sect113r2

113-bit binary field Weierstrass curve.

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

Parameters

Name	Value
m113	`113`
f(x) x^113 + x^9 + 1	`x^113 + x^9 + 1`
a0x00689918dbec7e5a0dd6dfc0aa55c7	`0x00689918dbec7e5a0dd6dfc0aa55c7`
b0x0095e9a9ec9b297bd4bf36e059184f	`0x0095e9a9ec9b297bd4bf36e059184f`
G(0x01a57a6a7b26ca5ef52fcdb8164797, 0x00b3adc94ed1fe674c06e695baba1d)	`(0x01a57a6a7b26ca5ef52fcdb8164797, 0x00b3adc94ed1fe674c06e695baba1d)`
n0x010000000000000108789b2496af93	`0x010000000000000108789b2496af93`
h0x2	`0x2`

Characteristics

OID:
1.3.132.0.5

SAGE

F.<x> = GF(2)[]
K = GF(2^113, name="x", modulus= x^113 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00689918dbec7e5a0dd6dfc0aa55c7), 0, 0, K.fetch_int(0x0095e9a9ec9b297bd4bf36e059184f)))
E.set_order(0x010000000000000108789b2496af93 * 0x2)
G = E(K.fetch_int(0x01a57a6a7b26ca5ef52fcdb8164797), K.fetch_int(0x00b3adc94ed1fe674c06e695baba1d))

F.<x> = GF(2)[]
K = GF(2^113, name="x", modulus= x^113 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00689918dbec7e5a0dd6dfc0aa55c7), 0, 0, K.fetch_int(0x0095e9a9ec9b297bd4bf36e059184f)))
E.set_order(0x010000000000000108789b2496af93 * 0x2)
G = E(K.fetch_int(0x01a57a6a7b26ca5ef52fcdb8164797), K.fetch_int(0x00b3adc94ed1fe674c06e695baba1d))

SAGE

JSON

{
  "name": "sect113r2",
  "desc": "",
  "oid": "1.3.132.0.5",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 113,
    "degree": 113,
    "poly": [
      {
        "coeff": "0x01",
        "power": 113
      },
      {
        "coeff": "0x01",
        "power": 9
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x00689918dbec7e5a0dd6dfc0aa55c7"
    },
    "b": {
      "raw": "0x0095e9a9ec9b297bd4bf36e059184f"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01a57a6a7b26ca5ef52fcdb8164797"
    },
    "y": {
      "raw": "0x00b3adc94ed1fe674c06e695baba1d"
    }
  },
  "order": "0x010000000000000108789b2496af93",
  "cofactor": "0x2"
}

{
  "name": "sect113r2",
  "desc": "",
  "oid": "1.3.132.0.5",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 113,
    "degree": 113,
    "poly": [
      {
        "coeff": "0x01",
        "power": 113
      },
      {
        "coeff": "0x01",
        "power": 9
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x00689918dbec7e5a0dd6dfc0aa55c7"
    },
    "b": {
      "raw": "0x0095e9a9ec9b297bd4bf36e059184f"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01a57a6a7b26ca5ef52fcdb8164797"
    },
    "y": {
      "raw": "0x00b3adc94ed1fe674c06e695baba1d"
    }
  },
  "order": "0x010000000000000108789b2496af93",
  "cofactor": "0x2"
}

JSON