c2tnb191v3

191-bit binary field Weierstrass curve.

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

Parameters

Name	Value
m191	`191`
f(x) x^191 + x^9 + 1	`x^191 + x^9 + 1`
a0x6c01074756099122221056911c77d77e77a777e7e7e77fcb	`0x6c01074756099122221056911c77d77e77a777e7e7e77fcb`
b0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8	`0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8`
G(0x375d4ce24fde434489de8746e71786015009e66e38a926dd, 0x545a39176196575d985999366e6ad34ce0a77cd7127b06be)	`(0x375d4ce24fde434489de8746e71786015009e66e38a926dd, 0x545a39176196575d985999366e6ad34ce0a77cd7127b06be)`
n0x155555555555555555555555610c0b196812bfb6288a3ea3	`0x155555555555555555555555610c0b196812bfb6288a3ea3`
h0x6	`0x6`

Characteristics

OID:
1.2.840.10045.3.0.7
Seed:
E053512DC684D696E676875615175067AE786D1F

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x6c01074756099122221056911c77d77e77a777e7e7e77fcb), 0, 0, K.fetch_int(0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8)))
E.set_order(0x155555555555555555555555610c0b196812bfb6288a3ea3 * 0x6)
G = E(K.fetch_int(0x375d4ce24fde434489de8746e71786015009e66e38a926dd), K.fetch_int(0x545a39176196575d985999366e6ad34ce0a77cd7127b06be))

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x6c01074756099122221056911c77d77e77a777e7e7e77fcb), 0, 0, K.fetch_int(0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8)))
E.set_order(0x155555555555555555555555610c0b196812bfb6288a3ea3 * 0x6)
G = E(K.fetch_int(0x375d4ce24fde434489de8746e71786015009e66e38a926dd), K.fetch_int(0x545a39176196575d985999366e6ad34ce0a77cd7127b06be))

SAGE

JSON

{
  "name": "c2tnb191v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.7",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 191,
    "degree": 191,
    "poly": [
      {
        "coeff": "0x01",
        "power": 191
      },
      {
        "coeff": "0x01",
        "power": 9
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x6c01074756099122221056911c77d77e77a777e7e7e77fcb"
    },
    "b": {
      "raw": "0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8"
    }
  },
  "generator": {
    "x": {
      "raw": "0x375d4ce24fde434489de8746e71786015009e66e38a926dd"
    },
    "y": {
      "raw": "0x545a39176196575d985999366e6ad34ce0a77cd7127b06be"
    }
  },
  "order": "0x155555555555555555555555610c0b196812bfb6288a3ea3",
  "cofactor": "0x6",
  "characteristics": {
    "seed": "E053512DC684D696E676875615175067AE786D1F"
  }
}

{
  "name": "c2tnb191v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.7",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 191,
    "degree": 191,
    "poly": [
      {
        "coeff": "0x01",
        "power": 191
      },
      {
        "coeff": "0x01",
        "power": 9
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x6c01074756099122221056911c77d77e77a777e7e7e77fcb"
    },
    "b": {
      "raw": "0x71fe1af926cf847989efef8db459f66394d90f32ad3f15e8"
    }
  },
  "generator": {
    "x": {
      "raw": "0x375d4ce24fde434489de8746e71786015009e66e38a926dd"
    },
    "y": {
      "raw": "0x545a39176196575d985999366e6ad34ce0a77cd7127b06be"
    }
  },
  "order": "0x155555555555555555555555610c0b196812bfb6288a3ea3",
  "cofactor": "0x6",
  "characteristics": {
    "seed": "E053512DC684D696E676875615175067AE786D1F"
  }
}

JSON