The aim of this paper is to reduce the number of operations in Cantor's algorithm for the Jacobian group of hyperelliptic curves for genus 4 in projective coordinates. Specifically, we developed explicit doubling and addition formulas for genus 4 hyperelliptic curves over binary fields with h(x) = 1. For these curves, we can perform a divisor doubling in… (More)
The aim of this paper is to make a contribution to the development of the new stronger cryptographic algorithm using chaotic systems and hyperelliptic curve. In this context, the Diffie-Hellman scheme is implemented with chaotic systems and ElGamal scheme is constructed with hyperelliptic curves. Futhermore, the complexity algorithm is determinated for… (More)
Recently, several research groups in cryptography have presented new elliptic curve model based on Edwards curves. These new curves were selected for their good performance and security perspectives. Cryptosystems based on elliptic curves in embedded devices can be vulnerable to Side-Channel Attacks (SCA), such as the Simple Power Analysis (SPA) or the… (More)
The aim of this paper is to development a very strong cryptographic systems using hyperelliptic Curves and Complete Synchronization for a Bidirectional Chaotic systems based on Lorenz attractor. Also performance simulations of SISO and MIMO systems over fading channels produce a benefit of 16dB for BER=10e −6 once the wireless channel is ensured.