Skip to main content

Search

## ed-255-mers

255-bit prime field TwistedEdwards curve.

Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.

$ax^2 + y^2 \equiv 1 + dx^2y^2$

### Parameters

NameValue
p0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03
a0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd02
d0xea97
n0x1fffffffffffffffffffffffffffffffdcf1a785eda6832eac49d1ed0436eb75
h0x04

### SAGE

p = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03K = GF(p)a = K(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd02)d = K(0xea97)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)# No generator definedE.set_order(0x1fffffffffffffffffffffffffffffffdcf1a785eda6832eac49d1ed0436eb75 * 0x04)# 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": "ed-255-mers",  "desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",  "form": "TwistedEdwards",  "field": {    "type": "Prime",    "p": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03",    "bits": 255  },  "params": {    "a": {      "raw": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd02"    },    "d": {      "raw": "0xea97"    }  },  "order": "0x1fffffffffffffffffffffffffffffffdcf1a785eda6832eac49d1ed0436eb75",  "cofactor": "0x04"}

© 2020 Jan Jancar | Built with Dox theme for Gatsby