Search Results (17)

In the digital information age, although digital images are widely used, the security issues associated with them have become increasingly severe. Consequently, ensuring secure image transmission has become a critical challenge in contemporary information security research. Chaotic systems are characterized by non-periodic behavior, strong dependence on initial conditions, and other favorable characteristics, and have been widely employed in the scrambling and diffusion processes of image encryption. Compared to classical chaotic maps, a quantum Logistic map exhibits better randomness and stronger sensitivity to initial values, effectively overcoming the attractor problem inherent in classical Logistic maps, thereby significantly enhancing the robustness of encryption methodologies. This article focuses on a innovative integration of a quantum Logistic map, hyper-chaotic Lorenz map, and DNA dynamic encoding technology, to design and implement a highly secure and efficient image encryption scheme. First, high-quality random number sequences are produced utilizing the quantum Logistic map, which is then employed to perform a scrambling operation on the image. Next, by integrating the chaotic sequences yielded from the hyper-chaotic Lorenz map with DNA dynamic encoding and operation rules, we implement a diffusion process, thereby increasing the strength of the image encryption. Experimental simulation results and multiple security analyses demonstrated that our encryption methodology achieved excellent encryption performance, effectively resisting a variety of attack strategies, and it holds significant potential for research on protecting image information through encryption. Full article

Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to $S_0$ and $S_{\pm }$ is also proven with the aid of a Lyapunov function and the definitions of both the $\alpha$-limit set and $\omega$-limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc. Full article

In this paper, we propose a secure image encryption method using compressive sensing (CS) and a two-dimensional linear canonical transform (2D LCT). First, the SHA256 of the source image is used to generate encryption security keys. As a result, the suggested technique is able to resist selected plaintext attacks and is highly sensitive to plain images. CS simultaneously encrypts and compresses a plain image. Using a starting value correlated with the sum of the image pixels, the Mersenne Twister (MT) is used to control a measurement matrix in compressive sensing. Then, the scrambled image is permuted by Lorenz’s hyper-chaotic systems and encoded by chaotic and random phase masks in the 2D LCT domain. In this case, chaotic systems increase the output complexity, and the independent parameters of the 2D LCT expand the key space of the suggested technique. Ultimately, diffusion based on addition and modulus operations yields a cipher-text image. Simulations showed that this cryptosystem was able to withstand common attacks and had adequate cryptographic features. Full article

Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaotic system and a 2D sinusoidally constrained polynomial hyper-chaotic map (2D-SCPM). Then, we elaborately developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM (MIEA-FCSM). The introduction of the fractional-order 3D Lorenz chaotic system with the fourth parameter not only enables MIEA-FCSM to have a significantly large key space but also enhances its overall security. Compared with recent alternatives, the structure of 2D-SCPM is simpler and more conducive to application implementation. In our proposed MIEA-FCSM, multi-channel fusion initially reduces the number of pixels to one-sixth of the original. Next, after two rounds of plaintext-related chaotic random substitution, dynamic diffusion, and fast scrambling, the fused 2D pixel matrix is eventually encrypted into the ciphertext one. According to numerous experiments and analyses, MIEA-FCSM obtained excellent scores for key space ($2^{541}$), correlation coefficients (<0.004), information entropy (7.9994), NPCR (99.6098%), and UACI (33.4659%). Significantly, MIEA-FCSM also attained an average encryption rate as high as 168.5608 Mbps. Due to the superiority of the new fractional-order chaotic system, 2D-SCPM, and targeted designs, MIEA-FCSM outperforms many recently reported leading image encryption algorithms. Full article

With the combined call for increased network throughput and security comes the need for high-bandwidth, unconditionally secure systems. Through the combination of true random number generators (TRNGs) for unique seed values, and four-dimensional Lorenz hyperchaotic systems implemented on a Stratix 10 Intel FPGA, we are able to implement 60 MB/s encryption/decryption schemes with 0% data loss on an unconditionally secure system with the NIST standard using less than 400 mW. Further, the TRNG implementation allows for unique encryption outputs for similar images while still enabling proper decryption. Histogram and adjacent pixel analysis on sample images demonstrate that without the key, it is not possible to extract the plain text from the encrypted image. This encryption scheme was implemented via PCIe for testing and analysis. Full article

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings. Full article

Radio frequency (RF) stealth anti-sorting technology is a research hotspot in the radar field. In this study, the signal design principles of anti-cluster and anti-SDIF sorting were investigated for processes of clustering pre-sorting and sequence-difference-histogram main sorting. Then, in accordance with the signal design principle, a 2D interleaving feedback hyperchaotic system based on the cosine-exponential was designed. A method to modulate the pulse repetition interval (PRI) of the signal parameters and carrier frequency with wide intervals through the hyperchaotic system was developed. Finally, we verified the correctness of the signal design principle, the performance of the hyperchaotic system, and the anti-sorting performance of the designed signal using simulations. The results showed that the signal design principle could guide the signal design. The hyperchaotic system outperformed the classical 1D and 2D chaotic systems and the classical 3D Lorenz systems in terms of randomness and complexity. Anti-cluster sorting and anti-SDIF sorting could be realized by anti-sorting signals modulated by a hyperchaotic system, with the anti-SDIF sorting performance being better than that of the PRI random jitter signal. Full article

Hyperchaotic complex behaviors often occur in nature. Some chaotic behaviors are harmful, while others are beneficial. As for harmful behaviors, we hope to transform them into expected behaviors. For beneficial behaviors, we want to enhance their chaotic characteristics. Aiming at the harmful hyperchaotic complex system, a tracking controller was designed to produce the hyperchaotic complex system track common expectation system. We selected sine function, constant, and complex Lorenz chaotic system as target systems and verified the effectiveness by mathematical proof and simulation experiments. Aiming at the beneficial hyperchaotic complex phenomenon, this paper extended the hyperchaotic complex system to the fractional order because the fractional order has more complex dynamic characteristics. The influences order change and parameter change on the evolution process of the system were analyzed and observed by MATLAB simulation. Full article

Security standards have been raised through modern multimedia communications technology, which allows for enormous progress in security. Modern multimedia communication technologies are concerned with fault tolerance technique and information security. As a primary method, there is widespread use of image encryption to protect image information security. Over the past few years, image encryption has paid more attention to combining DNA technologies in order to increase security. The objective here is to provide a new method for correcting color image encryption errors due to the uncertainty of DNA computing by using the fractional order hyperchaotic Lorenz system. To increase randomness, the proposed cryptosystem is applied to the three plain image channels: Red, Green, and Blue. Several methods were compared including the following: entropy, correlation, key sensitivity, key space, data loss attacks, speed computation, Number of Pixel changing rate (NPCR), and Unified Average Change Intensity randomness (UACI) tests. Consequently, the proposed scheme is very secure against a variety of cryptographic attacks. Full article

Many plaintext-related or non-plaintext-related image encryption algorithms based on chaotic systems have been found inefficient and insecure under chosen plaintext attacks. In this paper, a novel plaintext-related mechanism based on the peculiarity of plaintext DNA coding (PPDC) is presented and used to developed a symmetric image encryption algorithm. In our scheme, a hyper-chaotic Lorenz system is used to produce four chaotic sequences. Firstly, by using one chaotic sequence to control the DNA rules, the original image is encoded to obtain the image DNA coding and PPDC, and another chaotic sequence is encoded into a DNA sequence, which is used in the DNA XOR operation. Then, the processing of the remaining two chaotic sequences by using the PPDC is performed to obtain two key streams, which are used in the permutation stage. After performing the traditional permutation operation and DNA XOR operation, the cipher image is obtained. Because of the use of the PPDC, the key streams used in the permutation stage are related to the secret keys and plaintext image, which gives the encryption system higher plaintext sensitivity and security. The simulation experimental results and security analysis demonstrate that the proposed encryption system possesses high efficiency and security and can resist various typical attacks like exhaustive attack, statistical attack, and differential attack effectively. Full article

By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent with the theoretic analysis and numerical simulation. Full article

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer. Full article

This paper describes evolution of new active element that is able to significantly simplify the design process of lumped chaotic oscillator, especially if the concept of analog computer or state space description is adopted. The major advantage of the proposed active device lies in the incorporation of two fundamental mathematical operations into a single five-port voltage-input current-output element: namely, differentiation and multiplication. The developed active device is verified inside three different synthesis scenarios: circuitry realization of a third-order cyclically symmetrical vector field, hyperchaotic system based on the Lorenz equations and fourth- and fifth-order hyperjerk function. Mentioned cases represent complicated vector fields that cannot be implemented without the necessity of utilizing many active elements. The captured oscilloscope screenshots are compared with numerically integrated trajectories to demonstrate good agreement between theory and measurement. Full article

The aim of the paper was to analyze the given nonlinear problem by different methods of computation of the Lyapunov exponents (Wolf method, Rosenstein method, Kantz method, the method based on the modification of a neural network, and the synchronization method) for the classical problems governed by difference and differential equations (Hénon map, hyperchaotic Hénon map, logistic map, Rössler attractor, Lorenz attractor) and with the use of both Fourier spectra and Gauss wavelets. It has been shown that a modification of the neural network method makes it possible to compute a spectrum of Lyapunov exponents, and then to detect a transition of the system regular dynamics into chaos, hyperchaos, and others. The aim of the comparison was to evaluate the considered algorithms, study their convergence, and also identify the most suitable algorithms for specific system types and objectives. Moreover, an algorithm of calculation of the spectrum of Lyapunov exponents based on a trained neural network has been proposed. It has been proven that the developed method yields good results for different types of systems and does not require a priori knowledge of the system equations. Full article

The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP), and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully. Full article