Parameters

Characteristics

• OID:
  1.3.132.0.39
• Seed:
  2AA058F73A0E33AB486B0F610410C53A7F132310
• j-invariant:
  4214501753546941913223695905024629172637342244349568219783929342383426637975668846684512012478218604779111370893214803288669006084397110899225485839234972840008396689070376
• Trace of Frobenius:
  99534385013609758659469819150465382236412396452349171016760770327496674607579419075443
• Discriminant:
  2853329245261343535560086964181551296889298776106832980891560850944180011701123307905326019642652653533003482753023669016842884108172514870944140611113679225347419720217210
• 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(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a)))
E.set_order(0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 * 0x2)
G = E(K.fetch_int(0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19), K.fetch_int(0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b))

JSON

{
  "name": "sect571r1",
  "desc": "",
  "oid": "1.3.132.0.39",
  "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": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19"
    },
    "y": {
      "raw": "0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b"
    }
  },
  "order": "0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47",
  "cofactor": "0x2",
  "aliases": [
    "nist/B-571",
    "x963/ansit571r1"
  ],
  "characteristics": {
    "seed": "2AA058F73A0E33AB486B0F610410C53A7F132310",
    "j_invariant": "4214501753546941913223695905024629172637342244349568219783929342383426637975668846684512012478218604779111370893214803288669006084397110899225485839234972840008396689070376",
    "anomalous": false,
    "discriminant": "2853329245261343535560086964181551296889298776106832980891560850944180011701123307905326019642652653533003482753023669016842884108172514870944140611113679225347419720217210",
    "supersingular": false,
    "trace_of_frobenius": "99534385013609758659469819150465382236412396452349171016760770327496674607579419075443"
  }
}