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Design and Analysis of Some Cryptographically Robust Non-uniform Nonlinear Cellular Automata
Sandip Karmakar and Dipanwita Roy Chowdhury

Cellular Automata (CA) are studied as pseudo-random sequence generators. Pseudo-random sequence generation is the key to any cryptographic system. This paper investigates the merit of some special types of CA in cryptographic applications. It is argued that linear CA are not suitable for cryptography. Non-linear CA show high correlation. Hence, we have constructed a few non-uniform, nonlinear CA. We have modelled CA as Boolean function generators and analyzed the important cryptographic properties like balanced-ness, nonlinearity, resiliency and algebraic degree of the Boolean functions over iterations. Further, a newly proposed test on Boolean functions for cryptographic suitability, namely d-monomial test is experimented on those CA configurations. We have come up with three CA that are expected to be cryptographically good pseudo-random generators, when certain limitations are taken care of.

Keywords: Cellular automata, non-uniform nonlinear CA, cryptographic properties of cellular automata, pseudo-randomness, d-monomial test, cryptography

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