Designing bijective S-boxes using Algorithm Portfolios with limited time budgets

Abstract

Substitution boxes (S-boxes) are essential parts of symmetric-key cryptosystems. Designing S-boxes with satisfactory nonlinearity and autocorrelation properties is a challenging task for both theoretical algebraic methods and computational optimization algorithms. Algorithm Portfolios (APs) are algorithmic schemes where multiple copies of the same algorithm or different algorithms share the available computational resources, running concurrently or interchangeably on a number of processors. Recently, APs have gained increasing attention due to their remarkable efficiency in multidisciplinary applications. The present work is a preliminary study of parallel APs on the bijective S-boxes design problem. The proposed APs comprise two state-of-the-art heuristic algorithms, namely Simulated Annealing and Tabu Search, and they are parallelized according to the master-slave model without exchange of information among the constituent algorithms. The proposed APs are experimentally assessed on typical problem instances under limited time budgets. Different aspects of their performance is analyzed, suggesting that the considered APs are competitive in terms of solution quality and running time against their constituent algorithms as well as different approaches.