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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)

- R Ferreiro Pérez, J Muñoz Masqué
- 2005

The Pontryagin forms on 1-jet bundle of Riemannian metrics, are shown to provide, in a natural way, diffeomorphism-invariant pre-symplectic structures on the space of Riemannian metrics for dimensions n = 4r − 2. The equivariant Pontryagin forms provide canonical moment maps for these structures. In dimension two, the symplectic reduction corresponding to… (More)

Tseng et al. have introduced in 2003 an authenticated en-cryption scheme by using self-certified public keys. Based on this scheme several authors have proposed new signature schemes avoiding some attacks against the original proposal. In this paper we show that there is a weakness on all these schemes affecting both the authentication of the signer's… (More)