Chaos-based Systems Research Articles

Enhancing logistic chaotic map for improved cryptographic security in random number generation

The use of chaotic maps for cryptography is advantageous due to their desirable characteristics, including complexity, unpredictability, sensitivity to initial values and control parameters, and ergodicity. However, most chaos-based systems have limitations that make them impractical, such as low efficiency, insufficient security, and small keyspace. To overcome these challenges, this paper proposes an enhanced logistic map (ELM), a one-dimensional digital chaotic map based on the logistic map and anterior perturbation method. The ELM map leverages perturbations of chaotic states, leading to enhanced randomness, data distribution, and low correlation, with improved security properties. The ELM map is simple yet capable of generating large chaotic behavior. The findings show that the ELM map is highly secure and can be used in various cryptographic applications. A new pseudorandom number generator (PRNG) is also proposed based on a combination of ELM chaotic maps. The resulting PRNG is highly dependent on the chaotic properties of the maps and the combination rule. Statistical analysis shows that the proposed method is statistically secure, highlighting the potential of the ELM map for other cryptographic applications.

Lyapunov-based Fractional Order of Disturbance Observer and Sliding Mode Control for a Secure Communication of Chaos-based System

Lyapunov-based Fractional Order of Disturbance Observer and Sliding Mode Control for a Secure Communication of Chaos-based System

A Novel Disturbance Rejection Method Based on Robust Sliding Mode Control for the Secure Communication of Chaos-Based System

This paper mainly proposes a new disturbance observer (DO) for a secure communication system (SCS) of the chaos-based system (CBS). First, the fractional-order (FO) Chen chaotic system is remodeled by a Takagi–Sugeno (T–S) fuzzy system with the aim of softening in calculation. Second, the robust fixed-time was designed to synchronize two nonidentical chaotic systems. Third, a new disturbance observer was proposed to compensate for the disturbance and uncertainty of the secure communication system. Fourth, the proof of the proposed method based on Lyapunov condition together with simulation are given to illustrate the correctness and effectiveness of the proposed theory. The tested disturbance on the public channel was mostly compensated by the appropriately estimated disturbance value. The states of master and slave systems (MSSs) were closed to each other in fixed-time. These factors are used to confirm that the symmetry of two chaotic systems were obtained by the proposed control methods.

A Novel Scrambling Method Based on Coupling Mode Switching Strategy for Digital Chaos

The dynamical degradation of digital chaos brings serious defects to chaos-based digital systems and greatly restricts its applications. In this paper, we first discuss the integer logistic map (ILM) and calculate its cycle lengths under different precision. Then, a novel scrambling method based on coupling mode switching (CMS) strategy named CMSSM is proposed to enhance the chaotic features of digital chaos. Following the selection principles, we use three coupling mode candidates to construct 3CMSSM. Theoretical analysis shows that the output cycle length of 3CMSSM is three times that of scrambling methods used in single coupling mode (SCM) strategy. Numerical simulations are carried out to demonstrate the desirable statistical and dynamical properties of scrambled ILM. Finally, we design a (pseudo-random number generator) PRNG based on 3CMSSM. Both results of statistical test suites NIST SP800-22 and TestU01 show that the suggested PRNG has highly credible randomness compared to other algorithms.

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.

On the use of Egyptian fractions for stream ciphers

Within the scope of the mutual interference between modern number theory and chaos-based cryptography, and as it is well-known and already explored for the decimal or the continued fraction expansion of irrational numbers, interesting random-like behaviors seem to be hidden in Egyptian fraction expansions, thus suggesting new chaos-based encryption systems. In fact, at a practical level, and as will be shown through the present study, concatenation of involved denominators and binary expansion generally lead to pseudo-random streams which satisfactorily pass the NIST statistical test suite for randomness. Then, to a certain extent, and for cryptographic purposes, this can be considered as a new tool to complete the conventional class of already-in-use pseudo-random number generators. Some mathematical issues, however, have to be clarified, as for example the chaoticity of the process obtained after converting these denominators to fractional parts of a wandering sequence of real numbers in the unit interval. To the best of our knowledge, and from a cryptographic point of view, previous works on the subject are limited to statistical tests (and subsequent cryptographic analysis) of the resulting one-time pads or stream ciphers, but no rigorous study has been conducted to justify these methods within chaos theory. Considering Egyptian expansions as a working example and using the term “chaotic” in the sense of Devaney, this is what our proposal is aimed at in the present work.

Design and FPGA Implementation of a Pseudo-random Number Generator Based on a Hopfield Neural Network Under Electromagnetic Radiation

When implementing a pseudo-random number generator (PRNG) for neural network chaos-based systems on FPGAs, chaotic degradation caused by numerical accuracy constraints can have a dramatic impact on the performance of the PRNG. To suppress this degradation, a PRNG with a feedback controller based on a Hopfield neural network chaotic oscillator is proposed, in which a neuron is exposed to electromagnetic radiation. We choose the magnetic flux across the cell membrane of the neuron as a feedback condition of the feedback controller to disturb other neurons, thus avoiding periodicity. The proposed PRNG is modeled and simulated on Vivado 2018.3 software and implemented and synthesized by the FPGA device ZYNQ-XC7Z020 on Xilinx using Verilog HDL code. As the basic entropy source, the Hopfield neural network with one neuron exposed to electromagnetic radiation has been implemented on the FPGA using the high precision 32-bit Runge Kutta fourth-order method (RK4) algorithm from the IEEE 754-1985 floating point standard. The post-processing module consists of 32 registers and 15 XOR comparators. The binary data generated by the scheme was tested and analyzed using the NIST 800.22 statistical test suite. The results show that it has high security and randomness. Finally, an image encryption and decryption system based on PRNG is designed and implemented on FPGA. The feasibility of the system is proved by simulation and security analysis.

DCSK performance analysis of a chaos-based communication using a newly designed chaotic system

Abstract In this paper, a new chaotic system has been introduced and the fundamental properties of the system were investigated and presented using a bifurcation diagram, max Lyapunov exponent (LE) and phase portraits. The synchronization of the drive and response system has been done using the threshold control parameter. Later the differential chaos shift keying (DCSK) modulation scheme has been carried out for the system as it is the most efficient modulation scheme. The demodulator detects the data without the use of chaotic signal phase recovery, as it uses the non-coherent detection technique. The results were compared with other modulation schemes using the bit error rate (BER) graph. It reveals that the proposed chaos-based system could be used for secure communication. The system has been implemented using the MATLAB Simulink technique.

Wireless Chaos-Based Communication System: Literature Review

Since the early 1990s, a slew of chaotic-based communication systems have been proposed, all of which take advantage of chaotic waveform properties. The inspiration stems from the substantial benefits that this form of nonlinear signal offers. Many communication schemes and applications have been specifically designed for chaos-based communication systems to achieve this goal, with energy, data rate, and synchronization awareness being taken into account in most designs. However, non-coherent chaos-based systems have recently received a lot of attention in order to take advantage of the benefits of chaotic signals and non-coherent detection while avoiding the use of chaotic synchronization, which has poor performance in the presence of additive noise. This paper provides a thorough examination of all wireless radio frequency chaos-based communication systems. It begins by describing the difficulties of chaos implementations and synchronization processes, then moves on to a thorough literature review and study of chaos-based coherent techniques and their applications.

Analysis of Fourth-order Chaotic Circuit Based on the Memristor Model for Wireless Communication

The development by Hewlett-Packard of memristor, a fourth fundamental electronic component, has gained attention in the fields of memory technology and neuromorphic. As memristor components are not currently available commercially, modelling of memristors with associated circuit elements is required to build application circuits. In this work, based on the Hewlett-Packard memristor, we implement a new Chua’s chaotic circuit, which is a simple combination of electronic components which exhibit chaos. The nonlinear element in Chua’s circuit is substituted with an active memristor-based circuit consisting of a combination of negative resistor and TiO2-based memristor, which allows the circuit to exhibit chaos without scaling the differential equations and produces realistic voltages and currents across the circuit components. This paper indicates for the first time, chaotic oscillations are produced using memristor-based Chua’s circuit where actual physical equations, describing the memristor, are applied. The analysis of the proposed single memristor-based chaotic is discussed. Such a circuit is of interest in chaos-based systems for applications such as wireless communication.

Disturbance and Uncertainty Rejection-Based on Fixed-Time Sliding-Mode Control for the Secure Communication of Chaotic Systems

This study provides a new development regarding uncertainty and disturbance estimation (UDE) based on fixed-time sliding mode control (FTSMC) for the secure communication of electronic circuits in a chaos-based system. Takagi-Sugeno (T-S) fuzzy systems were used to remodel chaotic systems with the aim of softening the control design for the synchronization of the chaos-based system. The master and slave systems of the secure communication system were maintained in chaotic formats. The originality of the proposed uncertainty and disturbance estimator is a condition associated with the first derivative of these values being free. The stability of the system was proven by using the Lyapunov condition. The states of master and slave systems were used for encryption and decryption, respectively. Finally, the correction of the proposed control theories was verified by MATLAB simulations, the simulation of the electronic circuits in OrCAD capture software, and experiments involving electronic circuit communication.

Modeling and Analysis of Chaos-based Spread Spectrum Scheme using Irregular LDPC Code and Non-Coherent 16-DCSK under Fading and Jamming

In chaos-based spread spectrum systems, the use of spreading code and chaotic binary sequence expands the bandwidth of the information-bearing signal but this expansion results in SNR degradation under the constraint of constant channel capacity according to Hartley-Shannon law. To compensate for this drawback, our proposed model employs an irregular low-density parity-check (LDPC) code with its iterative decoding algorithm. Coupled with this forward error correction (FEC) coding, we used non-coherent (NC) 16-ary differential chaos shift keying (16-DCSK) that additionally provides the ability of data encryption due to its use of chaotic signals compared with the conventional modulation schemes. Analytical expressions of bit error probability (BEP) are derived under the assumption of the three-ray model along with partial band noise jamming (PBNJ) over a Rayleigh fading channel. Simulation results assert that the proposed system can mitigate the effect of PBNJ via lowering BEP by coding gain and processing gain under identical transmission power. It is also confirmed that a higher level of security can be provided by the use of proposed two iteration functions of Duffing Map-based chaotic binary sequence than the security level of one iteration function of Logistic Map, based on the balance and autocorrelation analysis.

Lightweight chaotic image encryption algorithm for real-time embedded system: Implementation and analysis on 32-bit microcontroller

The scintillating technological advancements have redefined the process of communication around the world. Banking, purchases, investments, emails, bill payments, etc. are being managed through online communications and needless to mention the linkage of these internet serves with embedded gadgets. A microcontroller being the low-cost solutions for real-time embedded applications has to handle rigid security algorithms for information security paradigm. The high level of sensitivity in chaos-based systems is highly suitable for the design of encryption schemes due to the randomness offered by them. The minimal memory resource and speed are the factors restricting the use of microcontrollers for implementing chaotic schemes that encrypt image data. This paper presents the design of a chaos-based image encryption algorithm with lightweight properties and its optimised implementation on a 32-bit microcontroller. This work also includes parameters related to the analysis of the security level and performance of the microcontroller that was missed to concentrate by the authors on their similar schemes reported in the literature. The level of safety of the proposed algorithm has been analysed via key sensitivity analysis, encryption quality analysis, randomness analysis, differential analysis, statistical analysis, visual analysis and attack analysis. Additionally, the results of performance analysis regarding smaller memory footprint and better throughput of proposed algorithm guarantee its suitability for real-time embedded applications.

Combinational domain-based encryption using FrWT and hyper-chaotic system for biometric data security

ABSTRACTAn efficient hyperchaos-based combinational domain encryption scheme for securing iris images during transmission over unsecured data networks or database storage is presented in this article. From the region of interest (ROI) of an iris image, distinctive features are strategically extracted for template creation. The significant part, i.e., the ROI of an iris image, is encrypted in a transformational domain and the nonsignificant region is encrypted in a spatial domain. The advantage of this encryption scheme is increased key space and high degree of security compared to 1-D chaos-based systems. Apart from security, another advantage is reduced computational time compared to conventional encryption schemes implemented in either the spatial or frequency domain. The proposed scheme inherits the advantages of increased key space due to transform orders of the fractional wavelet transform (FrWT) and complex dynamical characteristics of hyperchaos, making the proposed scheme resistant to attacks. The properties of the FrWT and hyperchaos complement each other, making the system efficient and highly robust. Experimental results indicate that the proposed scheme reduces the computational time without compromising the security. Further security analysis is done for various attacks such as differential, statistical, and perceptual attacks, which give promising results and indicate that the proposed encryption scheme is efficient and robust.

Implementing Boolean Functions in Hybrid Digital-Analog Systems

As Moore's Law winds down, we look to do more with less---more computing with fewer components, that is. One approach is ``chaos computing'', in which nonlinear dynamics is exploited to create any type of logic gate on the fly, almost instantly, from a single generic setup. Starting from super-stable initial conditions robust to noise, the authors combine a conventional digital circuit with an analog nonlinear circuit of just three transistors, to implement arbitrary Boolean functions $e\phantom{\rule{0}{0ex}}x\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}y$ faster than in prior architectures. This improves the reliability of chaos-based systems, and expands the scope of their potential applications.

Cryptanalysis of a Classical Chaos-Based Cryptosystem with Some Quantum Cryptography Features

The application of synchronization theory to build new cryptosystems has been a hot topic during the last two decades. In this paper, we analyze a recent proposal in this field. We pinpoint the main limitations of the software implementation of chaos-based systems designed on the grounds of synchronization theory. In addition, we show that the cryptosystem under evaluation possesses serious security problems that imply a clear reduction of the key space.

A Study on Chaos-Based System for Improved Encryption of Images

A Study on Chaos-Based System for Improved Encryption of Images

A Study on Chaos-Based System for Improved Encryption of Images

A Study on Chaos-Based System for Improved Encryption of Images

Prototype of a multi-user chaos-based system with correlator and support vector machine receivers

Multiuser communication techniques are used in modern wireless networks like cellular and wireless sensor networks. The design of the physical layer for these networks was based on the application of binary spreading sequences and a correlation receiver. This paper presents a design of a multiuser code division transceiver using a new method of communication based on the application of chaotic spreading sequences that can increase security of the system, and on a new technique of detecting the received signal using a support vector machine and a traditional correlation receiver. The two receivers are theoretically analyzed, including the derivation of the probability of error expression in a closed form for the fading channel, and then implemented in DSP technology on a 32-bit floating-point TigerSHARC DSP platform. The comparison of two implemented systems showed that the support vector machine solution improves the robustness of the system, sacrificing the speed of processing. The achievable bit rate for the correlator receiver was up to two times higher than for the support vector machine receiver.

Wireless Chaos-Based Communication Systems: A Comprehensive Survey

Since the early 1990s, a large number of chaos-based communication systems have been proposed exploiting the properties of chaotic waveforms. The motivation lies in the significant advantages provided by this class of non-linear signals. For this aim, many communication schemes and applications have been specially designed for chaos-based communication systems where energy, data rate, and synchronization awareness are considered in most designs. Recently, the major focus, however, has been given to the non-coherent chaos-based systems to benefit from the advantages of chaotic signals and non-coherent detection and to avoid the use of chaotic synchronization, which suffers from weak performance in the presence of additive noise. This paper presents a comprehensive survey of the entire wireless radio frequency chaos-based communication systems. First, it outlines the challenges of chaos implementations and synchronization methods, followed by comprehensive literature review and analysis of chaos-based coherent techniques and their applications. In the second part of the survey, we offer a taxonomy of the current literature by focusing on non-coherent detection methods. For each modulation class, this paper categorizes different transmission techniques by elaborating on its modulation, receiver type, data rate, complexity, energy efficiency, multiple access scheme, and performance. In addition, this survey reports on the analysis of tradeoff between different chaos-based communication systems. Finally, several concluding remarks are discussed.