d -Monomial Tests of Nonlinear Cellular Automata for Cryptographic Design

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Abstract

Pseudorandom generation is a key to any cryptographic application. Linear Cellular Automata are known as good pseudorandom generators. However, for cryptographic applications nonlinearity is essential for its security. But, nonlinear Cellular Automaton shows high correlation between the input to the automaton and its generated sequence. Hence, for cryptography Cellular Automata rules need to be nonlinear as well as satisfy additional properties. With this motivation, in this paper, we analyze nonlinear Cellular Automata with a newly developed statistical measure called d-monomial test. Finally, we propose a process of d-monomial characteristics addition to get cryptographically suitable Cellular Automata.