An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter.

Mariot, L., Saletta, M., Leporati, A., Manzoni, L. (2022). Heuristic search of (semi-)bent functions based on cellular automata. NATURAL COMPUTING, 21(3), 377-391 [10.1007/s11047-022-09885-3].

Heuristic search of (semi-)bent functions based on cellular automata

Mariot L.
;
Saletta M.;Leporati A.;
2022

Abstract

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter.
Articolo in rivista - Articolo scientifico
Bent functions; Cellular automata; Combinatorial search; Evolutionary strategies; Nonlinearity; Symmetric cryptography;
English
20-mag-2022
2022
21
3
377
391
none
Mariot, L., Saletta, M., Leporati, A., Manzoni, L. (2022). Heuristic search of (semi-)bent functions based on cellular automata. NATURAL COMPUTING, 21(3), 377-391 [10.1007/s11047-022-09885-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/408489
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