Parameters of the Fastest Cryptographically Strong Twisted Edwards Curves

Twisted Edwards Curves Revisited

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature ...

Twisted Edwards Curves

This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and sh...

Mean value formulas for twisted Edwards curves

R. Feng, and H. Wu recently established a certain mean-value formula for the x-coordinates of the n-division points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at http://eprint.iacr.org/2009/586.pdf ). We prove a similar result for both the x and y-coordinates on a twisted Edwards elliptic curve.

Efficient Construction of Cryptographically Strong Elliptic Curves

Division Polynomials for Twisted Edwards Curves

This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the n-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation.