c2pnb163v2

163-bit binary field Weierstrass curve.

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

Parameters

Name	Value
m163	`163`
f(x) x^163 + x^8 + x^2 + x^1 + 1	`x^163 + x^8 + x^2 + x^1 + 1`
a0x0108b39e77c4b108bed981ed0e890e117c511cf072	`0x0108b39e77c4b108bed981ed0e890e117c511cf072`
b0x0667aceb38af4e488c407433ffae4f1c811638df20	`0x0667aceb38af4e488c407433ffae4f1c811638df20`
G(0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5, 0x079f684ddf6684c5cd258b3890021b2386dfd19fc5)	`(0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5, 0x079f684ddf6684c5cd258b3890021b2386dfd19fc5)`
n0x03fffffffffffffffffffdf64de1151adbb78f10a7	`0x03fffffffffffffffffffdf64de1151adbb78f10a7`
h0x2	`0x2`

Characteristics

OID:
1.2.840.10045.3.0.2
Seed:
53814C050D44D696E67687561517580CA4E29FFD

SAGE

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^8 +  x^2 +  x^1 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0108b39e77c4b108bed981ed0e890e117c511cf072), 0, 0, K.fetch_int(0x0667aceb38af4e488c407433ffae4f1c811638df20)))
E.set_order(0x03fffffffffffffffffffdf64de1151adbb78f10a7 * 0x2)
G = E(K.fetch_int(0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5), K.fetch_int(0x079f684ddf6684c5cd258b3890021b2386dfd19fc5))

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^8 +  x^2 +  x^1 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0108b39e77c4b108bed981ed0e890e117c511cf072), 0, 0, K.fetch_int(0x0667aceb38af4e488c407433ffae4f1c811638df20)))
E.set_order(0x03fffffffffffffffffffdf64de1151adbb78f10a7 * 0x2)
G = E(K.fetch_int(0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5), K.fetch_int(0x079f684ddf6684c5cd258b3890021b2386dfd19fc5))

SAGE

JSON

{
  "name": "c2pnb163v2",
  "desc": "",
  "oid": "1.2.840.10045.3.0.2",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 8
      },
      {
        "coeff": "0x01",
        "power": 2
      },
      {
        "coeff": "0x01",
        "power": 1
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0108b39e77c4b108bed981ed0e890e117c511cf072"
    },
    "b": {
      "raw": "0x0667aceb38af4e488c407433ffae4f1c811638df20"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5"
    },
    "y": {
      "raw": "0x079f684ddf6684c5cd258b3890021b2386dfd19fc5"
    }
  },
  "order": "0x03fffffffffffffffffffdf64de1151adbb78f10a7",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "53814C050D44D696E67687561517580CA4E29FFD"
  }
}

{
  "name": "c2pnb163v2",
  "desc": "",
  "oid": "1.2.840.10045.3.0.2",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 8
      },
      {
        "coeff": "0x01",
        "power": 2
      },
      {
        "coeff": "0x01",
        "power": 1
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0108b39e77c4b108bed981ed0e890e117c511cf072"
    },
    "b": {
      "raw": "0x0667aceb38af4e488c407433ffae4f1c811638df20"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0024266e4eb5106d0a964d92c4860e2671db9b6cc5"
    },
    "y": {
      "raw": "0x079f684ddf6684c5cd258b3890021b2386dfd19fc5"
    }
  },
  "order": "0x03fffffffffffffffffffdf64de1151adbb78f10a7",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "53814C050D44D696E67687561517580CA4E29FFD"
  }
}

JSON