Maximum length cellular automaton sequences and its application

Abstract

In this paper, the maximum length linear binary cellular automaton (CA) sequence is considered. It is shown that all possible maximum length linear binary CA sequences, which are equivalent to maximum length linear binary feedback shift register (LFSR) sequences, can be constructed using linear simple CAs. A table of configurations of the n-cell maximum length simple CAs with its characteristic polynomials is obtained for 76 ⩽ n ⩽ 120. An application of the CAs to stream ciphers is indicated. In other applications, a maximum length LFSR may be replaced by a maximum length linear binary CA.