c2tnb191v1

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`
a0x2866537b676752636a68f56554e12640276b649ef7526267	`0x2866537b676752636a68f56554e12640276b649ef7526267`
b0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec	`0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec`
G(0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d, 0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb)	`(0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d, 0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb)`
n0x40000000000000000000000004a20e90c39067c893bbb9a5	`0x40000000000000000000000004a20e90c39067c893bbb9a5`
h0x2	`0x2`

Characteristics

OID:
1.2.840.10045.3.0.5
Seed:
4E13CA542744D696E67687561517552F279A8C84

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x2866537b676752636a68f56554e12640276b649ef7526267), 0, 0, K.fetch_int(0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec)))
E.set_order(0x40000000000000000000000004a20e90c39067c893bbb9a5 * 0x2)
G = E(K.fetch_int(0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d), K.fetch_int(0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb))

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus= x^191 +  x^9 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x2866537b676752636a68f56554e12640276b649ef7526267), 0, 0, K.fetch_int(0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec)))
E.set_order(0x40000000000000000000000004a20e90c39067c893bbb9a5 * 0x2)
G = E(K.fetch_int(0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d), K.fetch_int(0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb))

SAGE

JSON

{
  "name": "c2tnb191v1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.5",
  "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": "0x2866537b676752636a68f56554e12640276b649ef7526267"
    },
    "b": {
      "raw": "0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec"
    }
  },
  "generator": {
    "x": {
      "raw": "0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d"
    },
    "y": {
      "raw": "0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb"
    }
  },
  "order": "0x40000000000000000000000004a20e90c39067c893bbb9a5",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "4E13CA542744D696E67687561517552F279A8C84"
  }
}

{
  "name": "c2tnb191v1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.5",
  "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": "0x2866537b676752636a68f56554e12640276b649ef7526267"
    },
    "b": {
      "raw": "0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec"
    }
  },
  "generator": {
    "x": {
      "raw": "0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d"
    },
    "y": {
      "raw": "0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb"
    }
  },
  "order": "0x40000000000000000000000004a20e90c39067c893bbb9a5",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "4E13CA542744D696E67687561517552F279A8C84"
  }
}

JSON