Search Results (10)

In recent years, many chaos-based encryption algorithms have been proposed. Many of these are based on established designs and populate their S-boxes with values derived from chaotic maps, following conventional implementation strategies to enable comparison with their original non-chaotic counterparts. In contrast, this work proposes a novel approach: a Chaos-Based Substitution Box (CB-SBox) implementation, in which conventional ROM-based S-boxes are replaced by a digital circuit that directly executes a selected chaotic map. This method enables the construction of S-boxes with long word lengths through an FPGA-based programmable circuit that allows for variable S-box lengths, facilitating the analysis of S-boxes of varying sizes, and ultimately enhancing security, particularly for larger S-boxes, as demonstrated by increased resistance to linear and differential cryptanalysis. Furthermore, the proposed CB-SBox achieves reductions in both area and power consumption compared to size-comparable ROM-based S-boxes. A 19-bit chaos-based S-box consumes just 0.0238% of the area and 0.0241% of the power required by an equivalent ROM-implemented S-box while providing the same level of security. The inherent unpredictability of non-linear chaotic behavior causes the proposed chaos-based S-boxes to exhibit non-bijective characteristics, making them well suited for application in non-invertible cryptographic primitives, such as hash functions and Feistel networks. The proposed CB-SBox is implemented in a Feistel network as described in the literature, and the results are provided. Full article

The theory of critical curves determines the main characteristics of a discrete dynamical system in two dimensions. One important property that has garnered recent attention is the problem of chaos synchronization, along with the location of its chaotic attractors, basin boundaries, and bifurcation mechanisms. Varying the parameters of the maps reveals the instrumental role that these curves play, where the bifurcation leads to complex topological structures of the basins occurs by contact with the basin boundaries, resulting in the appearance or disappearance of some components of the basin. This study focuses on the properties of a discrete dynamical system consisting of two symmetrically coupled non-invertible maps, specifically those with an invariant one-dimensional submanifold (or one-dimensional maps). These maps exhibit a complex structure of basins with the coexistence of symmetric chaotic attractors, riddled basins, blow-out, on-off intermittency, and, most significantly, the appearance of chaotic synchronization with a correlation between all the characteristics. The numerical method of critical curves can be used to demonstrate a wide range of dynamic scenarios and explain the bifurcations that lead to their occurrence. These curves play a crucial role in a system of two symmetrically coupled maps, and their significance will be discussed. Full article

In the existing cancellable finger vein template protection schemes, the original biometric features cannot be well protected, which results in poor security. In addition, the performance of matching recognition performances after generating a cancellable template is poor. Therefore, a dual hashing index cancellable finger vein template protection based on Gaussian random mapping is proposed in this study. The scheme is divided into an enrollment stage and a verification stage. In the two stages, symmetric data encryption technology was used to generate encryption templates for matching. In the enrollment stage, first, the extracted finger vein features were duplicated to obtain an extended feature vector; then, this extended vector was uniformly and randomly permuted to obtain a permutation feature vector. The above two vectors were combined into a two-dimensional feature matrix. The extended and permuted feature vector made full use of the original biometric features and further enhanced the non-invertibility. Second, a random Gaussian projection vector with m$\times$q dimensions was generated, and a random orthogonal projection matrix was generated by the Schmidt orthogonalization of the previously generated random vector. This approach accurately transferred the characteristics of the biometric features to another feature space and ensured that the biological template is revocable. Finally, the inner product of the two-dimensional feature vector and random orthogonal projection matrix was obtained and superimposed into a row. The dual index values of the largest and second largest values were repeated m times to obtain a hash code for matching. The secondary maximum value index was introduced to adjust the error generated by the random matrix, which improved the recognition rate of the algorithm. In the verification stage, another hash code for matching was generated based on symmetric data encryption technology, and then the two hash codes were cross matched to obtain the final matching result. The experimental results show that this scheme attains good recognition performance with the PolyU and SDUMLA-FV databases, that it meets the design standard for cancellable biometric identification, and that it is robust to security and privacy attacks. Full article

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes. Full article

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes $Z_0,Z_2$ and $Z_4$ regions. Full article

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions. Full article

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained. Full article

We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game’s equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles. Full article

Considering the recent exponential growth in the amount of information processed in Big Data, the high energy consumed by data processing engines in datacenters has become a major issue, underlining the need for efficient resource allocation for more energy-efficient computing. We previously proposed the Best Trade-off Point (BToP) method, which provides a general approach and techniques based on an algorithm with mathematical formulas to find the best trade-off point on an elbow curve of performance vs. resources for efficient resource provisioning in Hadoop MapReduce. The BToP method is expected to work for any application or system which relies on a trade-off elbow curve, non-inverted or inverted, for making good decisions. In this paper, we apply the BToP method to the emerging cluster computing framework, Apache Spark, and show that its performance and energy consumption are better than Spark with its built-in dynamic resource allocation enabled. Our Spark-Bench tests confirm the effectiveness of using the BToP method with Spark to determine the optimal number of executors for any workload in production environments where job profiling for behavioral replication will lead to the most efficient resource provisioning. Full article

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but discover a problem that remains open. Full article