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B-233

233-bit binary field Weierstrass curve.
Also known as: sect233r1wap-wsg-idm-ecid-wtls11ansit233r1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m233
f(x) x^233 + x^74 + 1
a0x000000000000000000000000000000000000000000000000000000000001
b0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
G(0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b, 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052)
n0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
h0x2

Characteristics

  • OID:
    1.3.132.0.27
  • Seed:
    74D59FF07F6B413D0EA14B344B20A2DB049B50C3
  • j-invariant:
    4307676474001897771242333711874131057278497100044075715856582737706846
  • Trace of Frobenius:
    -206777407530349254000433718821372333
  • Discriminant:
    2760497980029204187078845502377898520307707256259003964398570147123373
  • Anomalous:
    false
  • Supersingular:
    false
  • CM-discriminant:
    6134885641591612255497560766468467091820697700856927382414879179085189
  • Conductor:
    3

SAGE

F.<x> = GF(2)[]
K = GF(2^233, name="x", modulus= x^233 + x^74 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad)))
E.set_order(0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 * 0x2)
G = E(K.fetch_int(0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b), K.fetch_int(0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052))


JSON

{
"name": "B-233",
"desc": "",
"oid": "1.3.132.0.27",
"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": "0x000000000000000000000000000000000000000000000000000000000001"
},
"b": {
"raw": "0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad"
}
},
"generator": {
"x": {
"raw": "0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b"
},
"y": {
"raw": "0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052"
}
},
"order": "0x1000000000000000000000000000013e974e72f8a6922031d2603cfe0d7",
"cofactor": "0x2",
"aliases": [
"secg/sect233r1",
"wtls/wap-wsg-idm-ecid-wtls11",
"x963/ansit233r1"
],
"characteristics": {
"seed": "74D59FF07F6B413D0EA14B344B20A2DB049B50C3",
"j_invariant": "4307676474001897771242333711874131057278497100044075715856582737706846",
"anomalous": false,
"cm_disc": "6134885641591612255497560766468467091820697700856927382414879179085189",
"conductor": "3",
"discriminant": "2760497980029204187078845502377898520307707256259003964398570147123373",
"supersingular": false,
"trace_of_frobenius": "-206777407530349254000433718821372333"
}
}

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