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E-222

222-bit prime field Edwards curve.

Curve from https://eprint.iacr.org/2013/647.pdf


x2+y2c2(1+dx2y2)x^2 + y^2 \equiv c^2 (1 + dx^2y^2)

Parameters

NameValue
p0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b
c0x01
d0x27166
G(0x19b12bb156a389e55c9768c303316d07c23adab3736eb2bc3eb54e51, 0x1c)
n0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf
h0x04


SAGE

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b
K = GF(p)
d = K(0x27166)
E = EllipticCurve(K, (0, K(2 * (1 + d)/(1 - d)^2), 0, K(1/(1 - d)^2), 0))
E.set_order(0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf * 0x04)
# This curve is a Weierstrass curve (SAGE does not support Edwards curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_edwards functions to convert the points.


JSON

{
"name": "E-222",
"desc": "Curve from https://eprint.iacr.org/2013/647.pdf",
"form": "Edwards",
"field": {
"type": "Prime",
"p": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffff8b",
"bits": 222
},
"params": {
"c": {
"raw": "0x01"
},
"d": {
"raw": "0x27166"
}
},
"generator": {
"x": {
"raw": "0x19b12bb156a389e55c9768c303316d07c23adab3736eb2bc3eb54e51"
},
"y": {
"raw": "0x1c"
}
},
"order": "0xffffffffffffffffffffffffffff70cbc95e932f802f31423598cbf",
"cofactor": "0x04"
}

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