c2tnb191v2

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`
a0x401028774d7777c7b7666d1366ea432071274f89ff01e718	`0x401028774d7777c7b7666d1366ea432071274f89ff01e718`
b0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01	`0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01`
G(0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10, 0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a)	`(0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10, 0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a)`
n0x20000000000000000000000050508cb89f652824e06b8173	`0x20000000000000000000000050508cb89f652824e06b8173`
h0x4	`0x4`

Characteristics

OID:
1.2.840.10045.3.0.6
Seed:
0871EF2FEF24D696E6768756151758BEE0D95C15

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x401028774d7777c7b7666d1366ea432071274f89ff01e718), 0, 0, K.fetch_int(0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01)))
E.set_order(0x20000000000000000000000050508cb89f652824e06b8173 * 0x4)
G = E(K.fetch_int(0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10), K.fetch_int(0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a))

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x401028774d7777c7b7666d1366ea432071274f89ff01e718), 0, 0, K.fetch_int(0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01)))
E.set_order(0x20000000000000000000000050508cb89f652824e06b8173 * 0x4)
G = E(K.fetch_int(0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10), K.fetch_int(0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a))

SAGE

JSON

{
  "name": "c2tnb191v2",
  "desc": "",
  "oid": "1.2.840.10045.3.0.6",
  "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": "0x401028774d7777c7b7666d1366ea432071274f89ff01e718"
    },
    "b": {
      "raw": "0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10"
    },
    "y": {
      "raw": "0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a"
    }
  },
  "order": "0x20000000000000000000000050508cb89f652824e06b8173",
  "cofactor": "0x4",
  "characteristics": {
    "seed": "0871EF2FEF24D696E6768756151758BEE0D95C15"
  }
}

{
  "name": "c2tnb191v2",
  "desc": "",
  "oid": "1.2.840.10045.3.0.6",
  "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": "0x401028774d7777c7b7666d1366ea432071274f89ff01e718"
    },
    "b": {
      "raw": "0x0620048d28bcbd03b6249c99182b7c8cd19700c362c46a01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x3809b2b7cc1b28cc5a87926aad83fd28789e81e2c9e3bf10"
    },
    "y": {
      "raw": "0x17434386626d14f3dbf01760d9213a3e1cf37aec437d668a"
    }
  },
  "order": "0x20000000000000000000000050508cb89f652824e06b8173",
  "cofactor": "0x4",
  "characteristics": {
    "seed": "0871EF2FEF24D696E6768756151758BEE0D95C15"
  }
}

JSON