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 errorcorrection 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.

Mariot, L., Leporati, A. (2016). Resilient Vectorial Functions and Cyclic Codes Arising from Cellular Automata. In 12th International Conference on Cellular Automata for Research and Industry, ACRI 2016; Fez; Morocco; 5-8 September 2016 (pp.34-44). Springer Verlag [10.1007/978-3-319-44365-2_4].

Resilient Vectorial Functions and Cyclic Codes Arising from Cellular Automata

MARIOT, LUCA
Primo
;
LEPORATI, ALBERTO OTTAVIO
Ultimo
2016

Abstract

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 errorcorrection 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.
No
paper
Cellular automata, Boolean functions, S-boxes, Resiliency, Linear feedback shift registers, Cyclic codes, Hamming codes
English
International Conference on Cellular Automata for Research and Industry (ACRI) SEP 05-08
9783319443645
Mariot, L., Leporati, A. (2016). Resilient Vectorial Functions and Cyclic Codes Arising from Cellular Automata. In 12th International Conference on Cellular Automata for Research and Industry, ACRI 2016; Fez; Morocco; 5-8 September 2016 (pp.34-44). Springer Verlag [10.1007/978-3-319-44365-2_4].
Mariot, L; Leporati, A
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/131952
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
Social impact