Generalized lexicographic multiobjective combinatorial optimization : application to cryptography

Zufiria Zatarain, Pedro Jose and Álvarez Cubero, José Antonio (2017). Generalized lexicographic multiobjective combinatorial optimization : application to cryptography. "Journal on Optimization", v. 27 (n. 4); pp. 2182-2201. ISSN 1052-6234. https://doi.org/10.1137/16M1107826.

Description

Title: Generalized lexicographic multiobjective combinatorial optimization : application to cryptography
Author/s:
  • Zufiria Zatarain, Pedro Jose
  • Álvarez Cubero, José Antonio
Item Type: Article
Título de Revista/Publicación: Journal on Optimization
Date: 2017
ISSN: 1052-6234
Volume: 27
Subjects:
Freetext Keywords: 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
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2015-67396-PUnspecifiedUnspecifiedRedes complejas: modelado, dinámica y aplicaciones

More information

Item ID: 50811
DC Identifier: http://oa.upm.es/50811/
OAI Identifier: oai:oa.upm.es:50811
DOI: 10.1137/16M1107826
Official URL: https://epubs.siam.org/doi/10.1137/16M1107826
Deposited by: Memoria Investigacion
Deposited on: 12 Sep 2018 15:51
Last Modified: 12 Sep 2018 15:51
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