcb40aab946bda29ca91f73af958afd9)))
E.set_order(0x03ffffffffffffffffffff48aab689c29ca710279b * 0x2)
G = E(K.fetch_int(0x0369979697ab43897789566789567f787a7876a654), K.fetch_int(0x00435edb42efafb2989d51fefce3c80988f41ff883))

JSON

{
  "name": "sect163r1",
  "desc": "A randomly generated curve, using the SECG/X9.62 method. 'However for historical reasons the method used to generate E from S differs slightly from the method described in ANSI X9.62 [X9.62]. Specifically the coefficient b produced from S is the reverse of the coefficient that would have been produced by the method described in ANSI X9.62.'",
  "oid": "1.3.132.0.2",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 7
      },
      {
        "coeff": "0x01",
        "power": 6
      },
      {
        "coeff": "0x01",
        "power": 3
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x07b6882caaefa84f9554ff8428bd88e246d2782ae2"
    },
    "b": {
      "raw": "0x0713612dcddcb40aab946bda29ca91f73af958afd9"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0369979697ab43897789566789567f787a7876a654"
    },
    "y": {
      "raw": "0x00435edb42efafb2989d51fefce3c80988f41ff883"
    }
  },
  "order": "0x03ffffffffffffffffffff48aab689c29ca710279b",
  "cofactor": "0x2",
  "aliases": [
    "x963/ansit163r1"
  ],
  "characteristics": {
    "seed": "24B7B137C8A14D696E6768756151756FD0DA2E5C",
    "j_invariant": "6799963281606188757260601154353010573009354190197",
    "anomalous": false,
    "cm_disc": "46768052394588893382517912915388390434351221854005",
    "conductor": "1",
    "discriminant": "10341149448350347985759700389662805134872097107929",
    "supersingular": false,
    "trace_of_frobenius": "1731532666194638619521227"
  }
}