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Due to inevitable power dissipation, it is said that nano-scaled computing devices should perform their computing processes in a reversible manner. This will be a large problem in constructing three-dimensional nano-scaled functional objects. Reversible cellular automata (RCA) are used for modeling physical phenomena such as power dissipation, by studying the dissipation of garbage signals. We construct a three-dimensional self-inspective self-reproducing reversible cellular automaton by extending the two-dimensional version SR(8). It can self-reproduce various patterns in three-dimensional reversible cellular space without dissipating garbage signals.

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We de ne a hexagonal partitioned cellular automaton (HPCA), and study logical universality of a reversible HPCA. We give a speci c 64-state reversible HPCA H 1 , and show that a Fredkin gate can be embedded in this cellular space. Since a Fredkin gate is known to be a universal logic element, logical universality of H 1 is concluded. Although the number of states of H 1 is greater than those of the previous models of reversible CAs having universality, the size of the con guration realizing a Fredkin gate is greatly reduced, and its local transition function is still simple. Comparison with the previous models, and open problems related to these model are also discussed.

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International audienceThe study of cellular automata rules suitable for cryptographic applications is under consideration. On one hand, cellular automata can be used to generate pseudo-random sequences as well as for the design of S-boxes in symmetric cryptography. On the other hand, Boolean functions with good properties like resiliency and non-linearity are usually obtained either by exhaustive search or by the use of genetic algorithms. We propose here to use some recent research in the classification of Boolean functions and to link it with the study of cellular automata rules. As a consequence of our technique, this also provides a mean to get Boolean functions with good cryptographic properties