On the existence of (9,3,5,240) resilient functions

Saber, Z.; Uddin, Mohammad Faisal; Youssef, Amr M.

doi:10.1109/tit.2006.872862

Cited by 16 publications

(12 citation statements)

References 8 publications

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“…EA and other nature-inspired optimization heuristics such as swarm intelligence algorithms have been extensively used to optimize the cryptographic properties of Boolean functions. Examples include Genetic Algorithms (GA) [33,24,21], Genetic Programming (GP) [6,13,34] and Particle Swarm Optimization (PSO) [36,25]. Most of these works usually focus on the use of EA and swarm intelligence algorithms as alternative constructions of Boolean functions with good cryptographic properties.…”

Section: Evolutionary Searchmentioning

confidence: 99%

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Mariot¹,

Saletta²,

Leporati³

et al. 2021

Preprint

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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, 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.

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Section: Evolutionary Searchmentioning

confidence: 99%

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Mariot¹,

Saletta²,

Leporati³

et al. 2021

Preprint

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“…Kavut, Maitra, and Yücel [34] (240, 7, 4, −24, −354176) Saber, Uddin, and Youssef [48] (240, 5, 4, −160, −524288) Read [47] (240, 5, 3, −32, −524288) Burnett [10] (240, 5, 4, −128, −524288) Stanicȃ and Sung [50] (240, 2, 2, −512, −524288) Misty 1 and KASUMI 9 × 9 S-box [1] (240, 2, 2, −512, −524288) Table 3 Comparison of profiles with n = 11, I = 0.…”

Section: Authors Profilementioning

confidence: 99%

“…These properties are characterized via several relevant criteria from the cryptographic perspective [43], usually posing a trade-off between them [19,36,11,54,51,16], so that the resultant design of robust Boolean functions looks for a compromise among these criteria [17,20,33,41,24,18,1,10,34,48,47,50,35,14,38,4,49,52]. The systematic selection of such criteria (not to mention the determination of their relative relevance) is an open issue in the existing literature on the subject matter.…”

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confidence: 99%

Generalized Lexicographic MultiObjective Combinatorial Optimization. Application to Cryptography

Zufiria¹,

Álvarez-Cubero²

2017

SIAM J. Optim.

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Abstract. This paper formalizes a family of prioritized multicriteria optimization problems and assesses the corresponding up-to-date known suboptimal solutions. The resulting framework is then employed to characterize and search for Boolean functions which are valuable for a robust symmetric (mainly block) cipher design. The proposed optimality definitions generalize the lexicographic method by establishing an ordered sequence of multiobjective combinatorial optimization problems, which, in turn, gathers the relative relevance of the criteria, so that the optimal solutions can be obtained from a sequential application of the Pareto efficiency. The relationship among the different formulable problems is characterized in terms of both their respective solutions sets and computing costs. Since, in practice, only a limited set of functions can be evaluated (i.e., are known), the best known Pareto efficient functions are also defined. Finally, this framework is employed to obtain new functions having known (Pareto) maximal robustness against linear, differential, randomness-based, interpolation, algebraic and correlation attacks.Key words. Pareto efficiency, combinatorial optimization, block cipher, S-box, balancedness, nonlinearity, algebraic degree, algebraic immunity, absolute indicator, sums-of-squares indicator, correlation immunity order, propagation criterion degree AMS subject classifications. 90C27, 90C29, 68P25, 4904 DOI. 10.1137/16M11078261. Introduction. In recent decades, multicriteria optimization (also known as multiobjective optimization or, in a more general setting, vector optimization) has become an expansive and mature field of research [9,21,28,32]. When operating in such a vast arena, different subfields can be considered depending on the mathematical structures in both the search and criteria sets and the analytical properties of the criteria (or cost) functions. In this framework, multiobjective combinatorial optimization (MOCO) addresses those problems wherein the search set is discrete, usually finite but huge, such that an exhaustive search is not computationally viable.The solution of a multiobjective problem is executed through the following two stages: the proper determination of the optimal solutions set and the multicriteria decision-making among the existing solutions, where preferences among the criteria play an important role. Accordingly, the most established classification of multiobjective techniques relies on the different manners of articulation of such preferences between those two stages: a priori (make decisions before searching), a posteriori (search before making decisions), and progressive (integrating search and decision [21]). In this context, the definition of user preferences among criteria and its application to the efficient design of evolutionary algorithms has been extensively addressed [8,7,23,22,25,26,30,46,53].

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“…Both aforementioned constructions depend on the nonlinear functions h i and h. Note that (9,3,5,240) [16] and (15, 1, -, 2 14 -2 6 -2 5 -2 4 -2 3 ) [17] functions are available. Based on the functions obtained in Examples 1 and 2, we obtain some new functions with good nonlinearity as follows.…”

Section: Remarkmentioning

confidence: 99%

Construction of resilient Boolean functions with high nonlinearity and good algebraic degree

Zhang

2015

Security Comm Networks

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Resilient Boolean functions with high nonlinearity and good algebraic properties play an important role in designing certain stream cipher schemes. In this paper, two construction methods are proposed to obtain such functions. It is shown that a class of resilient functions with high algebraic degree and currently best known nonlinearity can be constructed by using our technique. The algebraic immunity of the constructed functions is also analyzed.Maitra and Pasalic provided a generalized construction method for m-resilient functions in [8]. We first recall this construction that will play an important role in our paper.Security Comm. Networks (2015)

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On the existence of (9,3,5,240) resilient functions

Cited by 16 publications

References 8 publications

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Heuristic Search of (Semi-)Bent Functions based on Cellular Automata

Generalized Lexicographic MultiObjective Combinatorial Optimization. Application to Cryptography

Construction of resilient Boolean functions with high nonlinearity and good algebraic degree

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