Pseudorandom generators based on Lucas Sequences

A Di Porto, W Wolfowics


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.

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Copyright (c) 1993 Franco Eugeni

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.