Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.6
• Seed:
  0871EF2FEF24D696E6768756151758BEE0D95C15
• j-invariant:
  2767879892242809417853545352410453334959450040133228144236
• Trace of Frobenius:
  -99424717553083670833495147979
• Discriminant:
  150186265886833235036292851627975676141857315884353481217

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus=u^191 +  u^9 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x401028774d7777c7b7666d1366ea432071274f89ff01e718), 0, 0, K.from_integer(0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01)))
E.set_order(0x20000000000000000000000050508cb89f652824e06b8173 * 0x4)
G = E(K.from_integer(0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10), K.from_integer(0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a))

JSON

{
  "name": "c2tnb191v2",
  "desc": "",
  "oid": "1.2.840.10045.3.0.6",
  "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": "0x401028774d7777c7b7666d1366ea432071274f89ff01e718"
    },
    "b": {
      "raw": "0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10"
    },
    "y": {
      "raw": "0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a"
    }
  },
  "order": "0x20000000000000000000000050508cb89f652824e06b8173",
  "cofactor": "0x4",
  "characteristics": {
    "seed": "0871EF2FEF24D696E6768756151758BEE0D95C15",
    "discriminant": "150186265886833235036292851627975676141857315884353481217",
    "j_invariant": "2767879892242809417853545352410453334959450040133228144236",
    "trace_of_frobenius": "-99424717553083670833495147979"
  }
}