This paper deals with the theory and application of Cellular Automata (CA) for a class of block ciphers and stream ciphers. Based on CA state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme, These fundamental transformations are found to generate the simple (alternating) group of even permutations which in turn is a subgroup of the permutation group, These functions are implemented with a class of programmable cellular automata (PCA) built around rules 51, 153, and 195. Further, high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector (i.e., combining function) has been proposed as running key generators in stream ciphers, Both the schemes provide better security against different types of attacks. With a simple, regular, modular and cascadable structure of CA, hardware implementation of such schemes idealy suit VLSI implementation.>