Resilient Vectorial Functions and Cyclic Codes Arising from Cellular Automata

  • Luca Mariot
  • Alberto Leporati
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9863)


Most of the works concerning cryptographic applications of cellular automata (CA) focus on the analysis of the underlying local rules, interpreted as boolean functions. In this paper, we investigate the cryptographic criteria of CA global rules by considering them as vectorial boolean functions. In particular, we prove that the 1-resiliency property of CA with bipermutive local rules is preserved on the corresponding global rules. We then unfold an interesting connection between linear codes and cellular automata, observing that the generator and parity check matrices of cyclic codes correspond to the transition matrices of linear CA. Consequently, syndrome computation in cyclic codes can be performed in parallel by evolving a suitable linear CA, and the error-correction capability is determined by the resiliency of the global rule. As an example, we finally show how to implement the (7, 4, 3) cyclic Hamming code using a CA of radius \(r=2\).


Cellular automata Boolean functions S-boxes Resiliency Linear feedback shift registers Cyclic codes Hamming codes 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi Milano-BicoccaMilanoItaly
  2. 2.Laboratoire I3SUniversité Nice-Sophia AntipolisSophia AntipolisFrance

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