Finite fields and cryptology

Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics

In this paper, we present a classification of classes of elliptic curves defined over cubic extension of finite fields with odd characteristics, which have coverings over the finite fields therefore can be attacked by the GHS attack. We then show the density of these weak curves with hyperelliptic and non-hyperelliptic coverings respectively. In particular, we shown for elliptic curves defined ...

Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields

A simple generalization of El-Gamal cryptosystem to non-abelian groups

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equi...

Number of Jacobi quartic curves over finite fields

In this paper the number of Fq-isomorphism classes of Jacobi quartic curves, i.e., the number of Jacobi quartic curves with distinct jinvariants, over finite field Fq is enumerated.

A remark on the computation of cube roots in finite fields

We consider the computation of cube roots in finite fields. For the computation of square roots in finite fields, there are two typical methods; the Tonelli-Shanks method [9, 12] and the Cipolla-Lehmer method [4, 6]. The former can be extended easily to the case of r-th roots, which is called the Adleman-Manders-Miller method [1], but it seems to be difficult to extend the latter to more genera...

A Versatile Multi-Input Multiplier over Finite Fields

Multiplication of three elements over finite fields is used extensively in multivariate public key cryptography and solving system of linear equations over finite fields. This contribution shows the enhancements of multiplication of three elements over finite fields by using specific architecture. We firstly propose a versatile multi-input multiplier over finite fields. The parameters of this m...