Analysis of 90/150 CA Corresponding to the Power of Irreducible Polynomials
Un-Sook Choi, Sung-Jin Cho, Han-Doo Kim and Min-Jeong Kwon
Cattell et al. [3] and Cho et al. [7] showed that irreducible polynomials are CA-polynomials. However, it is unknown whether the power of a given irreducible polynomial is a CA-polynomial or not. In this paper, we show that all the powers of a given irreducible polynomial are CA-polynomials. Also we show that the number of 90/150 CA corresponding to [p(x)]m(m ≥ 1) is just two, where p(x) is an irreducible polynomial of degree greater than or equal to 2. And we propose a method of synthesizing 90/150 CA corresponding to [p(x)]m. This is an extension of the results of Cattell et al. [3], Cho et al. [6, 7], and Sabater et al. [1]. These 90/150 CA are applicable to model several nonlinear keystream generators with practical applications in symmetric cryptography, etc.
Keywords: Cellular automata, CA-polynomial, 90/150 CA, irreducible polynomial, power of irreducible polynomials.