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w-254-mont

254-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
p0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
b-0x2f72
n0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f
h0x01


SAGE

p = 0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc)
b = K(-0x2f72)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f * 0x01)

PARI/GP

p = 0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a = Mod(0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc, p)
b = Mod(-0x2f72, p)
E = ellinit([a, b])
E[16][1] = 0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f * 0x01
\\ No generator defined

JSON

{
"name": "w-254-mont",
"desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"bits": 254
},
"params": {
"a": {
"raw": "0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc"
},
"b": {
"raw": "-0x2f72"
}
},
"order": "0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f",
"cofactor": "0x01"
}

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