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2018 | OriginalPaper | Chapter

Inversion of Mutually Orthogonal Cellular Automata

Authors : Luca Mariot, Alberto Leporati

Published in: Cellular Automata

Publisher: Springer International Publishing

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Abstract

Mutually Orthogonal Cellular Automata (MOCA) are sets of bipermutive CA which can be used to construct pairwise orthogonal Latin squares. In this work, we consider the inversion problem of pairs of configurations in MOCA. In particular, we design an algorithm based on coupled de Bruijn graphs which solves this problem for generic MOCA, without assuming any linearity on the underlying bipermutive rules. Next, we analyze the computational complexity of this algorithm, remarking that it runs in exponential time with respect to the diameter of the CA rule, but that it can be straightforwardly parallelized to yield a linear time complexity. As a cryptographic application of this algorithm, we finally show how to design a (2, n) threshold Secret Sharing Scheme (SSS) based on MOCA where any combination of two players can reconstruct the secret by applying our inversion algorithm.

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previous chapter CARPenter: A Cellular Automata Based Resilient Pentavalent Stream Cipher

next chapter Eroders and Proliferation: Repairing that Goes Wrong

Benjamin, A.T., Bennett, C.D.: The probability of relatively prime polynomials. Math. Mag. 80(3), 196–202 (2007)MathSciNetCrossRef

Betel, H., de Oliveira, P.P.B., Flocchini, P.: Solving the parity problem in one-dimensional cellular automata. Nat. Comput. 12(3), 323–337 (2013)MathSciNetCrossRef

Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, 1st edn, pp. 257–397. Cambridge University Press, New York. (2010)

Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical systems. Math. Syst. Theory 3(4), 320–375 (1969)MathSciNetCrossRef

Keedwell, A.D., Dénes, J.: Latin Squares and Their Applications. Elsevier, New York City (2015)MATH

Mariot, L.: Cellular automata, Boolean functions and combinatorial designs (2018). https://boa.unimib.it/bitstream/10281/199011/2/phd_unimib_701962.pdf

Mariot, L., Formenti, E., Leporati, A.: Constructing orthogonal Latin squares from linear cellular automata. CoRR abs/1610.00139 (2016)

Mariot, L., Formenti, E., Leporati, A.: Enumerating orthogonal Latin squares generated by bipermutive cellular automata. In: Dennunzio, A., Formenti, E., Manzoni, L., Porreca, A.E. (eds.) AUTOMATA 2017. LNCS, vol. 10248, pp. 151–164. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58631-1_12CrossRefMATH

Mariot, L., Leporati, A.: Sharing secrets by computing preimages of bipermutive cellular automata. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2014. LNCS, vol. 8751, pp. 417–426. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11520-7_43CrossRefMATH

10.

Mariot, L., Leporati, A., Dennunzio, A., Formenti, E.: Computing the periods of preimages in surjective cellular automata. Nat. Comput. 16(3), 367–381 (2017)MathSciNetCrossRef

11.

Mariot, L., Picek, S., Jakobovic, D., Leporati, A.: Evolutionary algorithms for the design of orthogonal Latin squares based on cellular automata. In: Proceedings of the Genetic and Evolutionary Computation Conference. GECCO 2017, 15–19 July 2017, Berlin, Germany, pp. 306–313 (2017)

12.

Mariot, L., Picek, S., Leporati, A., Jakobovic, D.: Cellular automata based s-boxes. Cryptogr. Commun. (2018). https://doi.org/10.1007/s12095-018-0311-8

13.

del Rey, Á.M., Mateus, J.P., Sánchez, G.R.: A secret sharing scheme based on cellular automata. Appl. Math. Comput. 170(2), 1356–1364 (2005)MathSciNetMATH

14.

Richardson, D.: Tessellations with local transformations. J. Comput. Syst. Sci. 6(5), 373–388 (1972)MathSciNetCrossRef

15.

Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRef

16.

Stinson, D.R.: Combinatorial Designs - Constructions and Analysis. Springer, New York (2004). https://doi.org/10.1007/b97564CrossRefMATH

17.

Sutner, K.: De Bruijn graphs and linear cellular automata. Complex Syst. 5(1), 19–30 (1991)MathSciNetMATH

18.

Tompa, M., Woll, H.: How to share a secret with cheaters. J. Cryptol. 1(2), 133–138 (1988)MathSciNetMATH

Title: Inversion of Mutually Orthogonal Cellular Automata
Authors: Luca Mariot
Alberto Leporati
Publisher: Springer International Publishing
Book: Cellular Automata
Print ISBN: 978-3-319-99812-1

Electronic ISBN: 978-3-319-99813-8

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-99813-8_33

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