VLSI implementation of mod-p multipliers using homomorphisms and hybrid cellular automata

The VLSI implementation of mod-p multipliers, where p is prime, using homomorphisms and one-dimensional hybrid cellular automata (HCA) is presented. This new technique uses the maximum-length cycle produced by HCA, to realise implementation using the minimum possible number of cells in the array. A new theorem on homomorphisms shows how a cyclic group can be mapped into a state group of HCA, of smaller order, which can be implemented more simply than the original. The technique is demonstrated through the VLSI implementation of a modest, mod-127 multiplier.