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w-511-mers

511-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
p0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1f
a0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1c
b0x879da
n0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dbefa3f5ed9d839a2d4fe6ff516e87fa8d3e656a0f99fa1f0105f73b3b9d19f
h0x01


SAGE

p = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1f
K = GF(p)
a = K(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1c)
b = K(0x879da)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dbefa3f5ed9d839a2d4fe6ff516e87fa8d3e656a0f99fa1f0105f73b3b9d19f * 0x01)

PARI/GP

p = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1f
a = Mod(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1c, p)
b = Mod(0x879da, p)
E = ellinit([a, b])
E[16][1] = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dbefa3f5ed9d839a2d4fe6ff516e87fa8d3e656a0f99fa1f0105f73b3b9d19f * 0x01
\\ No generator defined

JSON

{
"name": "w-511-mers",
"desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1f",
"bits": 511
},
"params": {
"a": {
"raw": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe1c"
},
"b": {
"raw": "0x879da"
}
},
"order": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff8dbefa3f5ed9d839a2d4fe6ff516e87fa8d3e656a0f99fa1f0105f73b3b9d19f",
"cofactor": "0x01"
}

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