Pseudorandom generators based on Lucas Sequences

Abstract

Pseudo-random sequence generators are the heart of Stream-cipher systems. This work presents some design criteria for such generators. based on innovative methods. To this aim the Lucas Sequences, reduced modulo a prime p. are taken and suitably manipulated. Modular Exponentiation is the function used to attain the output sequences. The periodicity of the Lucas Sequences allows to define a lower bound for the period of the generated sequences; actually our purpose is to ensure that the sequences which are generated have a period greater than a prefixed value. Furthermore the cryptographic strength of these sequences relies on the one-wayness of the discrete logarithm problem.