A software system which uses a specially designed cellular automaton network to perform symmetric-key encryptions and decryptions of user-supplied input messages. The input messages are in the form of text or images or audio data. A mathematical function based on Fibonacci sequences in the complex domain is used to define interactions among the cells of the cellular automaton network. The outputs of the system are encryptions of the user inputs; a simple key inversion procedure enables the decrypting of the encrypted output. The system permits multiple encryptions of the input and this, in turn, requires multiple decryptions to obtain the original input.