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Recently a hybrid secure image encryption scheme based on Julia set and three-dimensional Lorenz chaotic system was suggested. The offered scheme was based on the multiplicative operation carried out by Julia set fractals and bitwise XOR which was implemented by the trajectories obtained from the Lorenz chaotic system. This paper presents the cryptanalysis of the scheme through a chosen-plaintext attack by taking three different chosen images. In this work, a practical chosen-plaintext attack is performed which reveals that the cryptosystem depending on only multiplication and bitwise XOR operation can be effortlessly attacked. The results of the analysis performed on the retrieved image reflect the effectiveness of the chosen-plaintext attack which fruitfully produces the original image.

Cell development from an undifferentiated stem cell to a differentiated one is essential in forming an organism. In this paper, various bifurcations of a stem cell during this process are studied using a model based on Furusawa and Kaneko’s hypothesis. Furusawa and Kaneko’s hypothesis tells that the gene expression of stem cells is chaotic. By developing to a differentiated cell, the gene expression in more order, which is the cause of losing pluripotency. In this model, the chaotic dynamics of gene expression in the stem cells become ordered during the developments. Various patterns and bifurcation points can be seen during development. The bifurcation points and their predictions during the process of cell development are studied in this paper. Some well-known critical slowing down indicators are used to show the variations of slowness during the cell’s development and predict the bifurcation points. It is vital since the unexpected changes of the state can cause a disaster. All of the indicators have a proper trend by approaching the bifurcation points and faring away.

Privacy of information is one of the most important and unavoidable issues in our digitally advance era. A huge amount of information transmitted over different servers and networking protocols. The sphere of digitally advanced world is tied with information in different forms of facilitations, which includes online banking systems, ecommerce and many more. Providing the ease of access, anything online makes our confidential information open to different threats. Therefore, to enjoy ease of access and at the same time secure our digital information from theft, we need a robust information security system. In this article, we have designed a novel and an efficient security system, which provides secrecy to our digital information. The designed encryption scheme is fundamentally a combination of chaos and nonlinear confusion components. We have developed a new mechanism of adding confusion, namely S8 permutation of double affine transformation to construct 40320 new substitution boxes (S-boxes) having nonlinearity 112 from a single S-box. Moreover, nonlinear Lorenz dynamical system is utilized to select any three S-boxes from 40320 newly generated nonlinear components. To add diffusion in our proposed algorithm, we have utilized Chirikov discrete iterative map. The excellence of an offered digital image encryption has been examined and evaluated with standard benchmarks. The simulation results reveal that the quality of the image encryption passes all these tests and is comparable to current benchmarks.

Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).

The security of digital content during transmission and storage through insecure communication links and databases is a challenging issue in today's world. In this article, an encryption scheme based on fractal Tromino and Chebyshev polynomial-based generated chaotic matrix is presented. The scheme fulfills the most fundamental aspect of encryption that is diffusion and confusion. For confusion highly non-linear, pre-defined S-boxes are used. The proposed scheme has been tested using state-of-the-art key performance indicators including differential analysis, statistical analysis. Information entropy analysis, mean square error, and NIST-based randomness analysis. The encrypted images have the highest practically achievable entropy of 7.999 and the time analysis shows that the proposed system is suitable for real-time implementation. The rest of the results indicates that the proposed cryptosystem possesses high immunity toward various attacks. The security analysis compared with the existing scheme shows the strength of the suggested scheme.

Recently, a photosensitive model has been proposed that takes into account nonlinear encoding and responses of photosensitive neurons that are subject to optical signals. In the model, a photocell term has been added to the well-known FitzHugh–Nagumo neuron, which results in a time-varying voltage source. The modified model exhibits most of the main characteristics of biological neurons, like spiking, bursting, and chaotic responses, but is also amenable to study the effect of optical signals. In this paper, we consider a small-world network of photosensitive neurons and study their collective behavior in dependence on interaction strength. We show that the network exhibits synchronization in a specific range of coupling strengths before transcending into a chimera state. We use the master stability function, a local-order parameter, as well as recurrence plots to verify the reported results.

In current years many chaos-based Substitution boxes (S-boxes) have been proposed. Recently, an image encryption technique based on multiple chaotic S-box was offered. This encryption method was based on the concept of confusion only produced by the implementation of the S-box. The concept of confusion utilized in the understudy technique can be smashed by using just one chosen-plaintext attack and a chosen-ciphertext attack. This article presents a detailed structure of two types of cryptographic attacks on the diffusion-based encryption scheme. The proposed attacks are successfully performed to retrieve the key with very little execution time by using just one chosen image which indicates the vulnerability of multiple chaotic S-boxes-based cryptosystems. The retrieved data is passed through some statistical analysis such as correlation, histogram, and entropy to check the correctness of recovered data.

The advancement in wireless communication has encouraged the process of data transferring through the Internet. The process of data sharing via the Internet is prone to several attacks. The sensitive information can be protected from hackers with the help of a process called Encryption. Owing to the increase in cyber-attacks, encryption has become a vital component of modern-day communication. In this article, an image encryption algorithm is suggested using dynamic substitution and chaotic systems. The suggested scheme is based upon the chaotic logistic map, chaotic sine maps and the dynamical substitution boxes (S-boxes). In the proposed scheme, the S-box selection is according to the generated sequence by deploying the chaotic sine map. To evaluate the robustness and security of the proposed encryption scheme, different security analysis like correlation analysis, information entropy, energy, histogram investigation, and mean square error are performed. The keyspace and entropy values of the enciphered images generated through the proposed encryption scheme are over 2278 and 7.99 respectively. Moreover, the correlation values are closer to zero after comparison with the other existing schemes. The unified average change intensity (UACI) and the number of pixel change rate (NPCR) for the suggested scheme are greater than 33, 99.50% respectively. The simulation outcomes and the balancing with state-of-the-art algorithms justify the security and efficiency of the suggested scheme.

In this paper a new 5D chaotic system with line equilibrium is designed and described to reveal its extreme multi-stability. Hence, all of the resulting attractors are hidden. The suggested system owns many complex dynamic behaviors in comparison with other chaotic systems. System initial state-associated complex dynamical behaviors are considered and we discover that it possesses an immeasurable number of coexisting attractors, which expresses the occurrence of extreme multi-stability. Besides, we also demonstrate the line equilibrium stability in detail, bifurcation diagrams, Lyapunov exponents, and basins of attraction. Also, in order to analyze the new 5D chaotic system we have considered the permutation entropy technique. Finally, the application of the novel 5D chaotic system with line equilibrium to the problem of chaos synchronization and secure communication through observer design is presented.

Coexistence of attractors with different or same type, multistability, is a complex behavior in nonlinear systems. This feature makes these systems applicable but difficult to control. Besides multistability, some new systems show megastability, existence of infinite number of coexisting attractors. In this paper, two simple megastable systems are presented in details. Moreover, these systems show hyperchaotic behavior which is rare in these types of systems as previously proposed systems mostly show chaos and periodic responses. To show the properties of these systems, nonlinear analytical tools are used in this article.

Chaotic encryption is a growing field for competently shielding visual data. As well as quantum encryption and substitution also play a significant role in applied fields owing to its prospective use in secure communication. This article offers new method for the encryption by utilizing quantum chaotic maps and continuous chaotic dynamical systems. Since chaotic maps are itself suitable for quality encryption coupled with quantum logistic encryption, substitution box stipulates highly secure encryption program. Quantum logistic map is combined with Liu and Rossler chaotic systems with the intention of improvement in efficiency of data randomness. Designed scheme ensures the security of data with the minimum time of encryption. Outcomes acquired from performance evaluation signifies that projected chaotic encryption program reveals high complexity and security.

The fractional order model of a glucose-insulin regulatory system is derived and presented. It has been extensively proved in the literature that fractional order analysis of complex systems can reveal interesting and unexplored features of the system. In our investigations we have revealed that the glucose-insulin regulatory system shows multistability and antimonotonicity in its fractional order form. To show the effectiveness of fractional order analysis, all numerical investigations like stability of the equilibrium points, Lyapunov exponents, and bifurcation plots are derived. Various biological disorders caused by an unregulated glucose-insulin system are studied in detail. This may help better understand the regulatory system.

Over the last few decades, different mediums of secure communication use chaos which is demonstrated by some nonlinear dynamical systems. Chaos shows unpredictable behavior and this characteristic is quite helpful in different encryption techniques and for multimedia security. In this work, the chaotic behavior of the improved Tent-Sine map is conferred and ultimately a new method to construct substitution-boxes is proposed. This new method explores the features of chaos through TSS map and algebraic Mobius transformation to generate strong S-boxes. The S-boxes are assessed using standard tests suit which includes nonlinearity, strict avalanche criterion, bit independence criterion, linear approximation probability and differential uniformity. Moreover, the proposed S-boxes show excellent statistical properties under majority logic criterions such as correlation, homogeneity, energy, entropy, contrast. The statistical encryption results are demonstrate the better performance of the proposed S-boxes when compared with some of state of the art S-boxes including AES, Gray, APA S8 AES, Skipjack and validate the suitability of anticipated method.

The recent decade has witnessed an exponential surge of digital content, especially multimedia and its applications. The security requirements of these innovative platforms necessitate the significance of enhancing advanced encryption schemes. In this paper, a novel encryption scheme is presented for real-time audio applications. The framework of the proposed scheme is grounded on the principles of confusion and diffusion. The confusion incorporates nonlinearity by the application of Mordell elliptic curves (MEC) and a symmetric group of permutations S8. The endurance of the proposed scheme is further enriched through the application of chaotic maps. The proposed scheme is intended to cater requirements of real-time voice communications in defense applications particularly warzones. The adoption of a modular design and fusion of chaotic maps makes the algorithm viable for numerous real-time audio applications. The security can further be enriched by incorporating additional rounds and number of S-boxes in the algorithm. The security and resistance of the algorithm against various attacks are gaged through performance evaluation and security measurements. The audio encryption scheme has the ability to tolerate noise triggered by a channel or induced by an invader. The decryption was successful and the resultant output was audible for noisy data. The overall results depict that the proposed audio encryption scheme contains an excellent cryptographic forte with the minimum computational load. These characteristics allow the algorithm to be a hotspot for modern robust applications.

Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

The recent decade has seen a tremendous escalation of multimedia and its applications. These modern applications demand diverse security requirements and innovative security platforms. In this manuscript, we proposed an algorithm for image encryption applications. The core structure of this algorithm relies on confusion and diffusion operations. The confusion is mainly done through the application of the elliptic curve and S8 symmetric group. The proposed work incorporates three distinct chaotic maps. A detailed investigation is presented to analyze the behavior of chaos for secure communication. The chaotic sequences are then accordingly applied to the proposed algorithm. The modular approach followed in the design framework and integration of chaotic maps into the system makes the algorithm viable for a variety of image encryption applications. The resiliency of the algorithm can further be enhanced by increasing the number of rounds and S-boxes deployed. The statistical findings and simulation results imply that the algorithm is resistant to various attacks. Moreover, the algorithm satisfies all major performance and quality metrics. The encryption scheme can also resist channel noise as well as noise-induced by a malicious user. The decryption is successfully done for noisy data with minor distortions. The overall results determine that the proposed algorithm contains good cryptographic properties and low computational complexity makes it viable to low profile applications.

With the exponential increase in communication sector, the risk of information management also increases. Although there is enormous input from the cybersecurity perspective, still a lot must be done. The substitution box is the most vital component in symmetric encryption algorithms, and various proposals have been presented using chaos. Unfortunately, the full potential of chaos in constructing substitution boxes has not been exploited before. In this paper, we have constructed strong and robust substitution boxes based on Boolean functions incorporating chaos. First, we have developed a new algebraic structure based on the Boolean functions. Second, we have incorporated logistic chaotic map with the proposed algebraic structure to construct strong and robust true-chaotic S-Boxes. Third, the constructed S-Boxes are tested against statistical and security analysis including linear and differential cryptanalysis to demonstrate their strength and robustness. The simulation results and analysis demonstrated that the constructed substitution boxes can resist well-known attacks. Finally, we have done the comparative analysis for statistical, security and cryptanalysis with other well-known works to demonstrate the superiority of our work.

Confidentiality of secret information is one of the mandatory issue of digitally modernized era of science and technology. Due to availability of several online web applications and social media usages nowadays, information is transmitted with ease. The privacy of these digital information can be addressed by using different encryption mechanisms. We have proposed digital information privacy preserving scheme based on three-dimensional chaotic self-exciting single disk homopolar system. Moreover, we have designed a circuit implementations of three-dimensional chaotic self-exciting single disk homopolar dynamical system. The suggested encryption scheme is tested against different security performance analyses which clearly reflects the affectedness of our encryption scheme.

Graphical abstract, Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits.

A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

Chaos-based encryption schemes have attracted many researchers around the world in the digital image security domain. Digital images can be secured using existing chaotic maps, multiple chaotic maps, and several other hybrid dynamic systems that enhance the non-linearity of digital images. The combined property of confusion and diffusion was introduced by Claude Shannon which can be employed for digital image security. In this paper, we proposed a novel system that is computationally less expensive and provided a higher level of security. The system is based on a shuffling process with fractals key along with three-dimensional Lorenz chaotic map. The shuffling process added the confusion property and the pixels of the standard image is shuffled. Three-dimensional Lorenz chaotic map is used for a diffusion process which distorted all pixels of the image. In the statistical security test, means square error (MSE) evaluated error value was greater than the average value of 10000 for all standard images. The value of peak signal to noise (PSNR) was 7.69(dB) for the test image. Moreover, the calculated correlation coefficient values for each direction of the encrypted images was less than zero with a number of pixel change rate (NPCR) higher than 99%. During the security test, the entropy values were more than 7.9 for each grey channel which is almost equal to the ideal value of 8 for an 8-bit system. Numerous security tests and low computational complexity tests validate the security, robustness, and real-time implementation of the presented scheme.

Thermal images play a vital character at nuclear plants, Power stations, Forensic labs biological research, and petroleum products extraction. Safety of thermal images is very important. Image data has some unique features such as intensity, contrast, homogeneity, entropy and correlation among pixels that is why somehow image encryption is trickier as compare to other encryptions. With conventional image encryption schemes it is normally hard to handle these features. Therefore, cryptographers have paid attention to some attractive properties of the chaotic maps such as randomness and sensitivity to build up novel cryptosystems. That is why, recently proposed image encryption techniques progressively more depends on the application of chaotic maps. This paper proposed an image encryption algorithm based on Chebyshev chaotic map and S8 Symmetric group of permutation based substitution boxes. Primarily, parameters of chaotic Chebyshev map are chosen as a secret key to mystify the primary image. Then, the plaintext image is encrypted by the method generated from the substitution boxes and Chebyshev map. By this process, we can get a cipher text image that is perfectly twisted and dispersed. The outcomes of renowned experiments, key sensitivity tests and statistical analysis confirm that the proposed algorithm offers a safe and efficient approach for real-time image encryption.

When we listen regarding quantum cryptography, the first thinking that comes up to mind is, how can there be any connection between physics and cryptographic ciphers. In fact, it comes into view that is one of the hottest research in the field of cryptology to exploit physics and has been confirmed as the important objective in the protection of digital data. The topic of quantum magnets and matrix Lorenz Systems has begun to draw increasing attention in recent years. In last decade, chaotic systems have been utilized in many encryption algorithms. In this regard, Lorenz chaotic system based on differential equations achieved more recognition because of its fundamental sensitivity to initial conditions and easiness in use. This manuscript has two parts. First, we have constructed substitution boxes (S-Boxes) based on quantum magnets and matrix Lorenz chaotic system and permutation of the symmetric group S256 and then designated an image encryption algorithm based on proposed S-boxes and Lorenz chaotic system. In cryptography, it is essential to construct secure S-Boxes to propose cryptographically strong systems. Recently, some image encryption techniques that are weak against robustness have been proposed based on chaotic S-boxes. In the first part of the manuscript, an S-Box design is proposed. Continuous-time Lorenz system is chosen as the chaotic system. The presented image encryption algorithm is based on two rounds of a novel chaotic substitution-permutation network uses proposed S-boxes for substitution purpose by iterations of the Lorenz chaotic system and special kind of permutation process to get the full cipher image. The proposed algorithms for S-box construction and image encryption give very good and coherent performance results when we analyze them with renowned analyses.

There have been many different investigations of nonlinear dynamical systems. In this paper, we introduce a new chaotic system. In the proposed system, the attractor can be modified by adding a nonlinear term to the third state equation, thereby generating six different self-excited chaotic attractors. Some dynamical properties such as Hopf bifurcation, bifurcation diagrams, and multistability of the proposed system are investigated. The new system shows topologically different attractors for all six cases. We investigate two cases in depth. We also use nonlinear feedback control to drive the system to equilibrium, using two cases for illustration. Qatar National-Library The publication of this article was funded by the Qatar National-Library.

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents&rsquo, spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system&rsquo, s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

In this paper, a new four-dimensional nonlinear oscillator is introduced. This oscillator is memristive and can exhibit chaotic behavior. A complete dynamical analysis is done on each parameter of this system by the help of bifurcation diagram and Lyapunov exponents’ diagram. In order to estimate parameters of the proposed system, we use a new cost function based on the similarity between return maps. Then, with the help of ions motion optimization method, we minimize the obtained cost function and find the exact value of parameters. Scopus

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of attraction of the coexisting attractors show chaos, stable fixed-points, and unbounded solutions. Furthermore, the 2D parameter space of the system is explored to find the optimum values of the parameters using the ALO (Ant Lion Optimizer) optimization algorithm.

The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems. Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics. In fact, the intricate structure between financial institutions can be obtained by using a network of financial systems. Therefore, in this paper, we consider a ring network of coupled symmetric chaotic finance systems, and investigate its behavior by varying the coupling parameters. The results show that the coupling strength and range have significant effects on the behavior of the coupled systems, and various patterns such as the chimera and multi-chimera states are observed. Furthermore, changing the parameters' values, remarkably influences on the oscillators attractors. When several synchronous clusters are formed, the attractors of the synchronized oscillators are symmetric, but different from the single oscillator attractor.

Chaotic jerk oscillators belong to the simplest chaotic systems. These systems try to model the behavior of dynamical systems efficiently. Jerk oscillators can be known as the most general systems in science, especially physics. It has been proved that every dynamical system expressed with an ordinary differential equation is able to describe as a jerky system in particular conditions. One of its main topics is investigating the collective behavior of chaotic jerk oscillators in the dynamical network. In this paper, the synchronizability of the identical network of jerk oscillators is examined in three different coupling configurations, which are velocity, acceleration, and jerk coupling, and the results are compared with each other.

This paper is concerned with the synchronization of two coupled hyperbolic-type Hopfield neural networks with a memristive synaptic connection. The results show that the coupling with no time-delay cannot lead to complete synchronization and increasing the coupling strength causes anti-phase synchronization. While adding time-delays to the coupling term not only changes the dynamical behavior of the network but also facilitates reaching the full synchronization manifold. The network is investigated in two different cases of single and multiple time-delays. The calculated average‌ synchronization error indicates that using two time-delays has a better effect on the synchronization of systems. However, the synchronization region is lessened by increasing the time-delay values.

In this manuscript, we have proposed an encryption algorithm to encrypt any digital data. The proposed algorithm is primarily based on the substitution-permutation in which the substitution process is performed by the S8 Substitution boxes. The proposed algorithm incorporates three different chaotic maps. We have analysed the behaviour of chaos by secure communication in great length, and accordingly, we have applied those chaotic sequences in the proposed encryption algorithm. The simulation and statistical results revealed that the proposed encryption scheme is secure against different attacks. Moreover, the encryption scheme can tolerate the channel noise as well; if the encrypted data is corrupted by the unauthenticated user or by the channel noise, the decryption can still be successfully done with some distortion. The overall results confirmed that the presented work has good cryptographic features, low computational complexity and resistant to the channel noise which makes it suitable for low profile mobile applications.

The protection of copyrights of digital media uploaded to the Internet is a growing problem. In this paper, first, we present a unified framework for embedding and detecting watermark in digital data. Second, a new robust watermarking scheme is proposed considering this concern. The proposed work incorporates three chaotic maps which specify the location for embedding the watermark. Third, a new chaotic map, the Extended Logistic map, is proposed in this work. The proposed map has a bigger range than logistic and cubic maps. It has shown good results in a bifurcation, sensitivity to initial conditions, and randomness tests. Furthermore, with the detailed analysis of initial parameters, it is justified that Extended Logistic map can be used in secure communication, particularly watermarking. Fourth, to check the robustness of proposed watermarking scheme, we have done a series of analyses and standard attacks. The results confirm that the proposed watermarking scheme is robust against visual and statistical analysis and can resist the standard attacks.

In this article, an optical image encryption algorithm with an information hiding technique is presented. In this algorithm, a secret image is implanted into the cover image. After that the stego-image is encrypted with the help of double random phase encoding algorithm and chaotic substitution box transformation. Also, we present a comparative analysis between images “without substitution box transformation”, “with substitution box transformation” and “with chaotic substitution box transformation”. Security test shows that image transform with chaotic substitution box transformation is better than others. Furthermore we analyze proposed encryption scheme with other existing techniques and come to close that our algorithm is better than others.

In this article, an optical image encryption algorithm based on chaotic baker’s map is presented. The stego-image is encrypted with the help of double random phase encoding algorithm and then produced disorder with the help of chaotic transformation. Security test shows that the reading of proposed algorithm is very close to the optimal values.

This manuscript is about a modified image encryption algorithm based on coupled map lattices and substitution box transformation. The places of the pixels of image are mix up by using chaotic tent map and after that employing delayed coupled map lattices and S-box transformation to puzzle the association between the original image and the encrypted image. The simulation results validate that the propose technique possesses better strength for realistic image encryption.

Chaos has been applied extensively in secure communication over the last decade, but most of the chaotic security protocols defined, are cryptographically weak or slow to compute. Also, study of chaotic phenomena as application in security area is not discussed in detail. In this paper, we have intensely studied chaos, their influence in secure communications and proposed a steganography technique in spatial domain for digital images based upon chaotic maps. By applying chaos effectively in secure communication, the strength of the overall anticipated algorithm has been increased to a significant level. In addition, few security statistical analyses such as correlation, entropy, energy, contrast, homogeneity, peak signal to noise ratio, and mean square error have also been carried out and shown that it can survive against various differential attacks such as the known message attack, known cover attack, known stego attack, and stego only attack.

The theory of chaos is applied to the construction of substitution boxes used in encryption applications. The synthesis process of the proposed substitution boxes is presented, which is based on chaotic Baker’s map and TDERC chaotic sequences. The objectives of the new substitution box are to provide enhanced resistance against differential and linear cryptanalysis. The constructed substitution boxes uses Galois field elements and relies on discrete chaotic maps while keeping differential and linear approximation probabilities to desired levels.

This paper presents an image encryption scheme based on complete shuffling algorithm: limited in the skew tent-map-predicated image cryptosystem and chaotic substitution box transformation. The proposed image encryption algorithm provides extra confusion due to the inclusion of a chaotic S-box. It is well known from the literature that simple image encryption based on a total shuffling scheme is not secure against a chosen cipher text attack. We then projected an extended algorithm which does well against a chosen cipher text attack. Furthermore we analyze the proposed technique for unified average changing intensity (UACI) and NPCR analysis to determine its strength.

A substitution box is used to induce nonlinearity in plaintext for encryption systems. Recently, the application of chaotic maps to encryption applications has resulted in some interesting nonlinear transformations. In this paper, we propose an efficient method to design nonlinear components for block ciphers that are based on TD-ERCS chaotic sequence. The new substitution box is analyzed for nonlinearity, bit independence, strict avalanche criterion, generalized majority logic criterion, and differential and linear approximation probabilities. The results show high resistance to differential and linear cryptanalysis in comparison to some recently proposed chaotic substitution boxes.

In this paper, we propose an image encryption algorithm that is based on GF(28) transformations, using the Arnold cat map and incorporating the nonlinear chaotic algorithm. The plain image is processed with the nonlinear chaotic algorithm and is shuffled iteratively with the Arnold cat map, while transforming the image pixel values into GF(28). We show that the encryption characteristics of this approach are better as compared to some well known encryption algorithms.

In this manuscript we present a novel scheme for image encryption based on S 8 substitution boxes and NCA chaotic sequence. Furthermore, we analyze the strength of the proposed algorithm by applying it to a color image and conclude that the projected algorithm can encrypt color image successfully and secure against many classic attacks.

In this paper, we synthesize substitution boxes by the use of chaotic logistic maps in linear fractional transformation. In order to introduce randomness in the construction of S-boxes, the data from the chaotic system is used in linear fractional transformation to add additional unpredictable behavior. The proposed S-box is tested for its strength in encryption applications. The nonlinearity characteristic of the proposed S-box is studied, and the strength of the cipher is quantized in terms of this property. In addition, the behavior of bit changes at the output of the cipher in comparison with the input is also studied. Similarly, the input/output differential is also evaluated for different bit patterns. The results of statistical analyses show superior performance of the proposed S-boxes.

A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the NCA (nonlinear chaotic algorithm) chaotic maps. The S-box so constructed has very optimal nonlinearity, bit independence criterion (BIC), strict avalanche criterion (SAC), differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes.

In this article, we propose a novel image encryption algorithm by using the linear fractional transformation (LFT) substitution boxes and tangent-delay for elliptic reflecting cavity (TD-ERCS) chaotic sequence. In addition, we apply the proposed approach to an image and come to know that the correlation analysis, UACI analysis, and NPCR analysis of proposed algorithm are much improved than many existing techniques and very easy to put into practice.

This paper is devoted to presenting a new technique for generating S-boxes based on a Lorenz system and S8 group of permutations. Within the algorithm, the initial condition is employed to drive the hyperchaotic Lorenz system to generate a chaotic sequence which is used to construct S-boxes. With different system conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC, BIC and differential approximation probability are found to hold in the obtained S-boxes from the proposed method. The analytic results indicate that all the criteria for designing robust S-boxes can be achieved. The comparison of the proposed S-box generating method with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Classification of information security techniques and its applications

In this paper, a method for obtaining cryptographically strong 8 × 8 substitution boxes (S-boxes) is presented. The method is based on chaotic baker’s map and a “mini version” of a new block cipher with block size 8 bits and can be easily and efficiently performed on a computer. The cryptographic strength of some 8 × 8 S-boxes randomly produced by the method is analyzed. The results show (1) all of them are bijective; (2) the nonlinearity of each output bit of them is usually about 100; (3) all of them approximately satisfy the strict avalanche criterion and output bits independence criterion; (4) they all have an almost equiprobable input/output XOR distribution. The computational graph for the encryption process of the proposed S-box.

The focus of this article is to construct substitution box based on tangent delay for elliptic cavity chaotic sequence and a particular permutation of symmetric group of permutations. The analysis result shows that the proposed S-box is very good against differential and linear type of attacks. Keywords: S-box, Nonlinearity, Bit independence criterion, SAC