Cellular Automata Encryption: the reverse algorithm, Z-parameter and chain-rules

Chain-rules are maximally chaotic cellular automata (CA) rules that can be constructed at random to provide a huge number of encryption keys – where the CA is run backwards to encrypt, forwards to decrypt. The methods are based on the 1D CA reverse algorithm for directly finding pre-images, and the resulting Z-parameter, and rely on the essential property that chain-rules have minimal in-degree in their basins of attraction, usually an in-degree of just one for larger systems.