A binary-field curve in optimal normal basis

Parameters

Characteristics

• OID:
  1.2.840.10045.3.0.14
• Seed:
  F851638CFA4D696E67687561517556513841BFAC

SAGE

F.<x> = GF(2)[]
K.<z> = GF(2^239, name="z", modulus= x^239 +  x^238 +  x^236 +  x^232 +  x^224 +  x^208 +  x^207 +  x^206 +  x^204 +  x^200 +  x^192 +  x^144 +  x^143 +  x^142 +  x^140 +  x^136 +  x^128 +  x^16 +  x^15 +  x^14 +  x^12 +  x^8 + 1)
def fetch_int(K, h):
	return sum(map(lambda ix: K(Integer(ix[1]) * z^(2^ix[0])), enumerate(h.binary())), K(0))
E = EllipticCurve(K, (1, fetch_int(K, 0x182DD45F5D470239B8983FEA47B8B292641C57F9BF84BAECDE8BB3ADCE30), 0, 0, fetch_int(K, 0x147A9C1D4C2CE9BE5D34EC02797F76667EBAD5A3F93FA2A524BFDE91EF28)))
E.set_order(0x200000000000000000000000000000474F7E69F42FE430931D0B455AAE8B * 0x04)
G = E(fetch_int(K, 0x034912AD657F1D1C6B32EDB9942C95E226B06FB012CD40FDEA0D72197C8104), fetch_int(K, ))

JSON

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  "name": "c2onb239v4",
  "desc": "A binary-field curve in optimal normal basis",
  "oid": "1.2.840.10045.3.0.14",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 239,
    "degree": 239,
    "poly": [
      {
        "coeff": "0x01",
        "power": 239
      },
      {
        "coeff": "0x01",
        "power": 238
      },
      {
        "coeff": "0x01",
        "power": 236
      },
      {
        "coeff": "0x01",
        "power": 232
      },
      {
        "coeff": "0x01",
        "power": 224
      },
      {
        "coeff": "0x01",
        "power": 208
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      {
        "coeff": "0x01",
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      },
      {
        "coeff": "0x01",
        "power": 206
      },
      {
        "coeff": "0x01",
        "power": 204
      },
      {
        "coeff": "0x01",
        "power": 200
      },
      {
        "coeff": "0x01",
        "power": 192
      },
      {
        "coeff": "0x01",
        "power": 144
      },
      {
        "coeff": "0x01",
        "power": 143
      },
      {
        "coeff": "0x01",
        "power": 142
      },
      {
        "coeff": "0x01",
        "power": 140
      },
      {
        "coeff": "0x01",
        "power": 136
      },
      {
        "coeff": "0x01",
        "power": 128
      },
      {
        "coeff": "0x01",
        "power": 16
      },
      {
        "coeff": "0x01",
        "power": 15
      },
      {
        "coeff": "0x01",
        "power": 14
      },
      {
        "coeff": "0x01",
        "power": 12
      },
      {
        "coeff": "0x01",
        "power": 8
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "normal"
  },
  "params": {
    "a": {
      "raw": "0x182DD45F5D470239B8983FEA47B8B292641C57F9BF84BAECDE8BB3ADCE30"
    },
    "b": {
      "raw": "0x147A9C1D4C2CE9BE5D34EC02797F76667EBAD5A3F93FA2A524BFDE91EF28"
    }
  },
  "generator": {
    "x": {
      "raw": "0x034912AD657F1D1C6B32EDB9942C95E226B06FB012CD40FDEA0D72197C8104"
    },
    "y": {
      "raw": ""
    }
  },
  "order": "0x200000000000000000000000000000474F7E69F42FE430931D0B455AAE8B",
  "cofactor": "0x04",
  "characteristics": {
    "seed": "F851638CFA4D696E67687561517556513841BFAC"
  }
}