A Discrete Particle Swarm Optimizer for the Design of Cryptographic Boolean Functions

A Particle Swarm Optimizer for the search of balanced Boolean functions with good cryptographic properties is proposed in this paper. The algorithm is a modified version of the permutation PSO by Hu, Eberhart and Shi which preserves the Hamming weight of the particles positions, coupled with the Hill Climbing method devised by Millan, Clark and Dawson to improve the nonlinearity and deviation from correlation immunity of Boolean functions. The parameters for the PSO velocity equation are tuned by means of two meta-optimization techniques, namely Local Unimodal Sampling (LUS) and Continuous Genetic Algorithms (CGA), finding that CGA produces better results. Using the CGA-evolved parameters, the PSO algorithm is then run on the spaces of Boolean functions from $n=7$ to $n=12$ variables. The results of the experiments are reported, observing that this new PSO algorithm generates Boolean functions featuring similar or better combinations of nonlinearity, correlation immunity and propagation criterion with respect to the ones obtained by other optimization methods

A survey of metaheuristic algorithms for the design of cryptographic Boolean functions

Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one should consider and cryptographic properties that need to be fulfilled makes the search for new Boolean functions still a very active domain. There are several options to construct appropriate Boolean functions: algebraic constructions, random search, and metaheuristics. In this work, we concentrate on metaheuristic approaches and examine the related works appearing in the last 25 years. To the best of our knowledge, this is the first survey work on this topic. Additionally, we provide a new taxonomy of related works and discuss the results obtained. Finally, we finish this survey with potential future research directions.</p

A characterisation of S-box fitness landscapes in cryptography

Substitution Boxes (S-boxes) are nonlinear objects often used in the design of cryptographic algorithms. The design of high quality S-boxes is an interesting problem that attracts a lot of attention. Many attempts have been made in recent years to use heuristics to design S-boxes, but the results were often far from the previously known best obtained ones. Unfortunately, most of the effort went into exploring different algorithms and fitness functions while little attention has been given to the understanding why this problem is so difficult for heuristics. In this paper, we conduct a fitness landscape analysis to better understand why this problem can be difficult. Among other, we find that almost each initial starting point has its own local optimum, even though the networks are highly interconnected

Heuristic search of (semi-)bent functions based on cellular automata

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 (CA), 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

Tutorials at PPSN 2016

PPSN 2016 hosts a total number of 16 tutorials covering a broad range of current research in evolutionary computation. The tutorials range from introductory to advanced and specialized but can all be attended without prior requirements. All PPSN attendees are cordially invited to take this opportunity to learn about ongoing research activities in our field

A survey on machine learning applied to symmetric cryptanalysis

In this work we give a short review of the recent progresses of machine learning techniques applied to cryptanalysis of symmetric ciphers, with particular focus on artificial neural networks. We start with some terminology and basics of neural networks, to then classify the recent works in two categories: "black-box cryptanalysis", techniques that not require previous information about the cipher, and "neuro-aided cryptanalysis", techniques used to improve existing methods in cryptanalysis

Information-Theoretic Secure Outsourced Computation in Distributed Systems

Secure multi-party computation (secure MPC) has been established as the de facto paradigm for protecting privacy in distributed computation. One of the earliest secure MPC primitives is the Shamir\u27s secret sharing (SSS) scheme. SSS has many advantages over other popular secure MPC primitives like garbled circuits (GC) -- it provides information-theoretic security guarantee, requires no complex long-integer operations, and often leads to more efficient protocols. Nonetheless, SSS receives less attention in the signal processing community because SSS requires a larger number of honest participants, making it prone to collusion attacks. In this dissertation, I propose an agent-based computing framework using SSS to protect privacy in distributed signal processing. There are three main contributions to this dissertation. First, the proposed computing framework is shown to be significantly more efficient than GC. Second, a novel game-theoretical framework is proposed to analyze different types of collusion attacks. Third, using the proposed game-theoretical framework, specific mechanism designs are developed to deter collusion attacks in a fully distributed manner. Specifically, for a collusion attack with known detectors, I analyze it as games between secret owners and show that the attack can be effectively deterred by an explicit retaliation mechanism. For a general attack without detectors, I expand the scope of the game to include the computing agents and provide deterrence through deceptive collusion requests. The correctness and privacy of the protocols are proved under a covert adversarial model. Our experimental results demonstrate the efficiency of SSS-based protocols and the validity of our mechanism design

On applications of simulated annealing to cryptology

Boolean functions are critical building blocks of symmetric-key ciphers. In most cases, the security of a cipher against a particular kind of attacks can be explained by the existence of certain properties of its underpinning Boolean functions. Therefore, the design of appropriate functions has received significant attention from researchers for several decades. Heuristic methods have become very powerful tools for designing such functions. In this thesis, we apply simulated annealing methods to construct Boolean functions with particular properties. Our results meet or exceed the best results of available theoretical constructions and/or heuristic searches in the literature, including a 10-variable balanced Boolean function with resiliency degree 2, algebraic degree 7, and nonlinearity 488 for the first time. This construction affirmatively answers the open problem about the existence of such functions. This thesis also includes results of cryptanalysis for symmetric ciphers, such as Geffe cipher and TREYFER cipher

Where Quantum Complexity Helps Classical Complexity

Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum computing. Nonetheless, there are defined boundaries to the capabilities of quantum computing. This paper concentrates on aggregating prior research efforts dedicated to solving intricate classical computational problems through quantum computing. The objective is to systematically compile an exhaustive inventory of these solutions and categorize a collection of demanding problems that await further exploration