We shall discuss the idea of finding all rational points on a curve C by first finding an associated collection of curves whose rational points cover those of C. This classical ...
Constructing pairing-friendly hyperelliptic curves with small ρ-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe...
The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower...
Abstract. We answer a question asked by Hajdu and Tengely: The only arithmetic progression in coprime integers of the form (a2 , b2 , c2 , d5 ) is (1, 1, 1, 1). For the proof, we ...
Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suit...
Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe...