c2pnb176w1

176-bit binary field Weierstrass curve.

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

Parameters

Name	Value
m176	`176`
f(x) x^176 + x^43 + x^2 + x^1 + 1	`x^176 + x^43 + x^2 + x^1 + 1`
a0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b	`0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b`
b0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2	`0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2`
G(0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798, 0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c)	`(0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798, 0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c)`
n0x010092537397eca4f6145799d62b0a19ce06fe26ad	`0x010092537397eca4f6145799d62b0a19ce06fe26ad`
h0xff6e	`0xff6e`

Characteristics

OID:
1.2.840.10045.3.0.4

SAGE

F.<x> = GF(2)[]
K = GF(2^176, name="x", modulus= x^176 +  x^43 +  x^2 +  x^1 + 1)
E = EllipticCurve(K, (1, K.from_integer(0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b), 0, 0, K.from_integer(0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2)))
E.set_order(0x010092537397eca4f6145799d62b0a19ce06fe26ad * 0xff6e)
G = E(K.from_integer(0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798), K.from_integer(0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c))

F.<x> = GF(2)[]
K = GF(2^176, name="x", modulus= x^176 +  x^43 +  x^2 +  x^1 + 1)
E = EllipticCurve(K, (1, K.from_integer(0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b), 0, 0, K.from_integer(0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2)))
E.set_order(0x010092537397eca4f6145799d62b0a19ce06fe26ad * 0xff6e)
G = E(K.from_integer(0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798), K.from_integer(0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c))

SAGE

JSON

{
  "name": "c2pnb176w1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.4",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 176,
    "degree": 176,
    "poly": [
      {
        "coeff": "0x01",
        "power": 176
      },
      {
        "coeff": "0x01",
        "power": 43
      },
      {
        "coeff": "0x01",
        "power": 2
      },
      {
        "coeff": "0x01",
        "power": 1
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b"
    },
    "b": {
      "raw": "0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2"
    }
  },
  "generator": {
    "x": {
      "raw": "0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798"
    },
    "y": {
      "raw": "0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c"
    }
  },
  "order": "0x010092537397eca4f6145799d62b0a19ce06fe26ad",
  "cofactor": "0xff6e"
}

{
  "name": "c2pnb176w1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.4",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 176,
    "degree": 176,
    "poly": [
      {
        "coeff": "0x01",
        "power": 176
      },
      {
        "coeff": "0x01",
        "power": 43
      },
      {
        "coeff": "0x01",
        "power": 2
      },
      {
        "coeff": "0x01",
        "power": 1
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0xe4e6db2995065c407d9d39b8d0967b96704ba8e9c90b"
    },
    "b": {
      "raw": "0x5dda470abe6414de8ec133ae28e9bbd7fcec0ae0fff2"
    }
  },
  "generator": {
    "x": {
      "raw": "0x8d16c2866798b600f9f08bb4a8e860f3298ce04a5798"
    },
    "y": {
      "raw": "0x6fa4539c2dadddd6bab5167d61b436e1d92bb16a562c"
    }
  },
  "order": "0x010092537397eca4f6145799d62b0a19ce06fe26ad",
  "cofactor": "0xff6e"
}

JSON