The security of sensitive data is a crucial issue in the information age. While the existing encryption protocols cannot always guarantee the required level of security due to the rapidly increasing computational capability of attackers, developing new cryptographically strong encryption techniques is of great importance in modern computer science. One of the advanced approaches in the field of cryptography is chaos-based encryption. In this study, we propose an efficient algorithm for arbitrary multimedia data encryption using the novel finite-difference scheme with adaptive symmetry based on the Gingerbreadman chaotic map. In the experimental part of the study, we use several analysis techniques to prove the presence of chaos in the dynamics of the reported discrete map and investigate the dependence between system dynamics and symmetry coefficient. Parametric chaotic sets and the largest Lyapunov exponent plots are given to evaluate the dynamics of the investigated finite-difference model. NIST statistical tests were applied to assess the properties of the developed pseudo-random numbers generator, and correlation analysis was performed to evaluate the secrecy of the encrypted image. It is experimentally shown, that varying the symmetry coefficient can significantly increase the keyspace for the encryption algorithm based on the symmetric Gingerbreadman map. The results of this study can be used to develop encryption software, including secure text messengers or stream data ciphers.

Composition is a powerful and simple approach for obtaining numerical integration methods of high accuracy order while preserving the geometric properties of a basic integrator. Adaptive step size control allows one to significantly increase the performance of numerical integration methods. However, there is a lack of efficient step size control algorithms for composition solvers due to some known difficulties in constructing a low-cost embedded local error estimator. In this paper, we propose a novel local error estimator based on a difference between the semi-implicit CD method and semi-explicit midpoint methods within a common composition scheme. We evaluate the performance of adaptive composition schemes with the proposed local error estimator, comparing it with the other state-of-the-art approaches. We show that composition ODE solvers with the proposed step size control algorithm possess higher numerical efficiency than known methods, by using a comprehensive set of nonlinear test problems.

A composition is a powerful tool for obtaining new numerical methods for solving differential equations. Composition ODE solvers are usually based on single-step basic methods applied with a certain set of step coefficients. However, multistep composition schemes are much less-known and investigated in the literature due to their complex nature. In this paper, we propose several novel schemes for solving ordinary differential equations based on the composition of adjoint multistep methods. Numerical stability, energy preservation, and performance of proposed schemes are investigated theoretically and experimentally using a set of differential problems. The applicability and efficiency of the proposed composition multistep methods are discussed.

A painting robot ARTCYBE is a machine developed to imitate an ability of a human painter to create realistic images with acrylic paints and a brush. In this paper a brushstroke rendering algorithm for this robot is presented. The algorithm converts a source bitmap image into a set of brushstrokes which we call a brushstroke map. The brushstroke map can be unambiguously transformed into a list of commands driving the painting robot. Simulated paintings obtained by proposed algorithm are represented. Advantages of the described algorithm in comparison to other known brushstroke rendering algorithms are discussed.

The subject of this study is the analysis algorithms for studying the behavior of the computer models of electronic circuits with advanced nonlinear elements. The paper gives an experimental comparison of four methods of obtaining two-parametric bifurcation diagrams: histogram of maximal values method, kernel density estimation method, sliding window technique and algorithm based on clusterization of recurrence density plot. The simple memristive circuit with chaotic multi-scroll attractor was chosen as an example for experimental part of the study. The following main results were obtained. Two new algorithms of chaotic system analysis were developed, combining the methods of bifurcation and recurrent analysis with mathematical statistics. New technique for creation of two-parametric high resolution bifurcation diagrams is proposed. This technique is based on sliding average window approach. We also propose the clustering method for plotting precise dynamical maps. The comparative analysis of proposed techniques is described, including the comparison with existing approaches. The study of computational efficiency is performed for integration numerical methods applied for the synthesis of discrete models of the circuit. By comparison of efficiency plots the optimal ordinary differential equation (ODE) solver for computer experiments with discrete models was chosen. The efficiency analysis has shown that the best ODE solver for simple memristive circuit simulation is the semi-implicit extrapolation algorithm of order eight. It is experimentally shown that sliding window average method is the most precise approach for creation of two-parametric bifurcation diagrams. The practical relevance of the obtained results is as follows. New methods of nonlinear systems analysis are applicable for creation of high precision simulation tools for circuits with advanced nonlinear elements. The applications are not limited to the electronic circuits simulation only but also include the possibility to locate hidden attractors in chaotic dynamical systems.