A technique for digital steganography using chaotic maps

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.     

An image encryption scheme based on a new hybrid chaotic map and optimized substitution box

Nonlinear Dynamics - This paper proposes a new hybrid chaotic map and a different way of using optimization technique to improve the performance of encryption algorithms. Compared to other chaotic...     

A secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps

Recently, biometric-based remote user authentication schemes along with passwords have drawn considerable attention in research. In 2011, Das proposed an improvement on an efficient biometric-based remote user authentication scheme using smart cards and claimed his scheme could resist various attacks. However, there are some weaknesses in Das’s scheme such as the privileged insider attack and the off-line password guessing attack. Besides, Das’s scheme also cannot provide user anonymity. To overcome these weaknesses, we shall propose a secure biometric-based remote user authentication with key agreement scheme using extended chaotic maps. The proposed scheme not only can resist the above-mentioned attacks, but also provide user anonymity.     

A three-party password-based authenticated key exchange protocol with user anonymity using extended chaotic maps

In this paper, we propose a scheme utilizing three-party password-based authenticated key exchange protocol with user anonymity using extended chaotic maps, which is more efficient and secure than previously proposed schemes. In order to enhance the efficiency and security, we use the extended chaotic maps to encrypt and decrypt the information transmitted by the user or the server. In addition, the proposed protocol provides user anonymity to guarantee the identity of users, which is transmitted in the insecure public network.     

A novel image encryption algorithm based on chaotic maps and GF(28) exponent transformation

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.     

A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems

In cryptographic systems, the encryption process relies on the nonlinear mapping of original data or plaintext to the secure data. The mapping of data is facilitated by the application of the substitution process embedded in the cipher. It is desirable to have resistance against differential cryptanalysis, which assists in providing clues about the composition of keys, and linear secret system, where a simple approximation is created to emulate the original cipher characteristics. In this work, we propose the use of nonlinear functional chaos-based substitution process which employs a continuous time Lorenz system. The proposed substitution system eliminates the need of independent round keys in a substitution-permutation network. The performance of the new substitution box is evaluated by nonlinearity analysis, strict avalanche criterion, bit independence criterion, linear approximation probability, and differential approximation probability.     

Parameter identification of chaotic systems using improved differential evolution algorithm

In this paper, an improved differential evolution algorithm, named the Taguchi-sliding-based differential evolution algorithm (TSBDEA), is proposed to solve the problem of parameter identification for Chen, Lü and Rossler chaotic systems. The TSBDEA, a powerful global numerical optimization method, combines the differential evolution algorithm (DEA) with the Taguchi-sliding-level method (TSLM). The TSLM is used as the crossover operation of the DEA. Then, the systematic reasoning ability of the TSLM is provided to select the better offspring to achieve the crossover, and consequently enhance the DEA. Therefore, the TSBDEA can be more robust, statistically sound, and quickly convergent. Three illustrative examples of parameter identification for Chen, Lü and Rossler chaotic systems are given to demonstrate the applicability of the proposed TSBDEA, and the computational experimental results show that the proposed TSBDEA not only can find optimal or close-to-optimal solutions but also can obtain both better and more robust results than the DEA.     

Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control

The model and the normalized state equations of the novel version of the Colpitts oscillator designed to operate in the ultra-high frequency range are presented. The circuit is investigated numerically and simulations demonstrate chaos in the microwave frequency range. Typical phase portrait, Lyapunov exponent and Lyapunov dimension are calculated using a piece-wise linear approximation of nonlinear I–V characteristic of the bipolar junction transistor. In addition, the feedback controller is applied to achieve chaos synchronization for two identical improved chaotic Colpitts oscillators. In the frame the nonlinear function of the system is used as a nonlinear feedback term for the stability of the error dynamics. Finally, numerical simulations show that this control method is feasible for this oscillator.     

Lyapunov spectrum of chaotic maps with a long-range coupling mediated by a diffusing substance

We investigate analytically and numerically coupled lattices of chaotic maps where the interaction is non-local, i.e., each site is coupled to all the other sites but the interaction strength decreases exponentially with the lattice distance. This kind of coupling models an assembly of pointlike chaotic oscillators in which the coupling is mediated by a rapidly diffusing chemical substance. We consider a case of a lattice of Bernoulli maps, for which the Lyapunov spectrum can be analytically computed and also the completely synchronized state of chaotic Ulam maps, for which we derive analytically the Lyapunov spectrum.     

A novel construction of chaotic dynamics base gliders in diffusion rule B2/S7

The dynamical behaviors of gliders (mobile localizations) in diffusion rule B2/S7 are quantitatively analyzed from the theory of symbolic dynamics in two-dimensional symbolic sequence space. Their intrinsic complexity is demonstrated by exploiting the relationship between one-dimensional and two-dimensional subshifts. Based on this rigorous approach and technique, the underlying chaos of the extant gliders and their combinations is characterized in a subtle way. It is demonstrated that they can be identified to distinct subsystems with very rich and complicated dynamics; that is, diffusion rule is topologically mixing and possesses positive topological entropy on each subsystem. This analytical assertion provides the fact that diffusion rule is covered with complex subsystems “almost everywhere”. Finally, it is worth mentioning that the procedure proposed in this paper is also applicable to all other gliders arising from the two-dimensional cellular automata therein. It is an extended discovery in both cellular automata and chaos theory.     

A novel memcapacitor and its application in a chaotic circuit

Nonlinear Dynamics - In this paper, a novel memcapacitor is designed by the SBT ( $$\hbox {Sr}_{0.95}\hbox {Ba}_{0.05}\hbox {TiO}_{{3}}$$ ) memristor and two capacitors. A fifth-order memcapacitor...     

Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors

Nonlinear Dynamics - Novel chaotic system designs and their engineering applications have received considerable critical attention. In this paper, a new three-dimensional chaotic system and its...     

An efficient approach for the construction of LFT S-boxes using chaotic logistic map

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.     

Cryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map

Nonlinear Dynamics - In this paper, we evaluate the security of an image cipher recently proposed. Three different cryptographic primitives, i.e., permutation, diffusion, and cyclic rotation, were...