wap-wsg-idm-ecid-wtls3

163-bit binary field Weierstrass curve.
Also known as: K-163 sect163k1 ansit163k1

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

Parameters

Name	Value
m163	`163`
f(x) x^163 + x^7 + x^6 + x^3 + 1	`x^163 + x^7 + x^6 + x^3 + 1`
a0x1	`0x1`
b0x1	`0x1`
G(0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8, 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9)	`(0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8, 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9)`
n0x04000000000000000000020108a2e0cc0d99f8a5ef	`0x04000000000000000000020108a2e0cc0d99f8a5ef`
h0x2	`0x2`

Characteristics

OID:
2.23.43.1.4.3

SAGE

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^7 +  x^6 +  x^3 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x1), 0, 0, K.fetch_int(0x1)))
E.set_order(0x04000000000000000000020108a2e0cc0d99f8a5ef * 0x2)
G = E(K.fetch_int(0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8), K.fetch_int(0x0289070fb05d38ff58321f2e800536d538ccdaa3d9))

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 +  x^7 +  x^6 +  x^3 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x1), 0, 0, K.fetch_int(0x1)))
E.set_order(0x04000000000000000000020108a2e0cc0d99f8a5ef * 0x2)
G = E(K.fetch_int(0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8), K.fetch_int(0x0289070fb05d38ff58321f2e800536d538ccdaa3d9))

SAGE

JSON

{
  "name": "wap-wsg-idm-ecid-wtls3",
  "desc": "",
  "oid": "2.23.43.1.4.3",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 7
      },
      {
        "coeff": "0x01",
        "power": 6
      },
      {
        "coeff": "0x01",
        "power": 3
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x1"
    },
    "b": {
      "raw": "0x1"
    }
  },
  "generator": {
    "x": {
      "raw": "0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8"
    },
    "y": {
      "raw": "0x0289070fb05d38ff58321f2e800536d538ccdaa3d9"
    }
  },
  "order": "0x04000000000000000000020108a2e0cc0d99f8a5ef",
  "cofactor": "0x2",
  "aliases": [
    "nist/K-163",
    "secg/sect163k1",
    "x963/ansit163k1"
  ]
}

{
  "name": "wap-wsg-idm-ecid-wtls3",
  "desc": "",
  "oid": "2.23.43.1.4.3",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 163,
    "degree": 163,
    "poly": [
      {
        "coeff": "0x01",
        "power": 163
      },
      {
        "coeff": "0x01",
        "power": 7
      },
      {
        "coeff": "0x01",
        "power": 6
      },
      {
        "coeff": "0x01",
        "power": 3
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x1"
    },
    "b": {
      "raw": "0x1"
    }
  },
  "generator": {
    "x": {
      "raw": "0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8"
    },
    "y": {
      "raw": "0x0289070fb05d38ff58321f2e800536d538ccdaa3d9"
    }
  },
  "order": "0x04000000000000000000020108a2e0cc0d99f8a5ef",
  "cofactor": "0x2",
  "aliases": [
    "nist/K-163",
    "secg/sect163k1",
    "x963/ansit163k1"
  ]
}

JSON