Oakley Group 3

155-bit binary field Weierstrass curve.

Defined in IETF in RFC2409, no generator present.

y^2 + xy \equiv x^3 + ax^2 + b

Parameters

Name	Value
m155	`155`
f(x) x^155 + x^62 + 1	`x^155 + x^62 + 1`
a0x0	`0x0`
b0x07338f	`0x07338f`
n0x0800000000000000000057db5698537193aef944	`0x0800000000000000000057db5698537193aef944`
h0x01	`0x01`

SAGE

F.<x> = GF(2)[]
K = GF(2^155, name="x", modulus= x^155 +  x^62 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0), 0, 0, K.fetch_int(0x07338f)))
E.set_order(0x0800000000000000000057db5698537193aef944 * 0x01)
# No generator defined

F.<x> = GF(2)[]
K = GF(2^155, name="x", modulus= x^155 +  x^62 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0), 0, 0, K.fetch_int(0x07338f)))
E.set_order(0x0800000000000000000057db5698537193aef944 * 0x01)
# No generator defined

SAGE

JSON

{
  "name": "Oakley Group 3",
  "desc": "Defined in IETF in RFC2409, no generator present.",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 155,
    "degree": 155,
    "poly": [
      {
        "coeff": "0x01",
        "power": 155
      },
      {
        "coeff": "0x01",
        "power": 62
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0"
    },
    "b": {
      "raw": "0x07338f"
    }
  },
  "order": "0x0800000000000000000057db5698537193aef944",
  "cofactor": "0x01"
}

{
  "name": "Oakley Group 3",
  "desc": "Defined in IETF in RFC2409, no generator present.",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 155,
    "degree": 155,
    "poly": [
      {
        "coeff": "0x01",
        "power": 155
      },
      {
        "coeff": "0x01",
        "power": 62
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0"
    },
    "b": {
      "raw": "0x07338f"
    }
  },
  "order": "0x0800000000000000000057db5698537193aef944",
  "cofactor": "0x01"
}

JSON