A randomly generated curve. 'E was selected from S as specified in ANSI X9.62 X9.62 in normal basis representation and converted into polynomial basis representation.'

Parameters

Characteristics

• OID:
  1.3.132.0.15
• Seed:
  85E25BFE5C86226CDB12016F7553F9D0E693A268
• j-invariant:
  924715273381456531451948543458511393546700947074
• Trace of Frobenius:
  -6224022517221266226059365
• Discriminant:
  2982236234343851336267446656627785008148015875581
• Anomalous:
  false
• Supersingular:
  false
• CM-discriminant:
  46768052394588893382517920870943573850256067434597
• 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(0x000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x020a601907b8c953ca1481eb10512f78744a3205fd)))
E.set_order(0x040000000000000000000292fe77e70c12a4234c33 * 0x2)
G = E(K.fetch_int(0x03f0eba16286a2d57ea0991168d4994637e8343e36), K.fetch_int(0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1))

JSON

{
  "name": "sect163r2",
  "desc": "A randomly generated curve. 'E was selected from S as specified in ANSI X9.62 [X9.62] in normal basis representation and converted into polynomial basis representation.'",
  "oid": "1.3.132.0.15",
  "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": "0x000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x020a601907b8c953ca1481eb10512f78744a3205fd"
    }
  },
  "generator": {
    "x": {
      "raw": "0x03f0eba16286a2d57ea0991168d4994637e8343e36"
    },
    "y": {
      "raw": "0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1"
    }
  },
  "order": "0x040000000000000000000292fe77e70c12a4234c33",
  "cofactor": "0x2",
  "aliases": [
    "nist/B-163",
    "x963/ansit163r2"
  ],
  "characteristics": {
    "seed": "85E25BFE5C86226CDB12016F7553F9D0E693A268",
    "j_invariant": "924715273381456531451948543458511393546700947074",
    "anomalous": false,
    "cm_disc": "46768052394588893382517920870943573850256067434597",
    "conductor": "1",
    "discriminant": "2982236234343851336267446656627785008148015875581",
    "supersingular": false,
    "trace_of_frobenius": "-6224022517221266226059365"
  }
}