Searching for a Cryptographic Model Based on the Pre-Image Calculus of Cellular Automata

Macedo, H.B.Lima, M.J.L.Oliveira, G.M.B.

Several cryptographic models based on cellular automata (CA) have been investigated in the literature. The parallel processing nature of CA is one of the major motivations to study them as fast ciphering and deciphering algorithms. This paper investigates the viability of using the reverse algorithm that performs pre-image calculus as a cipher method. Therefore, in the approach investigated here the ciphering process is accomplished by interacting CA lattice backward. This idea is similar to Gutowitz's model in which a kind of pre-image calculus is used to cipher the plaintext, while the CA is interacted forward to recover the original lattice starting from the ciphertext. In this previous model the ciphertext increases as the CA interacts backward. Here we are interested to use the reverse algorithm because it keeps the pre-image in a fixed size. The viability of this algorithm to ciphering is based on the prerogative that all lattice configurations have at least one pre-image. Therefore, we investigate if it is possible to find rule sets that guaranty the existence of one pre-image for any arbitrary lattice. The results show that Z parameter, join with its components Zleft and Zright, and the symmetry level (S) of the output bits of the rule transition can be used to specify rules with this desirable characteristic. Theses rule sets were found by using genetic algorithms.

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