- author = "Luca Mariot",
- title = "Cellular automata, boolean functions and combinatorial designs",
- title_fr = "Automates cellulaires, fonctions booleennes et dessins combinatoires",
- school = "Laboratoire d'Informatique, Signaux et Systemes de Sophia Antipolis (I3S), COMUE Universite Cote d'Azur and Universita degli studi di Milano - Bicocca",
- year = "2018",
- address = "France and Italy",
- month = Mar,
- keywords = "genetic algorithms, genetic programming, Cellular automata, Latin squares, S-boxes, Boolean functions, Fonctions booleennes, Automates cellulaires, S-boxes, Carres latins, automi cellulari, funzioni booleane, S-boxes, quadrati latini",
- hal_id = "tel-01812051",
- hal_version = "v1",
- number = "2018AZUR4011",
-
URL = "
https://theses.hal.science/tel-01812051",
-
URL = "https://theses.hal.science/tel-01812051v1/bibtex",
-
URL = "
https://theses.hal.science/tel-01812051v1/file/2018AZUR4011.pdf",
- size = "253 pages",
- abstract = "The goal of this thesis is the investigation of Cellular Automata (CA) from the perspective of Boolean functions and combinatorial designs. Beside its theoretical interest, this research finds its motivation in cryptography, since Boolean functions and combinatorial designs are used to construct Pseudo random Number Generators (PRNG) and Secret Sharing Schemes (SSS). The results presented in the thesis are developed along three research lines, organized as follows. The first line considers the use of heuristic optimization algorithms to search for Boolean functions with good cryptographic properties, to be used as local rules in CA-based PRNG. The main motivation is to improve Wolfram's generator based on rule 30, which has been shown to be vulnerable against two cryptanalytic attacks. The second line deals with vectorial Boolean functions induced by CA global rules. The first contribution considers the period of preimages of spatially periodic configurations in surjective CA, and analyze the cryptographic properties of CA global rules. The third line focuses on the combinatorial designs generated by CA, specifically considering Orthogonal Latin Squares (OLS), which are equivalent to SSS. In particular, an algebraic characterization of OLS generated by linear CA is given, and heuristic algorithms are used to build OLS based on nonlinear CA.",
-
notes = "French National Number(NNT) 2018AZUR4011
Supervisors: Alberto Leporati and Enrico Formenti",
