Curve41417
414-bit prime field TwistedEdwards curve.Parameters
SAGE
p = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffefK = 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"}