Sharing Secrets by Computing Preimages of Bipermutive Cellular Automata

A secret sharing scheme based on one-dimensional bipermutive cellular automata is discussed in this paper. The underlying idea is to represent the secret as a configuration of a bipermutive CA and to iteratively apply a preimage computation algorithm until a sufficiently long configuration to be splitted among the participants is obtained. The scheme is proved to be both perfect and ideal, and a simple extension is shown to induce a sequential access structure which eventually becomes cyclic, where the upper bound on the length of the cycles depends on the radius of the adopted local rule.