Linear hybrid cellular automata (LHCA) rule 90/150 based S-box

Most modern block cipher today comprises of single nonlinear element which is called as substitution box. It comes with various of size depending on the cipher input and the secret key. Various methods have been proposed in order to construct it. In this paper, a new construction method has been proposed that is based on linear hybrid cellular automata (LHCA) iteration. There are specific number of combinations of rule 150 and rule 90 of elementary cellular automata (ECA) with two states and three neighborhoods that generate maximum cycle sequence which usually adapted as pseudo random number generator. However, the sequence is actually the permutation of finite elements which is suitable for the S-Box construction. Within this paper context, we manipulate the sequence by varying the initial condition to produce about 8192 different S-Box with different security level from 32 different rule combination. The maximum nonlinearity that we could achieve is 108 with differential uniformity value of 8. � BEIESP.