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Problems and their solutions of the Fifth International Students' Olympiad in cryptography NSUCRYPTO'2018 are presented. We consider problems related to attacks on ciphers and hash functions, Boolean functions, quantum circuits, Enigma, etc. We discuss several open problems on orthogonal arrays, Sylvester matrices, and disjunct matrices. The problem of existing an invertible Sylvester matrix whose inverse is again a Sylvester matrix was completely solved during the Olympiad. [ABSTRACT FROM AUTHOR]

In this paper we investigate the efficiency of two immunological algorithms (CLONALG and opt-IA) in the evolution of Boolean functions suitable for use in cryptography. Although in its nature a combinatorial problem, we experiment with two representations of solutions, namely, the bitstring and the floating point based representation. The immunological algorithms are compared with two commonly used evolutionary algorithms – genetic algorithm and evolution strategy. To thoroughly investigate these algorithms and representations, we use four different fitness functions that differ in the number of parameters and difficulty. Our results indicate that for smaller dimensions immunological algorithms behave comparable with evolutionary algorithms, while for the larger dimensions their performance is somewhat worse. When considering only immunological algorithms, opt-IA outperforms CLONALG in most of the experiments. The difference in the representation for those algorithms is also clear where floating point works better with smaller problem sizes and bitstring representation works better for larger Boolean functions. [ABSTRACT FROM AUTHOR]

The role of Boolean functions is prominent in several areas including cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged over the years. There are still many combinations of design criteria left unexplored and in this matter evolutionary computation can play a distinct role. This article concentrates on two scenarios for the use of Boolean functions in cryptography. The first uses Boolean functions as the source of the nonlinearity in filter and combiner generators. Although relatively well explored using evolutionary algorithms, it still presents an interesting goal in terms of the practical sizes of Boolean functions. The second scenario appeared rather recently where the objective is to find Boolean functions that have various orders of the correlation immunity and minimal Hamming weight. In both these scenarios we see that evolutionary algorithms are able to find high-quality solutions where genetic programming performs the best. [ABSTRACT FROM AUTHOR]

Boolean functions represent an important primitive in the design of various cryptographic algorithms. There exist several well-known schemes where a Boolean function is used to add nonlinearity to the cipher. Thus, methods to generate Boolean functions that possess good cryptographic properties present an important research goal. Among other techniques, evolutionary computation has proved to be a well-suited approach for this problem. In this paper, we present three different objective functions, where each inspects important cryptographic properties of Boolean functions, and examine four evolutionary algorithms. Our research confirms previous results, but also sheds new insights on the effectiveness and comparison of different evolutionary algorithms for this problem. [ABSTRACT FROM AUTHOR]

Boolean functions have numerous applications in domains as diverse as coding theory, cryptography, and telecommunications. Heuristics play an important role in the construction of Boolean functions with the desired properties for a specific purpose. However, there are only sparse results trying to understand the problem's difficulty. With this work, we aim to address this issue. We conduct a fitness landscape analysis based on Local Optima Networks (LONs) and investigate the influence of different optimization criteria and variation operators. We observe that the naive fitness formulation results in the largest networks of local optima with disconnected components. Also, the combination of variation operators can both increase or decrease the network size. Most importantly, we observe correlations of local optima's fitness, their degrees of interconnection, and the sizes of the respective basins of attraction. This can be exploited to restart algorithms dynamically and influence the degree of perturbation of the current best solution when restarting. • Heuristics play an important role in Boolean functions construction. • Investigates how a range of different design decisions can affect the search for Boolean functions. • Conducts a Fitness Landscape Analysis (FLA) for Boolean functions using LONs. • Studies the effect of various decisions on the optimization of cryptographic properties. • Applies for the first time combined neighborhood strategies and considered in an FLA context. [ABSTRACT FROM AUTHOR]