Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.7
• Seed:
  E053512DC684D696E676875615175067AE786D1F
• j-invariant:
  1714337609183819713676888386761400501841082790083898065067
• Trace of Frobenius:
  -21751307834701491275992758225
• Discriminant:
  2795090396487148255149641564379414408025141010062808913384

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus=u^191 +  u^9 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x6c01074756099122221056911c77d77e77a777e7e7e77fcb), 0, 0, K.from_integer(0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8)))
E.set_order(0x155555555555555555555555610c0b196812bfb6288a3ea3 * 0x6)
G = E(K.from_integer(0x375d4ce24fde434489de8746e71786015009e66e38a926dd), K.from_integer(0x545a39176196575d985999366e6ad34ce0a77cd7127b06be))

JSON

{
  "name": "c2tnb191v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.7",
  "sources": [
    {
      "name": "ANSI X9.62",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 191,
    "degree": 191,
    "poly": [
      {
        "power": 191,
        "coeff": "0x01"
      },
      {
        "power": 9,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x6c01074756099122221056911c77d77e77a777e7e7e77fcb"
    },
    "b": {
      "raw": "0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8"
    }
  },
  "generator": {
    "x": {
      "raw": "0x375d4ce24fde434489de8746e71786015009e66e38a926dd"
    },
    "y": {
      "raw": "0x545a39176196575d985999366e6ad34ce0a77cd7127b06be"
    }
  },
  "order": "0x155555555555555555555555610c0b196812bfb6288a3ea3",
  "cofactor": "0x6",
  "characteristics": {
    "seed": "E053512DC684D696E676875615175067AE786D1F",
    "discriminant": "2795090396487148255149641564379414408025141010062808913384",
    "j_invariant": "1714337609183819713676888386761400501841082790083898065067",
    "trace_of_frobenius": "-21751307834701491275992758225"
  }
}