Chaos-based Cryptography Research Articles

Application of Reservoir Computers for Chaos Synchronization and Cracking Chaos-Based Cryptography in Fermionic 2D Thirring and 4D Gursey Models with Spinor Fields

Reservoir computers have recently become one of the most widely exploited model-free approaches to chaos synchronization due to their fast convergence speed and simple yet effective learning rules. In this study, reservoir computing has been utilized to emulate the dynamics of chaotic Thirring and Gursey systems. In the supervised learning of the reservoir, one-step ahead states of the dynamical systems have been employed as the teaching signals. After the training phase, the reservoir was first run autonomously and then weakly driven by chaotic systems. It has been shown that the trained reservoir computers can exhibit the same characteristics as the attractors of the learned chaotic systems, which enable their use in synchronization tasks of chaotic systems with possible application in cracking chaos-based cryptography. To investigate the effect of noise on the performance of reservoir computers, noise signals with different colors and amplitudes have been included in the transmitted signals. The obtained results indicate that the proposed scheme can provide lower error metrics for both models.

Towards Analysable Chaos-based Cryptosystems: Constructing Difference Distribution Tables for Chaotic Maps

Chaos-based cryptography has yet to achieve practical, real-world applications despite extensive research. A major challenge is the difficulty in analysing the security of these cryptosystems, which often appear ad hoc in design. Unlike conventional cryptography, evaluating the security margins of chaos-based encryption against attacks such as differential cryptanalysis is complex. This paper introduces a straightforward approach of using chaotic maps in cryptographic algorithms in a way that facilitates cryptanalysis. We demonstrate how a chaos-based substitution function can be constructed using fixed-point representation, enabling the application of conventional cryptanalysis tools such as the difference distribution table. As a proof-of-concept, we apply our method to the logistic map, showing that differential properties vary based on the initial state and number of iterations. Our findings demonstrate the feasibility of designing analysable chaos-based cryptographic components with well-understood security margins.

On the use of dynamical systems in cryptography

Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of papers. Yet, the field has not found its place in mainstream cryptography, largely due to persistent weaknesses in the presented systems. The goal of this paper is to help remedy this problem in two ways. The first is by providing a new algorithm that can be used to attack – and hence test the security of – stream ciphers based on the iteration of a chaotic map of the interval. The second is to cast discrete dynamical systems problems in a modern cryptographic and complexity theoretic language, so that researchers working in chaos-based cryptography can begin designing cryptographic protocols that have a better chance of meeting the extreme standards of modern cryptography.

A family of robust chaotic S-unimodal maps based on the Gaussian function

This research paper introduces a family of one-dimensional S-unimodal maps based on the Gaussian function, designed to exhibit robust chaos across a wide range of parameters. These maps are developed to display robust chaos by avoiding multiple fixed points that are primarily responsible for the coexisting attractors in 1D maps. The parameter space analysis reveals that chaotic behaviour is sustained across the entire parameter space, except for a very narrow region. The study employs a comprehensive computational approach, including quantitative measures such as sample entropy, Lyapunov exponent, and invariant measures. The uniformly higher values of sample entropy, uniform positive values of the Lyapunov exponent, and the existence of invariant measures in a region of parameter space confirm the presence of robust chaos in these maps. Such a promising class of robust chaotic maps may be potentially used in diverse fields such as chaos-based cryptography, pseudo-random number generation, communication systems, and more.

Towards accurate keyspace analysis of chaos-based image ciphers

In recent years, there has been a surge in new chaos-based cryptographic algorithms, many of which claim to have unusually large keyspaces. Although cryptographic primitives such as symmetric-key ciphers should have a secret keyspace large enough to resist brute force attacks, simply increasing the size of a secret key may not lead to improved security margins. An n-bit key may not necessarily have a keyspace of 2n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^n-1$$\\end{document} due to the key scheduling algorithm or how the key is used. In this paper, we cryptanalyse several chaos-based algorithms from the perspective of their key schedules. Our numerical analysis is based on the known-plaintext attack model, Kerckhoff’s principle and considers the number representations used for real number computation. Our analysis reveals that the actual security margins for these ciphers are significantly lower, some by a factor of over 2100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{100}$$\\end{document} than what was claimed. We then provide accurate keyspace estimates for these ciphers. Finally, we highlight alternative solutions for how secret keys can be used in the context of chaos-based cryptography and propose a simple key schedule as a proof of concept. Despite its simplicity, the proposed key schedule not only ensures that the keyspace matches the key length but also passes both the NIST and ENT statistical test suites, making it a viable option for generating secure cryptographic keys. Our work contributes towards addressing one of the fundamental problems in chaos-based cryptography that limits its real-world impact and reputation within the cryptographic community.

Dynamic analysis and circuit realization of a new controllable hyperchaotic system

Amidst the realm of hyper-chaotic systems, a notable deficiency is the absence of amplitude control and signal polarity. This paper addresses this limitation by introducing a new 4-D hyper-chaotic system with a hidden equilibrium-free attractor. The study focuses on amplitude control, achieved by adjusting a specific parameter, enabling manipulation of variable magnitudes while maintaining the overall signal. The offset boosting technique is investigated, enabling flexible shifting of the attractor in a desired direction. A real circuit experiment validates the proposed system’s practical applicability, confirming consistency with theoretical analysis and numerical simulations. Through introducing this new-found, the study holds significant importance for various fields, such as communications engineering and chaos-based cryptography, where precise control of signal characteristics is paramount.

A relative investigation of one-dimensional chaotic maps intended for light-weight cryptography in smart grid

Technology is quite important in today's contemporary society, especially when it comes to information transmission. The free and open interchange of data via networks is essential for the development of communication technologies. As a result, it is essential to ensure the security of transmitted data, especially digital data like readings from smart meters in smart grids. As a result, the study of chaos-based cryptography has received a great deal of interest in the realm of data security. Due to its favourable characteristics, including ergodicity, pseudo-randomness, non-periodicity, and sensitivity to beginning circumstances, chaotic maps have become a popular choice for data encryption. Researchers have concentrated on factors like the highest Lyapunov exponent and sensitivity to beginning circumstances while evaluating these maps. The MATLAB platform has been used to run simulations that produce bifurcation diagrams and calculate Lyapunov exponents in order to analyse and compare various chaotic maps. Further research is required since these experiments have shown considerable improvements in the chaotic behaviour of one-dimensional maps over time. There are two key areas covered by the review. On the basis of their bifurcation diagrams and Lyapunov exponents, it compares newly presented maps in the first place. It then looks at the techniques used to combine one-dimensional chaotic maps. The work shows the potential of chaotic maps for cryptography applications and emphasises the growing significance of data security in the digital age.

ANALYSIS OF NEW CHAOTIC MAP AND PERFORMANCE EVALUATION IN ITS APPLICATION TO DIGITAL COLOR IMAGE ENCRYPTION

In this research a new chaotic map which is a modification from composition of MS map and Improved logistics map is proposed. New map’s chaotic behavior is proven by the bifurcation diagram and Lyapunov exponent. This map will be used in chaos-based cryptography as a keystream generator and then it will be processed in the encryption and decryption algorithms through XOR operations. The results of the encryption and decryption processes were evaluated by several tests such as key sensitivity analysis, histogram analysis, correlation analysis, and image quality analysis. All the tests are doing to evaluate the performance new chaotic map in encryption of digital color image. Based on the results of several tests, a conclusion can be drawn that the encryption and decryption process is successful and difficult to attack with various kinds of attacks. The key that built from new chaotic map has a good sensitivity.

An Analysis Tool for Cryptographic Designs Based on Chaotic Systems

Chaos-based cryptography research is one of the application areas for chaotic systems. Numerous design studies have been put up that take use of the connection between chaos and cryptography. This study has demonstrated how to exploit this relationship to decrypt cryptography designs. It has been looked at if chaos analysis techniques may be used to analyze cryptography protocols. The effectiveness of random number generators has been evaluated using Lyapunov exponents, a chaos analysis technique. The findings of the investigation demonstrated that Lyapunov exponents can be utilized as a standard in assessing random number generators. The paper highlights the issues with the NIST test suite, a popular method of analysis for assessing the statistical characteristics of random number generators. These issues have been seen to not exist with the new test tool that has been suggested. These findings demonstrate that the suggested strategy can be successfully applied in a variety of future applications.

Enhancing chaos in multistability regions of Duffing map for an image encryption algorithm

This paper investigates and analyzes the dynamics of the two-dimensional Duffing map. Multistability behavior has been observed from the system numerically. Such behavior, especially the coexistence of chaotic and periodic attractors, is undesirable in the applications of chaos-based cryptography. Therefore, we design and implement a Sine–Cosine chaotification technique to enhance chaos in the multi-stable regions. Furthermore, this paper proposes a new image encryption algorithm to examine the performance of the generalized Duffing map in cryptography applications. Simulation results and security analysis reveal that the proposed algorithm can effectively encrypt and decrypt several image types with a high level of security.

Biomedical Image Encryption with a Novel Memristive Chua Oscillator Embedded in a Microcontroller

In this paper, a chaos-based encryption/decryption scheme using a novel memristive Chua oscillator to protect medical images is presented. The novel Chua oscillator is constructed by using the active voltage memristor in the nonlinear branch of the Chua oscillator. The chaotic dynamics behaviors are investigated using 1-D, 2-D bifurcation diagrams, time traces, basin of attractions, and largest Lyapunov exponent plot. The study reveals that the novel memristive Chua oscillator exhibits versatile transitions to chaos with interesting dynamics like multistability, spiking, and bursting oscillations just to name a few. These remarkable features are experimentally confirmed by a laboratory microcontroller-based setup. Thereafter, a chaos-based cryptography algorithm designed for biomedical images is built using pseudorandom number generated from the oscillator. The robustness and security tests undergone by the algorithm yielded high sensitivity on the encryption keys and resisted noise contamination as well as data loss. These results are encouraging and prove that the chaos-based cryptosystem built with the memristive Chua circuit–generated pseudorandom number is suitable for securing images in a healthcare system.

Robust Chaos With Novel 4-Transistor Maps

This brief presents four discrete-time chaotic map circuits, including three new map circuits and one that has been previously reported. The designs are hardware efficient as they each contain only four Metal Oxide Semiconductor (MOS) transistors. They offer robust chaotic performance with wide chaotic space and uniform entropic properties. The wide chaotic region is essential for applications where parametric perturbation can push the system out of the desirable chaotic region. The chaotic performance is analyzed using a bifurcation plot, Lyapunov exponent, correlation coefficient, sample entropy, and Shannon entropy, and improvement over previous transistor-level designs is demonstrated. The proposed method can be useful in applications such as random number generation, reconfigurable and flexible computing, side-channel attack mitigation, logic obfuscation, and chaos-based cryptography. A chaotic oscillator design is proposed and its application in a chaos-based reconfigurable logic gate is presented, as well.

An Effective Approach to Scramble Multiple Diagnostic Imageries Using Chaos-Based Cryptography

Medical image encryption could aid in preserving patient privacy. In this article, we provide a chaotic system-based medical picture encryption method. The diffusion and permutation architecture was used. The permutation based on plain image and chaotic keys is offered to shuffle the plain picture's pixels to other rows and columns, successfully weakening the strong connections between neighboring pixels. Diffusion is suggested to spread small changes of plain images to all of the pixels in cipher images to enhance the encryption effect. We analyze the chaotic behavior of the proposed system using various techniques and tests such as bifurcation plots, Lyapunov exponents, MSE, PSNR tests, and histogram analysis.

Quality Evaluation for Reconstructing Chaotic Attractors

Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning (initial conditions). Deciphering a message has to be without loss, and this paper will serve to choose the proper dynamical system to be used in chaos-based cryptography. The characterization of the chaotic attractors is the most important information in order to obtain the desired behavior. Here, observability and singularity are the main notions to be used for introducing an original term: quality observability index (q.o.i.). This is an original contribution for measuring the quality of the chaotic attractors. In this paper, the q.o.i. is defined and computed in order to confirm its usability.

Time Efficient Image Encryption-Decryption for Visible and COVID-19 X-ray Images Using Modified Chaos-Based Logistic Map.

In this pandemic situation, radiological images are the biggest source of information in healthcare and, at the same time, one of the foremost troublesome sources to analyze. Clinicians now-a-days must depend to a great extent on therapeutic image investigation performed by exhausted radiologists and some of the time analyzed and filtered themselves. Due to an overflow of patients, transmission of these medical data becomes frequent and maintaining confidentiality turns out to be one of the most important aspects of security along with integrity and availability. Chaos-based cryptography has proven a useful technique in the process of medical image encryption. The specialty of using chaotic maps in image security is its capability to increase the unpredictability and this causes the encryption robust. There are large number of literature available with chaotic map; however, most of these are not useful in low-precision devices due to their time-consuming nature. Taking into consideration of all these facts, a modified encryption technique is proposed for 2D COVID-19 images without compromising security. The novelty of the encryption procedure lies in the proposed design which is split into mainly three parts. In the first part, a variable length gray level code is used to generate the secret key to confuse the intruder and subsequently it is used as the initial parameter of both the chaotic maps. In the second part, one-stage image pixels are shuffled using the address code obtained from the sorting transformation of the first logistic map. In the final stage, a complete diffusion is applied for the whole image using the second chaotic map to counter differential and statistical attack. Algorithm validation is done by experimentation with visual image and COVID-19 X-ray images. In addition, a quantitative analysis is carried out to ensure a negligible data loss between the original and the decrypted image. The strength of the proposed method is tested by calculating the various security parameters like correlation coefficient, NPCR, UACI, and key sensitivity. Comparison analysis shows the effectiveness for the proposed method. Implementation statistics shows time efficiency and proves more security with better unpredictability.

Securing information using a proposed reliable chaos-based stream cipher: with real-time FPGA-based wireless connection implementation

In this paper, a robust chaos-based stream cipher (CBSC) is proposed. The novelty of this work is that it addresses all challenges confronting chaos-based cryptography. The PCBSC (proposed CBSC) has a robust synchronization circuit that mitigates the effect of channel noise, a perturbation block that overcomes the dynamical degradation, a robust encryption scheme, and an efficient control parameters’ generator that generates strong keys. According to the complexity evaluation, the improved chaotic map provides good statistical properties. This can be confirmed by the obtained high values of the statistical metrics (largest Lyapunov exponent, approximate entropy, permutation entropy, and sample entropy) used for the evaluation. According to the security analysis, the PCBSC has good security features and provides strong keys that ensure confusion property, as well as enough space to withstand brute-force attacks. On the other hand, the proposed encryption scheme proves its efficiency; the result of the differential attack clearly shows that the diffusion property is guaranteed. Additionally, the original images’ statistical properties are completely dispersed on the encrypted images. The obtained performance over noisy channels proves the synchronization circuit’s efficiency. When compared to other proposals, the PCBSC provides the best results. In addition, the PCBSC is implemented on an FPGA and evaluated in real-time over a wireless link.

Chaotic based multimedia encryption: a survey for network and internet security

Nowadays the security of multimedia data storage and transfer is becoming a major concern. The traditional encryption methods such as DES, AES, 3-DES, and RSA cannot be utilized for multimedia data encryption since multimedia data include an enormous quantity of redundant data, a very large size, and a high correlation of data elements. Chaos-based approaches have the necessary characteristics for dynamic multimedia data encryption. In the context of dynamical systems, chaos is extremely dependent on the initial conditions, non-convergence, non-periodicity, and exhibits a semblance of randomness. Randomness created from completely deterministic systems is a particularly appealing quality in the field of cryptography and information security. Since its inception in the early '90s, chaotic cryptography has seen a number of noteworthy changes. Throughout these years, several scientific breakthroughs have been made. This paper will give an overview of chaos-based cryptography and its most recent advances.

Multibiosignal chaotic encryption scheme based on spread spectrum and global diffusion process for e-health

E-health provides several remote health services highly convenient for patients. Nevertheless, inherent security risks are present in e-health such as data privacy since insecure communication channels are used to transmit data between patients and physicians or to cloud medical data storage. Nowadays, medical body area network provides a solution to continuous health monitoring with real-time updates of multibiosignal records in multiuser communication schemes for monitoring and early detection of medical conditions or diseases. In this paper, we propose to use chaos-based sequence direct spread spectrum technology and chaos-based cryptography to provide data privacy, high security and efficiency in monitoring multibiosignals in multiuser networks for e-health applications. First, each plain biosignal is modulated with sequence direct spread spectrum by using the chaotic Hénon map. Then, all modulated biosignals are summed to produce the modulated cryptogram. The modulated cryptogram is finally encrypted by using global diffusion process with the chaotic Hénon map to increase security by reducing the high autocorrelation of the modulated cryptogram. The experimental results are presented in a simulated multiuser scenario with 4 users (or patients) and 2 specialists (neurologist and cardiologist), with 12 biosignals acquired from database on the Internet, such as electroencephalograms, electromyograms, blood pressure signals, and electrocardiograms. A comprehensive security study is presented to show the high security, the high speed encryption, and the high noise interference robustness. According with the results, the proposed method can be used for secure multibiosignal monitoring in multiuser networks for e-health applications with high efficiency and security.

A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis

Data security represents an essential task in the present day, in which chaotic models have an excellent role in designing modern cryptosystems. Here, a novel oscillator with chaotic dynamics is presented and its dynamical properties are investigated. Various properties of the oscillator, like equilibria, bifurcations, and Lyapunov exponents (LEs), are discussed. The designed system has a center point equilibrium and an interesting chaotic attractor. The existence of chaotic dynamics is proved by calculating Lyapunov exponents. The region of attraction for the chaotic attractor is investigated by plotting the basin of attraction. The oscillator has a chaotic attractor in which its basin is entangled with the center point. The complexity of the chaotic dynamic and its entangled basin of attraction make it a proper choice for image encryption. Using the effective properties of the chaotic oscillator, a method to construct pseudo-random numbers (PRNGs) is proposed, then utilizing the generated PRNG sequence for designing secure substitution boxes (S-boxes). Finally, a new image cryptosystem is presented using the proposed PRNG mechanism and the suggested S-box approach. The effectiveness of the suggested mechanisms is evaluated using several assessments, in which the outcomes show the characteristics of the presented mechanisms for reliable cryptographic applications.

Enhanced design and hardware implementation of a chaos-based block cipher for image protection

Nowadays chaos-based cryptography systems are widely used to protect sensitive data. A variety of chaos-based cryptosystems with software implementation has been published in the literature. However, due to the rapid growth of connected devices, the development of hardware secure and low-resource cryptographic systems is necessary. In this paper, we enhance the design of one of our software cryptosystems and then we address its FPGA-based implementation. The improvement in the design consists essentially to introduce an Initial Vector (IV) entry to the Chaotic Pseudo Random Number Generator (CPRNG) thus allowing to generate a new dynamic keys for the confusion layer (using a modified 2-D cat map) and diffusion layer (using a logistic map) with each new execution of the system. The CPRNG is formed by XORred a discrete Skew Tent Map (STM) with a discrete Piecewise Linear Chaotic Map (PWLCM). The proposed cryptosystem, which operates in Cipher Block Chaining (CBC) mode, is controlled by a Finite State Machine (FSM) to ensure that both the encryption and decryption are performed by the same reconfigurable architecture. The system is implemented on a Xilinx XC7Z020 ZYNQ FPGA platform. The results obtained in terms of hardware implementation costs (logic resources, throughput, and efficiency) and in terms of security against cryptographic attacks demonstrate the effectiveness of the proposed chaos-based cryptosystem.