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sect163r2

163-bit binary field Weierstrass curve.

A randomly generated curve. 'E was selected from S as specified in ANSI X9.62 X9.62 in normal basis representation and converted into polynomial basis representation.'


Also known as: B-163ansit163r2
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m163
f(x) x^163 + x^7 + x^6 + x^3 + 1
a0x000000000000000000000000000000000000000001
b0x020a601907b8c953ca1481eb10512f78744a3205fd
G(0x03f0eba16286a2d57ea0991168d4994637e8343e36, 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1)
n0x040000000000000000000292fe77e70c12a4234c33
h0x2

Characteristics

  • OID:
    1.3.132.0.15
  • Seed:
    85E25BFE5C86226CDB12016F7553F9D0E693A268
  • j-invariant:
    924715273381456531451948543458511393546700947074
  • Trace of Frobenius:
    -6224022517221266226059365
  • Discriminant:
    2982236234343851336267446656627785008148015875581
  • Anomalous:
    false
  • Supersingular:
    false
  • CM-discriminant:
    46768052394588893382517920870943573850256067434597
  • Conductor:
    1

SAGE

F.<x> = GF(2)[]
K = GF(2^163, name="x", modulus= x^163 + x^7 + x^6 + x^3 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x020a601907b8c953ca1481eb10512f78744a3205fd)))
E.set_order(0x040000000000000000000292fe77e70c12a4234c33 * 0x2)
G = E(K.fetch_int(0x03f0eba16286a2d57ea0991168d4994637e8343e36), K.fetch_int(0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1))


JSON

{
"name": "sect163r2",
"desc": "A randomly generated curve. 'E was selected from S as specified in ANSI X9.62 [X9.62] in normal basis representation and converted into polynomial basis representation.'",
"oid": "1.3.132.0.15",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 163,
"degree": 163,
"poly": [
{
"coeff": "0x01",
"power": 163
},
{
"coeff": "0x01",
"power": 7
},
{
"coeff": "0x01",
"power": 6
},
{
"coeff": "0x01",
"power": 3
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x000000000000000000000000000000000000000001"
},
"b": {
"raw": "0x020a601907b8c953ca1481eb10512f78744a3205fd"
}
},
"generator": {
"x": {
"raw": "0x03f0eba16286a2d57ea0991168d4994637e8343e36"
},
"y": {
"raw": "0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1"
}
},
"order": "0x040000000000000000000292fe77e70c12a4234c33",
"cofactor": "0x2",
"aliases": [
"nist/B-163",
"x963/ansit163r2"
],
"characteristics": {
"seed": "85E25BFE5C86226CDB12016F7553F9D0E693A268",
"j_invariant": "924715273381456531451948543458511393546700947074",
"anomalous": false,
"cm_disc": "46768052394588893382517920870943573850256067434597",
"conductor": "1",
"discriminant": "2982236234343851336267446656627785008148015875581",
"supersingular": false,
"trace_of_frobenius": "-6224022517221266226059365"
}
}

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