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B-571

571-bit binary field Weierstrass curve.
Also known as: sect571r1ansit571r1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m571
f(x) x^571 + x^10 + x^5 + x^2 + 1
a0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
b0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
G(0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19, 0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b)
n0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47
h0x2

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(0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a)))
E.set_order(0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 * 0x2)
G = E(K.fetch_int(0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19), K.fetch_int(0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b))


JSON

{
"name": "B-571",
"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": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
},
"b": {
"raw": "0x2f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a"
}
},
"generator": {
"x": {
"raw": "0x303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19"
},
"y": {
"raw": "0x37bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b"
}
},
"order": "0x3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47",
"cofactor": "0x2",
"aliases": [
"secg/sect571r1",
"x963/ansit571r1"
],
"characteristics": {
"seed": "2AA058F73A0E33AB486B0F610410C53A7F132310",
"j_invariant": "4214501753546941913223695905024629172637342244349568219783929342383426637975668846684512012478218604779111370893214803288669006084397110899225485839234972840008396689070376",
"anomalous": false,
"discriminant": "2853329245261343535560086964181551296889298776106832980891560850944180011701123307905326019642652653533003482753023669016842884108172514870944140611113679225347419720217210",
"supersingular": false,
"trace_of_frobenius": "99534385013609758659469819150465382236412396452349171016760770327496674607579419075443"
}
}
JSON

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