Autômatos celulares unidimensionais caóticos com borda fixa aplicados à modelagem de um sistema criptográfico para imagens digitais

Abstract

Resumo: O principal objetivo da criptografia de dados é possibilitar que duas entidades se comuniquem ao longo de um canal inseguro, de tal forma que nenhuma outra entidade consiga decifrar a mensagem que é enviada. Muitos métodos de criptografia clássica já foram investigados para minimizar este problema. Uma nova abordagem para este tema são os Autômatos Celulares (ACs), atualmente estudados por sua capacidade de processar grandes volumes de dados em paralelo. Nesse trabalho é investigado um novo modelo de autômato celular para criptografia de imagens, que tem como característica o uso do cálculo de pré-imagens a partir de chaves caóticas. O modelo é denominado Border Chaotic Cellular Automata (BCCA) para cifragem. Resultados mostraram que o modelo tem grande potencial para a realização de cifragem de grandes volumes de dados.Palavras-chave: autômatos celulares, cálculo de pré-imagens, criptografia de imagens, processamento paralelo

A reversible system based on hybrid toggle radius-4 cellular automata and its application as a block cipher

“…The first suggestion about the employment of cellular automata models in cryptography was made by Wolfram [Wolfram (1985)], after his studies on the statistical properties of CA chaotic rules with radius 1, which can be used as pseudo-random number generators [Wolfram (1986)]. Since then, various studies on this topic have been made [Tomassini and Perrenoud (2000); Sen et al (2002); Vasantha et al (2015); Oliveira and Macêdo (2019); Benkiniouar and Benmohamed (2004); Nandi et al (1994); Gutowitz (1995); Oliveira et al (2004Oliveira et al ( , 2008Oliveira et al ( , 2010b; Silva et al (2016); Wolfram (1985); Wuensche (2008); Oliveira et al (2010a); Wuensche and Lesser (1992); Seredynski et al (2004); Yang et al (2016)], where the cryptographic models can be classified into three kinds of approaches.…”

“…However, since there is no guarantee of pre-image existence for all possible rule transitions, the major challenge in these previous models was to evaluate the characteristics of the rules to assure the existence of at least one pre-image for any possible lattice. An attempt to solve this problem was to use the Z parameter [Silva et al (2016)] in the rule specification. The method proposed in [Wuensche (2008)] is very similar to the initial method proposed in [Oliveira et al (2008)], despite being developed independently.…”

“…This specification was deeper investigated in [Oliveira et al (2010c)] and [Oliveira et al (2011)]. Additionally, a cryptographic model that employs a lattice with a fixed extra boundary was investigated in [Silva et al (2016)], which applies the reverse algorithm proposed by Wolfram. Even though the lattice increase is smaller than in Gutowitz's model, the final lattice is still larger than the plaintext, which increases the cost of sending encrypted in-formation, in addition to the aperiodic condition of the lattice hindering the good propagation of disturbances.…”

“…Even though later models, also based on CA toggle rules, sought to reduce these problems [Wuensche (2008); Oliveira et al (2004Oliveira et al ( , 2008Oliveira et al ( , 2010b; Silva et al (2016)], the solution proposed here is the only one that guarantees an appropriate propagation of the disturbance over the entire lattice, as well as keeping the size of the ciphertext the same as the plaintext. Aiming at ensuring a good perturbation propagation, the model investigated here uses a lattice with a periodic boundary condition, which allows a simple 1-bit disturbance to be propagated throughout the entire lattice, regardless of the position where this perturbation occurs and the direction of the rule sensitivity.…”