Hyperchaotic System Research Articles

A Novel Four-Dimensional Hyperchaotic System: Design, Dynamic Analysis, Synchronization, and Image Encryption

A Novel Four-Dimensional Hyperchaotic System: Design, Dynamic Analysis, Synchronization, and Image Encryption

Secure Image Encryption using E-Fractal-Based Non-Commutative Group and Hash Function

Due to the importance of data security at present, an encryption algorithm based on the principle of non-commutative group, hash function, and E-fractal has been proposed. Key generation depends on the array values generated by the braid group and using them as input to the SHA-3 (256) which increases the strength of the key because it generates values in one direction only. The results of the hash function are determined by the Lorenz hyper-chaotic system initial values, and four image-size arrays are generated as the final image-encryption keys using the RC4 algorithm. Then the use of the E-fractal diffusion method. To bolster the security of the encryption, it is employed to disperse the pixel values., adopting the control word that increases the randomness of the data. The security analysis of the proposed encryption algorithm demonstrates that it is difficult to decipher due to the presence of the hash function in addition to its easy implementation within seconds, and the efficiency scale was calculated that showed its strength in effectively resisting attacks by others.

A New 6D Hyperchaos-Based Medical Image Encryption Scheme Using k-Fibonacci Numbers

In the era of information technology, hospitals, medical centers, doctors and health specialists share millions of images. Securing these images is essential to maintaining patients’ privacy. Several cryptographic algorithms are implemented to meet the increasing demands of transmission systems. As a contribution to securing these data, we propose a novel robust and efficient algorithm. We randomly generate numbers from a six-dimensional hyperchaotic system and Arnold’s cat map to confuse the original images. The confused images are then diffused using a k-Fibonacci matrix. The performance of the proposed algorithm was evaluated using several parameters tested on a set of reference images of different sizes and modalities. The obtained results are conclusive and the performances are excellent, sometimes exceeding those found by other recent algorithms proposed in the literature.

Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method.

Offset boosting in a memristive hyperchaotic system

In this article, an autonomous memristive hyperchaotic system with multi-dimensional offset boosting is constructed and analyzed. Besides this, the oscillation can be rescaled by an independent controller in the memristor. Two independent constants are obtained for offset boosting with one or two variables, which provide two modes of offset boosting, including single control and synchronous reverse control. In addition, the offset of the variables is also modified by the system bifurcation parameters or combined with amplitude control. The multistability can also be identified according to the offset boosting. Finally, circuit implementation based on PCB is proposed to confirm the numerical simulations.

A universal method for constructing n-dimensional polynomial hyperchaotic systems with any desired positive Lyapunov exponents

Most existing chaotic maps have many defects in engineering applications, such as discontinuous parameter range, uneven output of chaotic sequences and dynamic degradation. Based on this, a generalized n-dimensional polynomial chaotic map is proposed in this paper. By setting the coefficient of the linear term and the order of the highest order term of the polynomial, a series of n-dimensional polynomial chaotic maps of specific Lyapunov exponents can be obtained. The system solves the defects of the above system well, in addition, one can get the desired number of positive Lyapunov exponents, and one can get the desired value of positive Lyapunov exponents. Then, the effectiveness of the map is verified by a specific numerical example, and its dynamic analysis shows that the map has complex dynamic behavior. Finally, the map is applied to secure communication technology. Compared with other chaotic maps of the same dimension, the maps can obtain a smaller bit error rate, indicating that the chaotic map is more suitable for chaotic secure communication applications.

Enhancing Key Exchange Security: Leveraging RSA Protocol in Encryption Algorithm Based on Hyperchaotic System

Enhancing Key Exchange Security: Leveraging RSA Protocol in Encryption Algorithm Based on Hyperchaotic System

Color image ROI encryption algorithm based on a novel 4D hyperchaotic system

The significance of safeguarding the security of image information has escalated significantly, owing to the exponential proliferation of digital images containing sensitive information being disseminated on the Internet. In this paper, we first propose a novel 4D hyperchaotic system and design a new image encryption algorithm in conjunction with the hyperchaotic system. The algorithm uses a split random swap permutation method to permute the image and combines the S-box to diffuse the image. To improve the diffusivity of this encryption algorithm, a cross-random diffusion method is designed to diffuse the image again. Then, we propose a region of interest (ROI) encryption scheme for images. This scheme can automatically identify irregular privacy targets in images and encrypt them. To ensure the security of the region of interest location information during transmission, the scheme compresses the location information of the privacy target using a run-length encoding technique and then embeds the compressed data into the ciphertext image using reversible steganography based on histogram shift. The experimental results and security analysis unequivocally demonstrate that the image encryption algorithm proposed in this paper exhibits robust resistance against a wide array of attacks, thereby ensuring a high level of security. Additionally, the devised image ROI encryption scheme effectively safeguards diverse privacy targets.

A Sine-coupled model for constructing N-dimensional non-degenerate discrete hyperchaotic map

The non-degenerate hyperchaotic systems with the maximum number of positive Lyapunov exponents (LEs) typically have better ergodicity, pseudo randomness, and stronger anti-degeneration property. Therefore, designing non-degenerate hyperchaotic maps with complex dynamics has attracted increasing attention from various research fields in recent years. By introducing the sine function, this paper proposes a construction model of N-dimensional non-degenerate discrete hyperchaotic map. To verify the effectiveness of this model, we provide three sub-maps of different dimensions based on this model as illustrative examples, and the dynamic behavior is explored using multiple numerical measures. The results demonstrate that the sub-maps with concise symmetric structures have complex dynamics, such as ultra-wide non-degenerate hyperchaotic parameter range, state transition phenomenon, and multistability. In particular, coexisting symmetric attractors and quasi-periodic curves switch periodically with the change of initial value. Furthermore, the hyperchaotic sequences generated by the three sub-maps have excellent performance, and the NIST test also further verifies the super randomness and unpredictability of these sequences. Finally, through the DSP hardware platform, the physical realizability of the sub-maps is verified successfully.

Image encryption algorithms based on two-dimensional discrete hyperchaotic systems and parallel compressive sensing

Image encryption algorithms based on two-dimensional discrete hyperchaotic systems and parallel compressive sensing

Diffusion-assisted quantum noise stream cipher for physical layer security in UFMC

Universal filtered multicarrier (UFMC) is a promising multicarrier technologies due to its ability to suppress inter symbol interference, increase frequency band utilization and provide flexible adaptation. However, it is vulnerable to illegal eavesdropping in the point-to-multipoint access transmission. Quantum noise stream cipher (QNSC), a classical physical layer encryption scheme, is inherent matched with the UFMC system. However, its security mainly depends on the length of the basis states, which is limited by the performance of commercial high-speed digital-to-analog converters (DACs). In this work, we propose a diffusion-assisted quantum noise stream cipher (DA-QNSC) scheme to enhance the security. Here, we introduce artificial noise generated by hyperchaotic system to pseudo expand the distribution of quantum noise, which will make it more difficult for eavesdroppers to crack plaintext information violently. We experimentally demonstrate the encrypted 16/4096-QAM, 16/16384-QAM, 16/65536-QAM DA-QNSC signals over 30-km standard single mode fiber (SSMF) transmission. Compared to the conventional QNSC systems, the proposed method achieves a 3.6 times improvement in the security with the same DAC resolution and has negligible impact on bit error ratio (BER) performance. For the 16/65536-QAM signal, the number of masked symbols (NMS) are increased from 910 to 3270.

Integrating Lorenz Hyperchaotic Encryption with Ring Oscillator Physically Unclonable Functions (RO-PUFs) for High-Throughput Internet of Things (IoT) Applications

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.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation (DNEQR) model that allows for simultaneous storage of two digital images in a quantum superposition state. Additionally, a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated, offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps. Based on the DNEQR model and the hyperchaotic system, a double quantum images encryption algorithm is proposed. Firstly, two classical plaintext images are transformed into quantum states using the DNEQR model. Then, the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences. These chaotic sequences are utilized to perform pixel value and position operations on the quantum image, resulting in changes to both pixel values and positions. Finally, the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences. The corresponding quantum circuits are also given. Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission, improves the encryption efficiency, and enhances anti-interference and anti-attack capabilities.

Matrix and Inverse Matrix Projective Synchronization of Chaotic and Hyperchaotic Systems with Uncertainties and External Disturbances

Matrix and Inverse Matrix Projective Synchronization of Chaotic and Hyperchaotic Systems with Uncertainties and External Disturbances

A new four-dimensional hyperchaotic system with hidden attractors and multistablity

This paper proposes a novel 4D hyperchaotic system with hidden attractors and coexisting attractors, which have no equilibrium points. The dynamic behavior of the system and five groups of coexisting attractors are analyzed by applying phase space diagrams, bifurcation diagrams and the Lyapunov exponents spectrum. Additionally, the system’s stable limit cycles and unstable periodic orbits were calculated through the variational method and then encoded using symbolic dynamics. The numerical results were verified via a circuit simulation, confirming the realizability of the novel hyperchaotic system in hardware facilities. Finally, we applied the active synchronization control method to the new system with remarkable results.

DNA image encryption algorithm based on serrated spiral scrambling and cross bit plane

In response to the problem of uneven information distribution in DNA encoding, in this article, a new DNA chaotic image encryption algorithm combining serrated spiral scrambling and cross bit plane using lookup table diffusion is proposed. First of all, a four-dimensional hyperchaotic system is proposed, which can produce four interrelated sequences. Next, perform serrated spiral scrambling and index scrambling on the plain image to change the position of pixels. Then DNA is encoded in combination with the crossed bit plane, and then the pixel size is changed by using the new look-up table diffusion. Lastly, DNA decoding is performed to obtain the encrypted image. The test of whether the feasibility and security of the algorithm have been improved can be obtained by analyzing the size of the experimental data and the degree of deviation from the ideal value. After comprehensive analysis, it is concluded that this paper has good encryption effect on the basis of encryption security has also been improved.

Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence

Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence

Complex-valued hyperchaos-assisted vector-valued artificial neural key coordination for improving security in the Industrial Internet of Things

This paper presents an innovative solution to the key exchange problem in the Industrial Internet of Things (IIoT) implementation. Communication between connected devices must be safe and effective if the IIoT is to continue its fast growth. A crucial part of safeguarding the security and integrity of data shared across the IIoT ecosystem is played by cryptographic key exchange approaches. To provide reliable cryptographic key exchange in the IIoT context, this paper offers a unique approach that makes use of hyperchaotic with complex values, variable parameters, and vector-valued neural synchronization. The method addresses the continued demand for effective cryptographic key exchange across IIoT devices by using drive–response techniques to speed up important applications. Long assessment times in conventional algorithms make it difficult to hide neuronal coordination. As a result, this paper offers a condensed evaluation of ANNs’ (Artificial Neural Networks) synchronization by coordinating ANNs for session key exchange using a hyperchaotic setting. The recommended approach has several benefits, including the following: (1) introducing a hyperchaotic system to generate synchronized input vectors for ANN synchronization; (2) The adaptive rules of parameters-based control procedures are constructed mathematically; (3) reciprocal alignment of vector-valued ANNs to form a neural network for establishing session keys throughout the IIoT network; and (4) relevant numerical simulations are carried out to assess the scheme’s consistency. The recommended approach performs better than other methods that have been published in the literature, widening up opportunities for more effective and reliable industrial applications.

A novel multi-scroll hyperchaotic system applicable for visually secure image cryptosystem using block compressive sensing

A novel multi-scroll hyperchaotic system applicable for visually secure image cryptosystem using block compressive sensing

Color image encryption algorithm based on novel 2D hyper-chaotic system and DNA crossover and mutation

Color image encryption algorithm based on novel 2D hyper-chaotic system and DNA crossover and mutation