Elena C. Laskari

Particle swarm optimization for integer programming

The investigation of the performance of the particle swarm optimization (PSO) method in integer programming problems, is the main theme of the present paper. Three variants of PSO are compared with the widely used branch and bound technique, on several integer programming test problems. Results indicate that PSO handles efficiently such problems, and in most cases it outperforms the branch and bound technique.

Particle swarm optimization for minimax problems

This paper investigates the ability of the Particle Swarm Optimization (PSO) method to cope with minimax problems through experiments on well-known test functions. Experimental results indicate that PSO tackles minimax problems effectively. Moreover, PSO alleviates difficulties that might be encountered by gradient-based methods, due to the nature of the minimax: objective function, and potentially lead to failure. The performance of PSO is compared with that of other established approaches, such as the sequential quadratic programming (SQP) method and a recently proposed smoothing technique.

Utilizing Evolutionary Computation Methods for the Design of S-Boxes

Among the most important components of many contemporary ciphers are the substitution boxes (S-boxes) and a great amount of research is devoted to their study. In this paper, a new methodology for designing strong S-boxes is proposed and two evolutionary computation methods, the particle swarm optimization and the differential evolution algorithm are employed to tackle the problem at hand. The obtained results are promising and indicate that this novel approach is effective

Cryptography and Cryptanalysis Through Computational Intelligence

The past decade has witnessed an increasing interest in the application of Computational Intelligence methods to problems derived from the field of cryptography and cryptanalysis. This phenomenon can be attributed both to the effectiveness of these methods to handle hard problems, and to the major importance of automated techniques in the design and cryptanalysis of cryptosystems. This chapter begins with a brief introduction to cryptography and Computational Intelligence methods. A short survey of the applications of Computational Intelligence to cryptographic problems follows, and our contribution in this field is presented. Specifically, some cryptographic problems are viewed as discrete optimization tasks and Evolutionary Computation methods are utilized to address them. Furthermore, the effectiveness of Artificial Neural Networks to approximate some cryptographic functions is studied. Finally, theoretical issues of Ridge Polynomial Networks and cryptography are presented. The experimental results reported suggest that problem formulation and representation are critical determinants of the performance of Computational Intelligence methods in cryptography. Moreover, since strong cryptosystems should not reveal any patterns of the encrypted messages or their inner structure, it appears that Computational Intelligence methods can constitute a first measure of the cryptosystems’ security.

Evolutionary operators in global optimization with dynamic search trajectories

One of the most commonly encountered approaches for the solution of unconstrained global optimization problems is the application of multi-start algorithms. These algorithms usually combine already computed minimizers and previously selected initial points, to generate new starting points, at which, local search methods are applied to detect new minimizers. Multi-start algorithms are usually terminated once a stochastic criterion is satisfied. In this paper, the operators of the Differential Evolution algorithm are employed to generate the starting points of a global optimization method with dynamic search trajectories. Results for various well-known and widely used test functions are reported, supporting the claim that the proposed approach improves drastically the performance of the algorithm, in terms of the total number of function evaluations required to reach a global minimizer.

Novel orbit based symmetric cryptosystems

During the last few years considerable effort has been devoted to research related to chaotic encryption. In this paper a new symmetric key cryptosystem that exploits the idea of nonlinear mappings and their fixed points to encrypt information is presented. Furthermore, a measure of the quality of the keys used is introduced. The experimental results indicate that the proposed cryptosystem is efficient and secure to ciphertext-only attacks. Finally, three modifications of the basic cryptosystem that render it more robust are presented and efficiency issues are discussed.

Transformations of two cryptographic problems in terms of matrices

The Discrete Logarithm and the Diffie-Hellman are two hard computational problems, closely related to cryptography and its applications. The computational equivalence of these problems has been proved only for some special cases. In this study, using LU-decomposition to Vandermonde matrices, we are able to transform the two problems in terms of matrices, thus giving a new perspective to their equivalence. A first study on matrix transformations for the Double and Multiple Discrete Logarithms is also presented.

Privacy preserving electronic data gathering

Most organizations, from private business to scientific institutes, own large information databases. Analysis of these databases can be very beneficial to the owner organizations, as it contributes to knowledge discovery. To extract broader and more accurate conclusions, knowledge discovery techniques need to be applied on a collection of databases of different organizations involved in the same field. This paper addresses two issues associated with electronic data gathering: confidentiality of the organization that supplies a particular database, and authentication of the provided data.

Aitken and Neville inverse interpolation methods for the Lucas logarithm problem

The Lucas function is a recently proposed one-way function used in public key cryptography. The security of cryptosystems based on the Lucas function relies on the difficulty of solving the Lucas logarithm problem. In this paper, the Lucas logarithm problem is studied using interpolation techniques. In particular, the inverse Aitken and the inverse Neville interpolation methods are applied to values of the Lucas sequence to obtain a polynomial that interpolates the Lucas logarithm. The results indicate that in all the considered instances of the problem a polynomial of low degree that interpolates the desired values exists.

Assessing the effectiveness of artificial neural networks on problems related to elliptic curve cryptography

Cryptographic systems based on elliptic curves have been introduced as an alternative to conventional public key cryptosystems. The security of both kinds of cryptosystems relies on the hypothesis that the underlying mathematical problems are computationally intractable, in the sense that they cannot be solved in polynomial time. In this paper, we study the performance of artificial neural networks on the computation of a Boolean function derived from the use of elliptic curves in cryptographic applications.