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w-512-mont

512-bit prime field Weierstrass curve.

Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.


y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a0xfe14fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
b0x185ed
n0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff638a8d792ee750298064aaf0b8498e61df3d3995064ed73b939628f17e98fdc9
h0x01


SAGE

p = 0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0xfe14fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc)
b = K(0x185ed)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff638a8d792ee750298064aaf0b8498e61df3d3995064ed73b939628f17e98fdc9 * 0x01)

PARI/GP

p = 0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a = Mod(0xfe14fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc, p)
b = Mod(0x185ed, p)
E = ellinit([a, b])
E[16][1] = 0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff638a8d792ee750298064aaf0b8498e61df3d3995064ed73b939628f17e98fdc9 * 0x01
\\ No generator defined

JSON

{
"name": "w-512-mont",
"desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"bits": 512
},
"params": {
"a": {
"raw": "0xfe14fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc"
},
"b": {
"raw": "0x185ed"
}
},
"order": "0xfe14ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff638a8d792ee750298064aaf0b8498e61df3d3995064ed73b939628f17e98fdc9",
"cofactor": "0x01"
}

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