Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.11
• Seed:
  D34B9A4D696E676875615175CA71B920BFEFB05D
• j-invariant:
  512751440895418153996773955648914462232268766226908206749443178722917416
• Trace of Frobenius:
  -317806026669043444686057064183337243
• Discriminant:
  835220090183511522333759023255701946035554591371971415066075271323618326

SAGE

F.<x> = GF(2)[]
K = GF(2^239, name="x", modulus=u^239 +  u^36 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x32010857077c5431123a46b808906756f543423e8d27877578125778ac76), 0, 0, K.from_integer(0x790408f2eedaf392b012edefb3392f30f4327c0ca3f31fc383c422aa8c16)))
E.set_order(0x2000000000000000000000000000000f4d42ffe1492a4993f1cad666e447 * 0x4)
G = E(K.from_integer(0x57927098fa932e7c0a96d3fd5b706ef7e5f5c156e16b7e7c86038552e91d), K.from_integer(0x61d8ee5077c33fecf6f1a16b268de469c3c7744ea9a971649fc7a9616305))

JSON

{
  "name": "c2tnb239v1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.11",
  "sources": [
    {
      "name": "ANSI X9.62",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 239,
    "degree": 239,
    "poly": [
      {
        "power": 239,
        "coeff": "0x01"
      },
      {
        "power": 36,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x32010857077c5431123a46b808906756f543423e8d27877578125778ac76"
    },
    "b": {
      "raw": "0x790408f2eedaf392b012edefb3392f30f4327c0ca3f31fc383c422aa8c16"
    }
  },
  "generator": {
    "x": {
      "raw": "0x57927098fa932e7c0a96d3fd5b706ef7e5f5c156e16b7e7c86038552e91d"
    },
    "y": {
      "raw": "0x61d8ee5077c33fecf6f1a16b268de469c3c7744ea9a971649fc7a9616305"
    }
  },
  "order": "0x2000000000000000000000000000000f4d42ffe1492a4993f1cad666e447",
  "cofactor": "0x4",
  "characteristics": {
    "seed": "D34B9A4D696E676875615175CA71B920BFEFB05D",
    "discriminant": "835220090183511522333759023255701946035554591371971415066075271323618326",
    "j_invariant": "512751440895418153996773955648914462232268766226908206749443178722917416",
    "trace_of_frobenius": "-317806026669043444686057064183337243"
  }
}