Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.38
• j-invariant:
  1
• Trace of Frobenius:
  -148380926981691413899619140297051490364542574180493936232912339534208516828973111459843
• Discriminant:
  1
• Anomalous:
  false
• Supersingular:
  false

SAGE

F.<x> = GF(2)[]
K = GF(2^571, name="x", modulus= x^571 +  x^10 +  x^5 +  x^2 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001 * 0x4)
G = E(K.fetch_int(0x26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972), K.fetch_int(0x349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3))

JSON

{
  "name": "K-571",
  "desc": "Koblitz curve.",
  "oid": "1.3.132.0.38",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 571,
    "degree": 571,
    "poly": [
      {
        "coeff": "0x01",
        "power": 571
      },
      {
        "coeff": "0x01",
        "power": 10
      },
      {
        "coeff": "0x01",
        "power": 5
      },
      {
        "coeff": "0x01",
        "power": 2
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x26eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972"
    },
    "y": {
      "raw": "0x349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3"
    }
  },
  "order": "0x20000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001",
  "cofactor": "0x4",
  "aliases": [
    "secg/sect571k1",
    "x963/ansit571k1"
  ],
  "characteristics": {
    "j_invariant": "1",
    "anomalous": false,
    "discriminant": "1",
    "supersingular": false,
    "trace_of_frobenius": "-148380926981691413899619140297051490364542574180493936232912339534208516828973111459843"
  }
}