Chaos Map Research Articles

Image encryption using dynamic DNA encoding and pixel scrambling using composite chaotic maps

In this digital world, encryption plays an important role in various domains. Securing the information is the main goal when transfer of information takes place. Image encryption is a very important part of this as it applies to various domains like medical, multimedia, defence etc. A new method for image encryption is proposed here taking into account the “confusion-diffusion” structure. While working with secure data, requirements like fast computation, compression and processing are important issues. Deoxyribonucleic Acid (DNA) encoding has the capability to cope up with this requirement. In this paper a new algorithm is proposed based on composite chaos map for pixel scrambling and hence image encryption. First the algorithm takes the image and XORs with a composite chaotic map which further goes into dynamic DNA encoding followed by pixel scrambling which results in the image being very random thus it becomes less prone to attacks. The method discussed performs efficiently as shown in the experimental results.

Bifurcations, Hidden Chaos and Control in Fractional Maps

Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems.

Chaos for multivalued maps and induced hyperspace maps

• It is the first paper dealing really with chaos for multivalued maps in the relatioship with the induced hypermaps in hyperspaces. • Topological entropy for multivalued maps forces the one for induced hypermaps, but not vice versa. • Robinson’s chaos for multivalued maps is reversely forced by the on efor thr induced hypermaps Let ( X, d ) be a compact metric space and φ: X ⊸ X be a multivalued map. At first, we will extend for these maps the notions of a topological entropy and Robinson’s chaos from a single-valued into a multivalued setting and show their basic properties. Then, for a subclass of multivalued continuous maps with compact values, we will clarify their relationship to the induced (hyper)maps φ * : K ( X ) → K ( X ) in the hyperspace ( K ( X ) , d H ) , endowed with the Hausdorff metric d H , where K ( X ) consists of all compact subsets of X . Concretely, we will show that a positive topological entropy h (φ) of φ implies a positive topological entropy h (φ*) of φ*. On the other hand, Robinson’s chaos to φ* implies in a reverse way Robinson’s chaos to φ.

Fractional chaos maps with flower pollination algorithm for chaotic systems’ parameters identification

Meta-heuristic optimization algorithms are the new gate in solving most of the complicated nonlinear systems. So, improving their robustness, reliability, and convergence speed is the main target to meet the requirements of various optimization problems. In the current work, three different fractional-order chaos maps (FC-maps), which have been introduced recently, are incorporated with the fundamental flower pollination algorithm to tune its parameters adaptively. These maps are fractional logistic map, fractional sine map, fractional tent map, and their integer-order versions. As a result, fractional chaotic FPA (FC-FPA) is proposed. The FC-FPA has been mathematically tested over 10-, 30-, 50-, and 100-dimensional CEC 2017 benchmark functions. Moreover, the influence of merging FC-maps with FPA is investigated in case of increasing the number of maximum evaluation functions based on the ten functions of CEC 2020. Additionally, to assess the superiority of the proposed FC-FPA algorithm for more complicated optimization problems, it has been tested to extract the parameters of different chaotic systems with and without added noise. In addition, it is tested on the identification of the corresponding parameters for the chaotic behavior in brush-less DC motor. The results of the fractional version of CFPA are compared with that of integer CFPA and standard FPA via an extensive statistical analysis. Furthermore, a nonparametric statistical test is employed to affirm the superiority of the proposed fractional variants of CFPA. It is evident that the performance of FPA is highly influenced by integrating the fractional-order chaos maps as the introduced FC-FPA variants provide a better accurate and more consistent results as well as a higher speed of convergence especially upon using the fractional sine map.

Efficient parallel and fast convergence chaotic Jaya algorithms

Abstract The Jaya algorithm is a recent heuristic approach for solving optimisation problems. It involves a random search for the global optimum, based on the generation of new individuals using both the best and the worst individuals in the population, thus moving solutions towards the optimum while avoiding the worst current solution. In addition to its performance in terms of optimisation, a lack of control parameters is another significant advantage of this algorithm. However, the number of iterations needed to reach the optimal solution, or close to it, may be very high, and the computational cost can hamper compliance with time requirements. In this work, a chaotic two-dimensional (2D) map is used to accelerate convergence, and parallel algorithms are developed to alleviate the computational cost. Coarse- and fine-grained parallel algorithms are developed, the former based on multi-populations and the latter at the individual level, and in both cases these are accelerated by an improved (computational) use of the chaos map.

Retina Image and Bat-Inspird Algorithm for Artificial Key Generation

The process of key generation is utilized in different applications based on encryption techniques. Thecharacteristics of the generated key should satisfy the required security as potential. The traditionaltechniques used for generating keys are based on various equations based on chaos maps or modulation formaking these keys as one-time pads. Also, there are many techniques that utilized the block cipher or hashfunction for generating keys. In this paper, a retina image and bat-inspired algorithm are used for generatingsecure keys. Several processes have been applied to the input retina images like enhancement and edgedetection processes. In the proposed technique, some parameters are adjusted for controlling the results andevery output represents a bat solution and depending on the fitness function, the keys are generated. Thesegenerated keys are tested and evaluated using NIST tests. As a case study, some images are encrypted usingthe generated keys and the obtained encrypted images passed all the required security tests.

An Optimization Method for an Integrated Energy System Scheduling Process Based on NSGA-II Improved by Tent Mapping Chaotic Algorithms

The integrated energy system is a vital part of distributed energy industries. In addition to this, the optimal economic dispatch model, which takes into account the complementary coordination of multienergy, is an important research topic. Considering the constraints of power balance, energy supply equipment, and energy storage equipment, a basic model of optimal economic dispatch of an integrated energy system is established. On this basis, a multiobjective function solving algorithm of NSGA-II, based on tent map chaos optimization, is proposed. The proposed model and algorithm are applied. The simulation results show that the optimal economic scheduling model of the integrated energy system established in this paper can provide a more economic system operation scheme and reduce the operation cost and risks associated with an integrated energy system. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) multiobjective function solving algorithm, based on tent map chaos optimization, has better performance and efficiency.

Intelligent Metallurgical Data Statistics Software Encryption based on Real-Time Double Encryption Algorithm

One-way encryption in the traditional encryption system of smart phone makes mobile phone easy to be attacked by the outside world, resulting in poor security performance. In order to solve this problem, a design of security encryption system for smart phone software based on real-time dual encryption is proposed. The method of resource verification integrity is designed, and a group of congruence numbers is added to the software’s sensing resources to perform module operations and homomorphic encryption operations to generate encrypted data. In the reversible hiding process of dual encryption for real-time mobile phone information, chaotic sequence is used to realize the global scrambling of mobile phone information location. According to another new set of chaotic sequence, the 0bit and 1bit are scrambled in the information value of mobile phones. Chaos mapping is used to generate chaotic sequences and are associated with the mobile phone information to ensure that the dual encryption of mobile information can resist the selection of message attack. The experimental results show that the maximum confidentiality of the system can reach 96%, which is of practical value.

Adaptive Dynamic Disturbance Strategy for Differential Evolution Algorithm

To overcome the problems of slow convergence speed, premature convergence leading to local optimization and parameter constraints when solving high-dimensional multi-modal optimization problems, an adaptive dynamic disturbance strategy for differential evolution algorithm (ADDSDE) is proposed. Firstly, this entails using the chaos mapping strategy to initialize the population to increase population diversity, and secondly, a new weighted mutation operator is designed to weigh and combinemutation strategies of the standard differential evolution (DE). The scaling factor and crossover probability are adaptively adjusted to dynamically balance the global search ability and local exploration ability. Finally, a Gauss perturbation operator is introduced to generate a random disturbance variation, and to accelerate premature individuals to jump out of local optimization. The algorithm runs independently on five benchmark functions 20 times, and the results show that the ADDSDE algorithm has better global optimization search ability, faster convergence speed and higher accuracy and stability compared with other optimization algorithms, which provide assistance insolving high-dimensionaland complex problems in engineering and information science.

A self-recovery watermarking scheme based on block truncation coding and quantum chaos map

To take into account the invisibility, recovery quality, detection ability, and security, a new digital image fragile watermarking method based on block truncation coding (BTC) and quantum chaos map is proposed. In this method generates the authentication watermark for each 4 × 4 block and generates the recovery watermark for each 2 × 2 block by block truncation coding. For each block, the block truncation coding is used to classify the image blocks into smooth blocks and rough blocks. For different blocks, recovery data can be generated by allocating fewer bits to the smooth blocks and more bits to the rough blocks to encoding the block content. Quantum chaos map is used to generate the block mapping sequence for embedding recovery watermark to improve the shortcoming of watermarking such as small keyspace and low security. The experimental results show that the proposed scheme improves the quality of watermarked and recovered images. Additionally, this approach achieves higher security than the existing methods, under different attacks, such as general tampering, collage attack, content-only, and a hybrid attack.

Fractional chaotic ensemble particle swarm optimizer for identifying the single, double, and three diode photovoltaic models’ parameters

Solar Photovoltaic is a widely used renewable energy resource, and hence, the accurate and effective modeling of the PV system is crucial in real-time. The accurate PV modeling helps to predict the performance of the PV plant. In this paper, authors have proposed a novel optimization algorithm named Fractional Chaotic Ensemble Particle Swarm Optimizer (FC-EPSO) to model solar PV modules accurately. This article focused on the modeling of single, double, and three diodes models based on experimental data under different environmental conditions. In FC-EPSO, a new approach in the meta-heuristic algorithms is proposed, where fractional chaos maps are incorporated into the algorithm to enhance its accuracy and reliability. FC-EPSO variants performance is evaluated based on three-different experimental datasets, in which two are widely utilized for commercial applications, while the third is measured in the laboratory under four different irradiance and temperature levels. For validation purposes, several statistical analyses and comparisons are carried out with the recent state-of-the-art algorithms. The statistical measures and comparative studies illustrate the accuracy and consistency of the proposed algorithm. The introduced technique is capable of emulating the experimental datasets with less deviation, a fast convergence rate, and short execution time.

Chaos-based Vortex Search algorithm for solving inverse kinematics problem of serial robot manipulators with offset wrist

Vortex Search (VS) algorithm is a single-solution-based optimization algorithm that requires the high maximum number of iterations (NOI) to solve optimization problems. In this study, two methods were proposed to reduce the required maximum NOI of the VS algorithm. These methods are based on using ten chaos maps with the VS algorithm and provide improvements in the exploration and exploitation abilities of the algorithm for reducing the required maximum NOI. Ten chaos-based VS algorithms (CVSs) were obtained by combining these methods with the VS algorithm. The performances of the CVS algorithms were tested by fifty benchmark functions. The results were evaluated in terms of some statistical values and a pairwise statistical test, Wilcoxon Signed-Rank Test. According to the results, it was found that the CVS algorithm obtained by using the Gauss–Mouse chaos map was the best algorithm. And also, it was shown that the proposed CVS algorithm performs better than the classical VS algorithm, even when its maximum NOI was ten times less than the maximum NOI of the VS algorithm. Additionally, the effects of the proposed methods in the exploration and the exploitation abilities of the VS algorithm were visually shown and a comparison about algorithm processing time was presented. In order to test the performance of the proposed CVS algorithm in solving the real-world optimization problems, the inverse kinematics problem of a six Degrees Of Freedom (DOF) serial robot manipulator with offset wrist was solved with both the proposed CVS algorithm and the VS algorithm for two different types of trajectories. The results showed that the proposed algorithm outperforms the VS algorithm in terms of the objective function values and position errors of the end-effector of the serial robot manipulator.

A Pareto-optimal evolutionary approach of image encryption using coupled map lattice and DNA

Evolutionary algorithms are generally a suitable approach for optimization problems, having more than one conflicting objectives. For many complicated engineering optimization problems, multi-objective formulations are treated as realistic models. The paper presents and implements a Pareto-optimal image encryption algorithm that uses coupled map lattice (CML) chaos function and deoxyribonucleic acid (DNA) combination to encrypt an image. The discussed work uses multi-objective genetic algorithm (MOGA) to get the optimized results. The proposed two-step algorithm uses pseudo-random number generators, the chaotic method CML and DNA to create an initial population of DNA masks in its initial stage. The MOGA is applied in the second stage to obtain the best mask for encrypting the given plain image. The focus is on the generation of Pareto fronts by using the Pareto generation method of multi-objective optimization. The paper evaluates the performance of the implemented work using standard metrics like key sensitivity, secret key space, number of pixel change rate, unified average changed intensity, entropy, histogram and correlation coefficient. It also discusses the impact of using a genetic algorithm that uses more than one fitness function as the objective for encrypting images.

Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer Variants for Permanent Magnet Synchronous Motor Models Parameters Estimation

Chaotic response in the permanent magnet synchronous motor (PMSM) is an undesirable performance that may affect motor stability. This unexpected behavior occurs due to the disruption in the system parameters and load disturbance. To control this unwanted performance, it’s essential to introduce a robust method to determine the PMSM model parameters efficiently and expeditiously. Two PMSM models depending on the type of its nonlinear differential equations are investigated. The first one is the integer-order PMSM model, while the other is the fractional-order model. In this work, novel developed optimization variants called chaotic heterogeneous comprehensive learning particle swarm optimizer (CHCLPSO) is proposed. In CHCLPSO, the standard heterogeneous comprehensive learning particle swarm optimizer (HCLPSO) is cooperated into ten different chaos maps to adjust some of its parameters. Six CHCLPSO variables are introduced in addition to the standard HCLPSO version to estimate the parameters of the integer-order and the fractional-order PMSM models that are corresponding to the chaotic behavior. A comparison among the results of the introduced variants and the original algorithm is carried out. Moreover, a comprehensive comparison with other recent algorithms is performed. The primary outcome proves that the chaos maps have a remarkable influence in both of the consistency and the accuracy of the results of the HCLPSO with less execution time over the integer and the fractional-order models, especially CHCLPSO-III and CHCLPSO-V with sinusoidal and piecewise maps, respectively.

Efficient optimization technique for multiple DG allocation in distribution networks

In the last few decades, interest in the integration of Distributed Generators (DGs) into distribution networks has been increased due to their benefits such as enhance power system reliability, reduce the power losses and improve the voltage profile. These benefits can be increased by determining the optimal DGs allocation (location and size) into distribution networks. This paper proposes an efficient optimization technique to optimally allocate the multiple DG units in distribution networks. This technique is based on Sine Cosine Algorithm (SCA) and chaos map theory. As any random search-based optimization algorithm, SCA faces some issues such as low convergence rate and trapping in local solutions during the exploration and exploitation phases. This issue can be addressed by developing Chaotic SCA (CSCA). CSCA is mainly based on the iterative chaotic map which used to update the random parameters of SCA instead of using the random probability distribution. The iterative chaotic map is applied for single and multi-objective SCA. The proposed technique is validated using two stranded IEEE radial distribution feeders; 33 and 69-nodes. Comprehensive comparison among the proposed technique, the original SCA, and other competitive optimization techniques are carried out to prove the effectiveness of CSCA. Finally, a complete study is performed to address the impact of the intermittent nature of renewable energy resource on the distribution system. Hence, typical loads and generation (represented in PV power) profiles are applied. The result proves that the CSCA is more efficient to solve the optimal multiple DGs allocation with minimum power loss and high convergence rate.

Day-ahead optimal bidding strategy of microgrid with demand response program considering uncertainties and outages of renewable energy resources

In restructured electricity markets, microgrids are becoming smarter, more reliable and more economic electricity providers with respect to the incorporation of advanced smart grid technologies, distributed energy resources, efficient energy storage systems, and demand response programs (DRPs). Moreover, better bidding strategies, prepared by MG operators, boost the profits of MG market players. But, highly intermittent nature of renewable energy resources and their higher rate of outages make bidding strategies inefficient. To solve these issues, this study suggests an optimal bidding strategy considering uncertainty of renewable energy resources and DRP based on their outage probabilities. Tent chaos mapping is used to generate load scenarios and all possible renewable power output scenarios within the confidence intervals in non-repetitive and adaptive manner. Reserve and penalty costs for incorrect estimation of renewable energies are invoked to design more robust bidding. Moreover, the risk of participation in the competitive energy market is assessed using CVaR criteria. The proposed bidding model is optimized using mixed integer nonlinear programming. ‘Value of stochastic solution’ is used to investigate the efficiency of the stochastic programming in uncertainty integration into the bidding problem.

PROPOSING A NEW METHOD FOR ENCRYPTING SATELLITE IMAGES BASED ON HASH FUNCTION AND CHAOS PARAMETERS

Abstract. Due to the importance of providing security in satellite imagery and their transmission, in this paper, a new method for encrypting satellite images based on Hash key-based symmetric cryptographic algorithm is proposed which is developed by combining the generated key and chaos mapping parameters. The benefits of this algorithm are high security, high sensitivity and using dynamic encryption blocks. The proposed algorithm consists of three main parts: in the first section, the encryption key is created using the SHA-512 Hash function. In the second section, the initial values and the parameters of the mapping Chaos are determined by the algebraic functions that are related to the primary key. In the third section, with the help of the encryption block, the encrypted image is finally obtained. The purpose of this article is to increase the security of encrypting satellite images by creating an unspecified encryption block to deal with a variety of attacks. In this regard, both aspects of security and performance of the proposed algorithm have been analysed and the results are evaluated.

2D Hybrid chaos map for image security transform based on framelet and cellular automata

One of the most important data in the social networks is image, so improving the existing methods can be essential to obtain a safe environment for transforming. In this paper, we provide some safe ways to transfer images securely by using cryptography and steganography methods. In order to enhance the security of the image transmission, we introduce a new type of uniformly distributed 2D hybrid chaos map based on Logistic, Sine and Tent maps, and use the cellular automata and discrete framelet transform in the proposed algorithms and also mix the position of the image pixels by applying kinds of shifts. To show that the proposed algorithms are able to resist various attacks, different types of simulation results and security analysis are used.

Fractional Chaos Maps with Flower Pollination Algorithm for Partial Shading Mitigation of Photovoltaic Systems

Solar Photovoltaic (PV) systems have become prominent and have attained the attention of energy engineers, governments and researchers. To achieve the maximum benefit from the PV system in spite of its nonlinear characteristic and environmental conditions, finding a robust maximum power point tracking method is essential. Over two decades, various researchers proposed numerous MPPT methods, but they failed to evaluate their methods on consistency, reliability, and robustness over several numbers of runs. Most of the researchers examined one configuration and they did not to consider the dynamic change in the irradiation conditions. Therefore, in this manuscript, the authors introduced a novel optimization technique Fractional chaotic Flower Pollination Algorithm (FC-FPA), by merging fractional chaos maps with flower pollination algorithm (FPA). The proposed technique, help FPA in extracting the Global Maximum Power Point (GMPP) under different partial shading patterns including with different PV array configurations. The proposed FC-FPA technique is tested and evaluated over 5 different patterns of partial shading conditions. The first three patterns are tested over 4S configuration made with Shell S36 PV module. The other two patterns are applied to the 4S2P configuration of Shell SM55 PV panels. The performance of the proposed variant is investigated by tracking the GMPP for abruptly changing shade pattern. Exclusive statistical analysis is performed over several numbers of runs. Comparison with perturb and observe MPPT technique is established. These results confirm that, the proposed method shows fast convergence, zero oscillation and rapid response for the dynamic change in irradiation with consistent behavior.

Hybrid image encryption algorithm based on 3D chaotic system and choquet fuzzy integral

In this paper, a novel image encryption algorithm based on 3D hybrid chaotic system and choquet fuzzy integral is introduced. To construct an algorithm with high sensitivity and least losing, we introduce a new type of 3D hybrid chaos map which has uniformly distributed, and apply choquet fuzzy integral using B-spline functions as membership grades to confuse and diffuse the pixels. Finally, simulation results and various security analysis illustrate that this algorithm possess a high security and resist various attacks.