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Fp254BNb

254-bit prime field Weierstrass curve.

Curve used in https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf


Also known as: bn254
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0x2523648240000001ba344d80000000086121000000000013a700000000000013
a0x00
b0x02
G(0x2523648240000001ba344d80000000086121000000000013a700000000000012, 0x01)
n0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d
h0x01

Characteristics

  • j-invariant:
    0
  • Trace of Frobenius:
    129607518034317099905336561907183648775
  • Discriminant:
    16798108731015832284940804142231733909889187121439069848933715426072753862995
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    12
  • CM-discriminant:
    67192434924063329139763216568926935639427140967721962295829525142383831810117
  • Conductor:
    1

SAGE

p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
K = GF(p)
a = K(0x00)
b = K(0x02)
E = EllipticCurve(K, (a, b))
G = E(0x2523648240000001ba344d80000000086121000000000013a700000000000012, 0x01)
E.set_order(0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d * 0x01)

PARI/GP

p = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
a = Mod(0x00, p)
b = Mod(0x02, p)
E = ellinit([a, b])
E[16][1] = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d * 0x01
G = [Mod(0x2523648240000001ba344d80000000086121000000000013a700000000000012, p), Mod(0x01, p)]

JSON

{
"name": "Fp254BNb",
"desc": "Curve used in https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x2523648240000001ba344d80000000086121000000000013a700000000000013",
"bits": 254
},
"params": {
"a": {
"raw": "0x00"
},
"b": {
"raw": "0x02"
}
},
"generator": {
"x": {
"raw": "0x2523648240000001ba344d80000000086121000000000013a700000000000012"
},
"y": {
"raw": "0x01"
}
},
"order": "0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d",
"cofactor": "0x01",
"aliases": [
"bn/bn254"
],
"characteristics": {
"j_invariant": "0",
"anomalous": false,
"cm_disc": "67192434924063329139763216568926935639427140967721962295829525142383831810117",
"conductor": "1",
"discriminant": "16798108731015832284940804142231733909889187121439069848933715426072753862995",
"embedding_degree": "12",
"torsion_degrees": [
{
"full": 3,
"least": 3,
"r": 2
},
{
"full": 2,
"least": 2,
"r": 3
},
{
"full": 8,
"least": 8,
"r": 5
},
{
"full": 6,
"least": 6,
"r": 7
}
],
"supersingular": false,
"trace_of_frobenius": "129607518034317099905336561907183648775"
}
}

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