Linear complexity of some sequences derived from hyperelliptic curves of genus 2

On the linear complexity profile of some sequences derived from elliptic curves

For a given elliptic curve E over a finite field of odd characteristic and a rational function f on E we first study the linear complexity profiles of the sequences f(nG), n = 1, 2, . . . which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many f where Hess and Shparlinski’s result does not apply. Moreover, we study the linear complexiti...

Weighted Coordinates on Genus 2 Hyperelliptic Curves

Isomorphism Classes of Hyperelliptic Curves of Genus 2 over Fq

We give the exact number and representatives of the isomorphism, which preserves infinity, classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2 in most cases. These results have applications to hyperelliptic curve cryptography.

Implementation of Tate Pairing on Hyperelliptic Curves of Genus 2

Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al[3] and Galbraith[8] provided efficient algorithms for Tate pairing on y = x − x + b in characteristic 3 and Duursma and Lee[6] gave a closed formula for Tate pairing on y = x − x + d in characteristic p. In this paper, we present completely general and expl...

Constructing hyperelliptic curves of genus 2 suitable for cryptography

In this article we show how to generalize the CM-method for elliptic curves to genus two. We describe the algorithm in detail and discuss the results of our implementation.