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K-233

233-bit binary field Weierstrass curve.

Koblitz curve.


Also known as: sect233k1wap-wsg-idm-ecid-wtls10ansit233k1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m233
f(x) x^233 + x^74 + 1
a0x000000000000000000000000000000000000000000000000000000000000
b0x000000000000000000000000000000000000000000000000000000000001
G(0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126, 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3)
n0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf
h0x4

Characteristics

  • OID:
    1.3.132.0.26
  • j-invariant:
    1
  • Trace of Frobenius:
    -137381546011108235394987299651366779
  • Discriminant:
    1
  • Anomalous:
    false
  • Supersingular:
    false
  • CM-discriminant:
    6134885641591612255497560766468467084110046420941258648476388160195683

SAGE

F.<x> = GF(2)[]
K = GF(2^233, name="x", modulus= x^233 + x^74 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf * 0x4)
G = E(K.fetch_int(0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126), K.fetch_int(0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3))


JSON

{
"name": "K-233",
"desc": "Koblitz curve.",
"oid": "1.3.132.0.26",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 233,
"degree": 233,
"poly": [
{
"coeff": "0x01",
"power": 233
},
{
"coeff": "0x01",
"power": 74
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x000000000000000000000000000000000000000000000000000000000000"
},
"b": {
"raw": "0x000000000000000000000000000000000000000000000000000000000001"
}
},
"generator": {
"x": {
"raw": "0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126"
},
"y": {
"raw": "0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3"
}
},
"order": "0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf",
"cofactor": "0x4",
"aliases": [
"secg/sect233k1",
"wtls/wap-wsg-idm-ecid-wtls10",
"x963/ansit233k1"
],
"characteristics": {
"j_invariant": "1",
"anomalous": false,
"cm_disc": "6134885641591612255497560766468467084110046420941258648476388160195683",
"discriminant": "1",
"supersingular": false,
"trace_of_frobenius": "-137381546011108235394987299651366779"
}
}

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