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Curve41417

414-bit prime field TwistedEdwards curve.

Curve from https://cr.yp.to/talks/2013.09.16/slides-djb-20130916-a4.pdf


ax2+y21+dx2y2ax^2 + y^2 \equiv 1 + dx^2y^2

Parameters

NameValue
p0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef
a0x01
d0xe21
G(0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595, 0x22)
n0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79
h0x08


SAGE

p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef
K = GF(p)
a = K(0x01)
d = K(0xe21)
E = EllipticCurve(K, (K(-1/48) * (a^2 + 14*a*d + d^2),K(1/864) * (a + d) * (-a^2 + 34*a*d - d^2)))
def to_weierstrass(a, d, x, y):
return ((5*a + a*y - 5*d*y - d)/(12 - 12*y), (a + a*y - d*y -d)/(4*x - 4*x*y))
def to_twistededwards(a, d, u, v):
y = (5*a - 12*u - d)/(-12*u - a + 5*d)
x = (a + a*y - d*y -d)/(4*v - 4*v*y)
return (x, y)
G = E(*to_weierstrass(a, d, K(0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595), K(0x22)))
E.set_order(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79 * 0x08)
# This curve is a Weierstrass curve (SAGE does not support TwistedEdwards curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_twistededwards functions to convert the points.


JSON

{
"name": "Curve41417",
"desc": "Curve from https://cr.yp.to/talks/2013.09.16/slides-djb-20130916-a4.pdf",
"form": "TwistedEdwards",
"field": {
"type": "Prime",
"p": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffef",
"bits": 414
},
"params": {
"a": {
"raw": "0x01"
},
"d": {
"raw": "0xe21"
}
},
"generator": {
"x": {
"raw": "0x1a334905141443300218c0631c326e5fcd46369f44c03ec7f57ff35498a4ab4d6d6ba111301a73faa8537c64c4fd3812f3cbc595"
},
"y": {
"raw": "0x22"
}
},
"order": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffeb3cc92414cf706022b36f1c0338ad63cf181b0e71a5e106af79",
"cofactor": "0x08"
}

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