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B-283

283-bit binary field Weierstrass curve.
Also known as: sect283r1ansit283r1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m283
f(x) x^283 + x^12 + x^7 + x^5 + 1
a0x00000000000000000000000000000000000000000000000000000000000000000000001
b0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
G(0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053, 0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4)
n0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307
h0x2

Characteristics

  • OID:
    1.3.132.0.17
  • Seed:
    77E2B07370EB0F832A6DD5B62DFC88CD06BB84BE
  • j-invariant:
    627751430426462883238147702498843470781790640735057151432982237133924095803873168483
  • Trace of Frobenius:
    2863663306391796106224371145726066910599667
  • Discriminant:
    4821813576056072374006997780399081180312270030300601270120450341205914644378616963829
  • Anomalous:
    false
  • Supersingular:
    false
  • CM-discriminant:
    62165404551223330269422781018352605012557015986005158288261890887273791400499761341965
  • Conductor:
    1

SAGE

F.<x> = GF(2)[]
K = GF(2^283, name="x", modulus= x^283 + x^12 + x^7 + x^5 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5)))
E.set_order(0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 * 0x2)
G = E(K.fetch_int(0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053), K.fetch_int(0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4))


JSON

{
"name": "B-283",
"desc": "",
"oid": "1.3.132.0.17",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 283,
"degree": 283,
"poly": [
{
"coeff": "0x01",
"power": 283
},
{
"coeff": "0x01",
"power": 12
},
{
"coeff": "0x01",
"power": 7
},
{
"coeff": "0x01",
"power": 5
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x00000000000000000000000000000000000000000000000000000000000000000000001"
},
"b": {
"raw": "0x27b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5"
}
},
"generator": {
"x": {
"raw": "0x5f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053"
},
"y": {
"raw": "0x3676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4"
}
},
"order": "0x3ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307",
"cofactor": "0x2",
"aliases": [
"secg/sect283r1",
"x963/ansit283r1"
],
"characteristics": {
"seed": "77E2B07370EB0F832A6DD5B62DFC88CD06BB84BE",
"j_invariant": "627751430426462883238147702498843470781790640735057151432982237133924095803873168483",
"anomalous": false,
"cm_disc": "62165404551223330269422781018352605012557015986005158288261890887273791400499761341965",
"conductor": "1",
"discriminant": "4821813576056072374006997780399081180312270030300601270120450341205914644378616963829",
"supersingular": false,
"trace_of_frobenius": "2863663306391796106224371145726066910599667"
}
}

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