Evolutionary algorithms-assisted construction of cryptographic boolean functions

In the last few decades, evolutionary algorithms were successfully applied numerous times for creating Boolean functions with good cryptographic properties. Still, the applicability of such approaches was always limited as the cryptographic community knows how to construct suitable Boolean functions with deterministic algebraic constructions. Thus, evolutionary results so far helped to increase the confidence that evolutionary techniques have a role in cryptography, but at the same time, the results themselves were seldom used. This paper considers a novel problem using evolutionary algorithms to improve Boolean functions obtained through algebraic constructions. To this end, we consider a recent generalization of Hidden Weight Boolean Function construction, and we show that evolutionary algorithms can significantly improve the cryptographic properties of the functions. Our results show that the genetic algorithm performs by far the best of all the considered algorithms and improves the nonlinearity property in all Boolean function sizes. As there are no known algebraic techniques to reach the same goal, we consider this application a step forward in accepting evolutionary algorithms as a powerful tool in the cryptography domain. Cyber Securit

Evolutionary algorithms for designing reversible cellular automata

Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography, and reversible computing. In this work, we formulate the search of a specific class of RCA – namely, those whose local update rules are defined by conserved landscapes – as an optimization problem to be tackled with Genetic Algorithms (GA) and Genetic Programming (GP). In particular, our experimental investigation revolves around three different research questions, which we address through a single-objective, a multi-objective, and a lexicographic approach. In the single-objective approach, we observe that GP can already find an optimal solution in the initial population. This indicates that evolutionary algorithms are not needed when evolving only the reversibility of such CA, and a more efficient method is to generate at random syntactic trees that define the local update rule. On the other hand, GA and GP proved to be quite effective in the multi-objective and lexicographic approach to (1) discover a trade-off between the reversibility and the Hamming weight of conserved landscape rules, and (2) observe that conserved landscape CA cannot be used in symmetric cryptography because their Hamming weight (and thus their nonlinearity) is too low.Cyber Securit

Cellular automata based S-boxes

Cellular Automata (CA) represent an interesting approach to design SubstitutionBoxes (S-boxes) having good cryptographic properties and low implementation costs. From the cryptographic perspective, up to now there have been only ad-hoc studies about specific kinds of CA, the best known example being the χ nonlinear transformation used in Keccak. In this paper, we undertake a systematic investigation of the cryptographic properties of S-boxes defined by CA, proving some upper bounds on their nonlinearity and differentialuniformity. Next, we extend some previous published results about the construction of CAbased S-boxes by means of a heuristic technique, namely Genetic Programming (GP). In particular, we propose a “reverse engineering” method based on De Bruijn graphs to determine whether a specific S-box is expressible through a single CA rule. Then, we use GP to assess if some CA-based S-box with optimal cryptographic properties can be describedby a smaller CA. The results show that GP is able to find much smaller CA rules defining the same reference S-boxes up to the size 7 × 7, suggesting that our method could be used to find more efficient representations of CA-based S-boxes for hardware implementations. Finally, we classify up to affine equivalence all 3 × 3 and 4 × 4 CA-based S-boxes.Special Issue on Boolean Functions and Their Applications Accepted author manuscriptCyber Securit

What Is Your MOVE: Modeling Adversarial Network Environments

Finding optimal adversarial dynamics between defenders and attackers in large network systems is a complex problem one can approach from several perspectives. The results obtained are often not satisfactory since they either concentrate on only one party or run very simplified scenarios that are hard to correlate with realistic settings. To truly find which are the most robust defensive strategies, the adaptive attacker ecosystem must be given as many degrees of freedom as possible, to model real attacking scenarios accurately. We propose a coevolutionary-based simulator called MOVE that can evolve both attack and defense strategies. To test it, we investigate several different but realistic scenarios, taking into account features such as network topology and possible applications in the network. The results show that the evolved strategies far surpass randomly generated strategies. Finally, the evolved strategies can help us to reach some more general conclusions for both attacker and defender sides.Virtual/online event due to COVID-19Cyber Securit

Towards an evolutionary-based approach for natural language processing

Tasks related to Natural Language Processing (NLP) have recently been the focus of a large research endeavor by the machine learning community. The increased interest in this area is mainly due to the success of deep learning methods. Genetic Programming (GP), however, was not under the spotlight with respect to NLP tasks. Here, we propose a first proof-of-concept that combines GP with the well established NLP tool word2vec for the next word prediction task. The main idea is that, once words have been moved into a vector space, traditional GP operators can successfully work on vectors, thus producing meaningful words as the output. To assess the suitability of this approach, we perform an experimental evaluation on a set of existing newspaper headlines. Individuals resulting from this (pre-)training phase can be employed as the initial population in other NLP tasks, like sentence generation, which will be the focus of future investigations, possibly employing adversarial co-evolutionary approaches.Accepted author manuscriptCyber Securit

Artificial Intelligence for the Design of Symmetric Cryptographic Primitives

This chapter provides a general overview of AI methods used to support the design of cryptographic primitives and protocols. After giving a brief introduction to the basic concepts underlying the field of cryptography, we review the most researched use cases concerning the use of AI techniques and models to design cryptographic primitives, focusing mainly on Boolean functions, S-boxes and pseudorandom number generators. We then point out two interesting directions for further research on the design of cryptographic primitives where AI methods could be applied in the future.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Cyber Securit

Fitness landscape analysis of dimensionally-aware genetic programming featuring feynman equations

Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionally-aware genetic programming search spaces on a subset of equations from Richard Feynman’s well-known lectures. We define an initialisation procedure and an accompanying set of neighbourhood operators for conducting the local search within the physical unit constraints. Our experiments show that the added information about the variable dimensionality can efficiently guide the search algorithm. Still, further analysis of the differences between the dimensionally-aware and standard genetic programming landscapes is needed to help in the design of efficient evolutionary operators to be used in a dimensionally-aware regression.Accepted author manuscriptCyber Securit