One-dimensional Chaotic Systems Research Articles

Medical image encryption system based on a simultaneous permutation and diffusion framework utilizing a new chaotic map

In telemedicine, diverse medical images transmitted between doctors and patients contain sensitive personal information. Thus, there is an urgent need for reliable and efficient medical image encryption to protect these medical images during transmission. In this paper, a simultaneous permutation and diffusion framework (SPDF) is introduced for medical image encryption based on a new chaotic map. Firstly, combining the Chebyshev map and the iterative chaotic map with infinite collapse (ICMIC), we propose a one-dimensional chaotic system (1D-CICMIC) which exhibits higher ergodicity and unpredictability compared to other 1D chaotic maps through comprehensive analyses. Secondly, in order to enhance permutation effect, we modify traditional Josephus traversing with a dynamic scrambling method where the scrambling scheme of the current pixel depends on the value of the previous diffused pixel. Thirdly, we develop a simultaneous permutation and diffusion framework, wherein the diffusion is embedded into the modified Josephus traversing to prevent attackers from targeting the scrambling and diffusion phases separately. Finally, based on 1D-CICMIC and SPDF, an encryption system is proposed. It adopts plaintext correlation in the diffusion operation, which strikes a balance between ciphertext sensitivity and plaintext sensitivity, offering resistance against chosen-plaintext attack (CPA), noise attack and data loss. Simulation results show that the proposed algorithm has high encryption efficiency and can withstand various common attacks.

Fingerprint image encryption based on chaos and nonlinear dynamic “X” model diffusion

It is analyzed that the important part of the fingerprint image is concentrated in one part of the image, and the gray image is the part with useful information in the whole image. Therefore, this paper combines a new fingerprint image encryption algorithm proposed by combining two new one-dimensional chaotic systems, nonlinear functions, and rules with a dynamic "X" model. We propose two new one-dimensional chaotic systems, one is Sin-Cos chaotic system (SCCS) and the other is Cos-Cos chaotic system (CCCS). Firstly, the fingerprint image is binarized and the contour is extracted to get the area of the fingerprint in the image. Then, for the fingerprint area, a round of encryption is carried out by using nonlinear rules and 24 rules of the dynamic X model. Then the whole image is separated into several parts according to the fingerprint position, read into a sequence at one time, and the whole fingerprint image is scrambled and diffused synchronously by using nonlinear rules and functions. The entropy, NPCR, and UACI of the algorithm are very close to the ideal value, and the performance in time efficiency is passable. The algorithm is extremely secure in a large number of test performance analysis results.

Design of Pseudo-random Sequence Generator based on Three-dimensional Discrete Chaotic System

In this paper, a pseudo-random sequence generator with better randomness is constructed through the targeted improvement of chaotic system. Firstly, a new three-dimensional discrete chaotic system is proposed on the basis of the existing one-dimensional logistic chaotic system by improving and optimizing the dimensionality and coupling mode, and its Lyapunov exponent and other characteristics are analyzed; then, based on the chaotic system, a pseudo-random sequence generator is designed by using post-processing and heterodyne, etc.; after that, the performance of the pseudo-random sequence is discussed by using the evaluation methods of relevance, homogeneity, and NIST test. After that, the performance of the pseudo-random sequence is discussed using correlation, uniformity, NIST test and other evaluation methods. The results show that the three-dimensional discrete chaotic system has good chaotic properties, and the pseudo-random sequence generator based on this three-dimensional discrete chaotic system has good random performance and can pass the NIST test. The work in this paper provides an idea for the improvement of logistic mapping chaotic system and enriches the application form of pseudorandom sequence generator in information security.

Novel chaotic image cryptosystem using dynamic DNA coding

This study aims to solve the problem of small key space in image cryptosystems based on logistic mapping. First, a new one-dimensional (1D) chaotic system, with a wide continuous chaotic interval, a large Lyapunov exponent and obvious chaotic characteristics are presented. Subsequently, a novel image encryption algorithm based on the new 1D chaotic system and dynamic DNA encoding is designed. Compared with other DNA coding methods, the proposed image encryption algorithm encodes chaotic sequences and ensures that the sequence elements at different positions correspond to different DNA coding schemes. This will help to overcome the fixity of DNA coding and make the proposed dynamic DNA coding easy to operate and implement. Finally, the cipher image is obtained by scrambling and bit XOR operation based on the chaotic sequences. The fixed DNA coding method is compared with other chaotic image encryption schemes, and the experimental results indicate that the image encryption algorithm has higher security and can resist common attacks.

On a Symmetric Image Cryptosystem Based on a Novel One-Dimensional Chaotic System and Banyan Network

In this paper, a Banyan network with high parallelism and nonlinearity is used for the first time in image encryption to ensure high complexity and randomness in a cipher image. To begin, we propose a new 1-D chaotic system (1-DSCM) which improves the chaotic behavior and control parameters’ structure of the sin map. Then, based on 1-DSCM, a Banyan network, and SHA-256 hash function, a novel image encryption algorithm is conducted. Firstly, a parameter is calculated using SHA-256 hash function and then employed to preprocess the plaintext image to guarantee high plaintext sensitivity. Secondly, a row–column permutation operation is performed to gain the scrambled image. Finally, based on the characteristic of DNA encoding, a novel DNA mapping is constructed using an N=4 Banyan network and is used to diffuse the scrambled image. Simulation results show that the 1-DSCM has excellent performance in chaotic behavior and that our encryption algorithm exhibits strong robustness against various attacks and is suitable for use in modern cryptosystems.

Visualized Multiple Image Selection Encryption Based on Log Chaos System and Multilayer Cellular Automata Saliency Detection

For the security of multiple image regions of interest, this paper designs a multi-image visual encryption algorithm based on region of interest (ROI). Firstly, a new one-dimensional chaotic system (1-DLCP) is proposed. The performance analysis shows that the system has better dynamic behavior. Then, the salient parts of multiple images are extracted using multilayer cellular automata saliency detection. The measured matrix generated by the proposed chaotic system compresses the extracted plaintext images respectively. The compressed image and the extracted salient parts are recombined into one image, and a scrambling-diffusion synchronization operation is performed on the recombined image to obtain a secret image. The final embedding stage uses integer wavelet transform (IWT) to embed the secret image into a color carrier image. It is worth mentioning that this design scheme not only reconstructs the significant part without damage, but also reduces the storage space.

A Color Image Encryption Method Based on Dynamic Selection Chaotic System and Singular Value Decomposition

As the basis for guiding business process decisions, flowcharts contain sensitive information pertaining to process-related concepts. Therefore, it is necessary to encrypt them to protect the privacy or security of stakeholders. Using the principles of image singular value decomposition, chaotic system randomness, and neural network camouflage, a business flow chart encryption method based on dynamic selection chaotic system and singular value decomposition is proposed. Specifically, a dynamic selected chaotic system is constructed based on the nonlinear combination of one-dimensional chaotic system Logistics and Sine, and its randomness is verified. Next, using the neural network, the process image is merged into a gray matrix. The double-bit unitary matrix scrambling based on singular value decomposition is then proposed. Subsequently, using the dynamic selected chaotic system, a new sub-division diffusion method is proposed, which combines, diffuses, and performs weighted superposition to generate a matrix after diffusion and compression. Finally, the asymmetric encryption method encrypts the color image and reduces its dimensionality into a single grayscale ciphertext, and the decryption process is not the reverse of the encryption process. Simulation results and performance analysis show that the proposed image encryption scheme has good encryption performance.

Multibiometric Images Encryption Method Based on Fast Fourier Transform and Hyperchaos

Biometric images are an important means of personal identity verification and identification and are related to personal privacy and property security. To address the problems of poor security and low image reconstruction quality in the encryption and transmission of multibiometric images, a multibiometric images encryption method based on Fast Fourier Transform (FFT) and hyperchaotic system is proposed. First, the FFT is used to transform the multibiometric images from spatial to frequency domain. Then, the initial values of the hyperchaotic Lorenz system are generated using a one-dimensional chaotic logistic system to generate the key stream. Combined with the recoding rules of matrix reconstruction and scrambling without repetition of using multimatrix, the multiple matrices of amplitude and phase in the transform domain are reconstructed to be multiple RGB three-channel color images by using the inverse fast Fourier transform. Then, we combine the two diffusion methods of additive mode and Galois domain diffusion on each color channel to perform confusion and diffusion. Finally, the multiple grayscale images are encrypted to become multiple color images. The experimental results demonstrate that the method can effectively defend against various attacks. In addition, it solves the problem of low reconstruction accuracy that exists in the field of multiple images security.

Image encryption algorithm based on 1D-SFACF with cross-cyclic shift and adaptive diffusion

In this paper, a new one-dimensional chaotic system is proposed, which is called one-dimensional sine-fractional-adjusted-cosine-fractional (1D-SFACF). The dynamic behavior of the 1D-SFACF is analyzed by LE, bifurcation graph, trajectory, and cobweb plot. Compared to most one-dimensional chaotic systems, the 1D-SFACF has good cryptographic properties, such as larger parameter space and better chaotic behavior. Based on the excellent expressiveness of the 1D-SFACF, we design a secure image encryption algorithm using 1D-SFACF, called the image encryption algorithm based on 1D-SFACF (SFACF-IE). SFACF-IE is divided into four steps. First, the control parameters and initial values of 1D-SFACF are generated through a natural noise using a hash function. Secondly, an adaptive diffusion strategy is proposed. The starting position of the plaintext diffusion is adaptively changed according to the characteristics of the plaintext. Then, use a cross-cyclic shift to scramble. Finally, a hash function is used to generate a feedback key, the scrambled image is the input of the hash function, and the ciphertext is obtained by diffusing again. Experimental evaluations show that the algorithm is resistant to common attacks.

One-Dimensional Quadratic Chaotic System and Splicing Model for Image Encryption

Digital image transmission plays a very significant role in information transmission, so it is very important to protect the security of image transmission. Based on the analysis of existing image encryption algorithms, this article proposes a new digital image encryption algorithm based on the splicing model and 1D secondary chaotic system. Step one is the algorithm of this article divides the plain image into four sub-parts by using quaternary coding, and these four sub-parts can be coded separately. Only by acquiring all the sub-parts at one time can the attacker recover the useful plain image. Therefore, the algorithm has high security. Additionally, the image encryption scheme in this article used a 1D quadratic chaotic system, which makes the key space big enough to resist exhaustive attacks. The experimental data show that the image encryption algorithm has high security and a good encryption effect.

Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding

In this paper, a new one-dimensional fractional chaotic map is proposed and an image encryption scheme based on parallel DNA coding is designed by using the chaotic map. The mathematical model of the new chaotic system combines a sine map and a fraction operation. Compared with some traditional one-dimensional chaotic systems, the new chaotic system has a larger range of chaotic parameters and better chaotic characteristics, which makes it more suitable for applications in information encryption. In addition, an image encryption algorithm based on parallel DNA coding is proposed, which overcomes the shortcoming of common DNA coding-based image encryption algorithms. Parallel computing significantly increases the speed of encryption and decryption algorithms. The initial key of the cryptosystem is designed to be related to the SHA-3 hash value of the plaintext image so that the algorithm can resist a chosen-plaintext attack. Simulation experiments and security analysis results show that the proposed image encryption scheme has good encryption performance and less time overhead, and has strong robustness to noise and data loss attacks, which indicates that the proposed image encryption scheme has good application potential in secure communication applications.

Chaotic Mapping-Based Anti-Sorting Radio Frequency Stealth Signals and Compressed Sensing-Based Echo Signal Processing Technology.

Radio frequency (RF) stealth anti-sorting technology can improve the battlefield survival rate of radar and is one of the research hotspots in the radar field. In this study, the signal design principle of anti-sequential difference histogram (SDIF) sorting was explored for the main sorting algorithm of the SDIF. Furthermore, we designed a piecewise linear chaotic system with interval number parameterization based on random disturbance and proposed a method to modulate the repetition period of widely spaced signal pulses using a chaotic system. Then, considering the difficulty of the traditional signal processing method to measure the velocity of the highly random anti-sorting signals designed in this paper, we used compressed sensing (CS) technology to process the echoes of the signals to solve the velocity and distance of the detection targets. Finally, simulation verification was performed from the correctness of the signal design principle, the performance of the chaotic system, the anti-sorting performance of the designed signals and the recovery and reconstruction performance of the signals by CS. The results show that: (a) the signal design principle presented in this paper can guide the signal design correctly; (b) the performance of the piecewise linear chaotic system with interval number parameterization is better than that of the classical one-dimensional chaotic system; (c) the anti-sorting signal modulated by the chaotic system can achieve anti-SDIF sorting, and the anti-sorting signals designed in this paper can be processed to obtain the velocity and distance of the targets.

Novel One-Dimensional Chaotic System and Its Application in Image Encryption

Designing a chaotic system with a simple structure and complex dynamic behavior is one of the main tasks of chaotic cryptography. This paper designs a new 1D chaotic system called 1D two-parameters-sin-cos (1D-TPSC). Compared with high-dimensional chaotic systems, the 1D-TPSC has a simple structure and is easy to implement with software. The Lyapunov exponent analyzes the parameter space of the 1D-TPSC in a chaotic state. Furthermore, using sensitivity analysis, cobweb plot, and bifurcation diagram to verify that the sequence generated by 1D-TPSC has good performance. In addition, the 1D-TPSC has also been applied in chaotic image encryption. Arnold mapping is used to scramble the plaintext, and random XOR is used to diffuse the scrambled image. Simulation experiments show that the method can remarkably resist standard attack methods.

A Novel Hyperchaotic 2D-SFCF with Simple Structure and Its Application in Image Encryption.

In this paper, a novel image encryption algorithm is proposed based on hyperchaotic two-dimensional sin-fractional-cos-fractional (2D-SFCF), called sin-fractional-cos-fractional image-encryption (SFCF-IE). The 2D-SFCF is constructed from two one-dimensional cosine fractional (1-DCFs), and it has a more complex chaotic behavior with a larger parameter space than one-dimensional chaotic systems. Compared with the two-dimensional (2D) chaotic system, the 2D-SFCF has a simple structure, and the parameter space in the chaotic state is continuous, which is beneficial to generating the keystream in the cryptosystem. Therefore, in the novel image encryption algorithm, we use the 2D-SFCF to generate the keystream of the cryptosystem. The encryption algorithm is a process of scrambling and diffusion. Different from common diffusion methods, the diffusion starting position of the SFCF-IE is randomly generated, enhancing the algorithm’s security. Simulation experiments show that the image encrypted by this algorithm has better distribution characteristics and can resist common attack methods.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication.

The physical implementation of the continuous-time memristor makes it widely used in chaotic circuits, whereas the discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize the memristor model, and the discretized model also meets the three fingerprints characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling of the proposed memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

Exponential sine chaotification model for enhancing chaos and its hardware implementation

Chaotic systems have been intensively studied for their roles in many applications, such as cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using the exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and it was found that enhanced chaotic maps have much more complicated dynamic behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulated three enhanced chaotic maps using a digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. The results verified that the ESCM can make previous chaos maps competitive for usage in image encryption.

Application of machine learning in intelligent encryption for digital information of real-time image text under big data

In the context of big data, the exploration of the application effect of machine learning in intelligent encryption for real-time image text digital information aims to improve the privacy information security of people. Aiming at the problem of digital information leakage of real-time image text, the convolutional neural network is introduced and improved by adding a preprocessing module to form AlexNet, to encrypt the digital information of real-time image text. Besides, to take into account both the security effect and the real-time performance of the system, the image text is encrypted by the chaotic sequence generated by a one-dimensional chaotic system called Logistic-Sine and a multi-dimensional chaotic system named Lorenz. In this way, a real-time image text encryption model is constructed by combining the chaotic function and AlexNet. Finally, a simulation experiment is performed to analyze the performance of this model. The comparative analysis indicates that the recognition accuracy of feature extraction of image text by the intelligent encryption model reaches 94.37%, which is at least 3.05% higher than that of other neural network models by scholars in related fields. In the security analysis of image text encryption, the information entropy of pixel values at (0, 0) of the proposed model is close to the ideal value 8. Meanwhile, the value of the number of pixels change rate is generally more than 99.50%, and the value of the unified average changing intensity is generally more than 33.50%. This demonstrates that the model has good security in resisting attacks. Therefore, the constructed model can provide good security guarantee under the premise of ensuring the recognition accuracy, which can provide experimental basis for improving the security performance of real-time image text data in the future.

Optimal Image Based Information Hiding with One-dimensional Chaotic Systems and Dynamic Programming

Information hiding is a technology aimed at the secure hiding of important information into digital documents or media. In this paper, a new approach is proposed for the secure hiding of information into gray scale images. The hiding is performed in two stages. In the first stage, the binary bits in the sequence of information are shuffled and encoded with a set of integer keys and a system of one-dimensional logistic mappings. In the second stage, the resulting sequence is embedded into the gray values of selected pixels in the given image. A dynamic programming method is utilized to select the pixels that minimize the difference between a cover image and the corresponding stego image. Experiments show that this approach outperforms other information hiding methods by 13.1% in Peak Signal to Noise Ratio (PSNR) on average and reduces the difference between a stego image and its cover image to 0 in some cases.

A 2D Chaotic Oscillator for Analog IC

In this paper, we have proposed the design of an analog two-dimensional (2D) discrete-time chaotic oscillator. 2D chaotic systems are studied because of their more complex chaotic behavior compared to one-dimensional (1D) chaotic systems. The already published works on 2D chaotic systems are mainly focused either on the complex analytical combinations of familiar 1D chaotic maps such as Sine map, Logistic map, Tent map, and so on, or off-the-shelf component-based analog circuits. Due to complex hardware requirements, neither of them is feasible for hardware-efficient integrated circuit (IC) implementations. To the best of our knowledge, this proposed work is the first-ever report of an analog 2D discrete-time chaotic oscillator design that is suitable for hardware-constrained IC implementations. The chaotic performance of the proposed design is analyzed with bifurcation plots, the transient response, 2D Lyapunov exponent, and correlation coefficient measurements. It is demonstrated that the proposed design exhibits promising chaotic behavior with low hardware cost. The real-world application of the proposed 2D chaotic oscillator is presented in a random number generator (RNG) design. The applicability of the RNG in cryptography is verified by passing the generated random sequence through four standard statistical tests namely, NIST, FIPS, TestU01, and Diehard.

An Image Encryption Algorithm Based on a New Hybrid Power Exponent Chaotic System

Aiming at the problem of a small parameter value range when a one-dimensional chaotic system presents a chaotic state, this paper proposes a new type of hybrid power exponential chaotic system (HPECS). HPECS combines the classic one-dimensional Sine chaotic system to form a new chaotic system (HPECS-SS). Experiments show that the obtained new chaotic system has better chaotic performance, a more extensive parameter value range, and higher sensitivity. Simultaneously, on the basis of HPECS-SS, a new image encryption algorithm is proposed. The algorithm uses the key generated by the SHA-512 algorithm and HPECS-SS to iteratively output the chaotic sequence, SFY algorithm combines the chaotic sequence to perform two rounds of scrambling on the plaintext sequence to obtain the scrambling sequence, and finally, through the modulus operation to diffuse the scrambling sequence to form the encryption matrix of the plaintext image, simulation experiment analysis shows that the algorithm has a large key space, good encryption effect, and security; the pixel change rate (NPCR) and the normalized average change intensity (UACI) are close to ideal values which can resist various cryptanalysis and attacks.