c2pnb163v3

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`
a0x07a526c63d3e25a256a007699f5447e32ae456b50e	`0x07a526c63d3e25a256a007699f5447e32ae456b50e`
b0x03f7061798eb99e238fd6f1bf95b48feeb4854252b	`0x03f7061798eb99e238fd6f1bf95b48feeb4854252b`
G(0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb, 0x5b935590c155e17ea48eb3ff3718b893df59a05d0)	`(0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb, 0x5b935590c155e17ea48eb3ff3718b893df59a05d0)`
n0x03fffffffffffffffffffe1aee140f110aff961309	`0x03fffffffffffffffffffe1aee140f110aff961309`
h0x2	`0x2`

Characteristics

OID:
1.2.840.10045.3.0.3
Seed:
50CBF1D95CA94D696E676875615175F16A36A3B8

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(0x07a526c63d3e25a256a007699f5447e32ae456b50e), 0, 0, K.fetch_int(0x03f7061798eb99e238fd6f1bf95b48feeb4854252b)))
E.set_order(0x03fffffffffffffffffffe1aee140f110aff961309 * 0x2)
G = E(K.fetch_int(0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb), K.fetch_int(0x5b935590c155e17ea48eb3ff3718b893df59a05d0))

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(0x07a526c63d3e25a256a007699f5447e32ae456b50e), 0, 0, K.fetch_int(0x03f7061798eb99e238fd6f1bf95b48feeb4854252b)))
E.set_order(0x03fffffffffffffffffffe1aee140f110aff961309 * 0x2)
G = E(K.fetch_int(0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb), K.fetch_int(0x5b935590c155e17ea48eb3ff3718b893df59a05d0))

SAGE

JSON

{
  "name": "c2pnb163v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.3",
  "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": "0x07a526c63d3e25a256a007699f5447e32ae456b50e"
    },
    "b": {
      "raw": "0x03f7061798eb99e238fd6f1bf95b48feeb4854252b"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb"
    },
    "y": {
      "raw": "0x5b935590c155e17ea48eb3ff3718b893df59a05d0"
    }
  },
  "order": "0x03fffffffffffffffffffe1aee140f110aff961309",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "50CBF1D95CA94D696E676875615175F16A36A3B8"
  }
}

{
  "name": "c2pnb163v3",
  "desc": "",
  "oid": "1.2.840.10045.3.0.3",
  "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": "0x07a526c63d3e25a256a007699f5447e32ae456b50e"
    },
    "b": {
      "raw": "0x03f7061798eb99e238fd6f1bf95b48feeb4854252b"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2f9f87b7c574d0bdecf8a22e6524775f98cdebdcb"
    },
    "y": {
      "raw": "0x5b935590c155e17ea48eb3ff3718b893df59a05d0"
    }
  },
  "order": "0x03fffffffffffffffffffe1aee140f110aff961309",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "50CBF1D95CA94D696E676875615175F16A36A3B8"
  }
}

JSON