We propose a reduced equation for hyperelliptic curves of genus 2 over finite fields F q of q elements with characteristic different from 2 and 5. We determine the number of isomorphism classes of genus-2 hyperelliptic curves having an F q-rational Weierstrass point. These results have applications to hyperelliptic curve cryptography.
Vaudenay's cryptanalysis to Chor-Rivest cryptosystem is not applicable if the parameters p and h of the finite field are both prime integers. This case is analyzed below and the parameters for which such cryptosys-tem is cryptographically interesting are listed. Regrettably the resulting cryptosystems are not very efficient in practice.
—Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhãskara (BB) equation. The BB equation is the quadratic Diophantine equation equation nx 2 + k = y 2 , where k is an integer and n is a positive integer such that √ n is irrational. For the particular case k = 1, the equation is called the Pell equation. The… (More)