Chaotic Image Encryption Using Hopfield and Hindmarsh-Rose Neurons Implemented on FPGA

Efficient digital design of the nonlinear behavior of Hindmarsh-Rose neuron model in large-scale neural population

Spiking networks, as the third generation of neural networks, are of great interest today due to their low power consumption in cognitive processes. This important characteristic has caused the hardware implementation techniques of spiking networks in the form of neuromorphic systems attract a lot of attention. For the first time, the focus is on the digital implementation based on CORDIC approximation of the Hindmarsh-Rose (HR) neuron so that the hardware implementation cost is lower than previous studies. If the digital design of a neuron is done efficient, the possibility of implementing a population of neurons is provided for the feasibility of low-consumption implementation of high-level cognitive processes in hardware, which is considered in this paper through edge detector, noise removal and image magnification spiking networks based on the proposed CORDIC_HR model. While using less hardware resources, the proposed HR neuron model follows the behavior of the original neuron model in the time domain with much less error than previous study. Also, the complex nonlinear behavior of the original and the proposed model of HR neuron through the bifurcation diagram, phase space and nullcline space analysis under different system parameters was investigated and the good follow-up of the proposed model was confirmed from the original model. In addition to the fact that the individual behavior of the original and the proposed neurons is the same, the functional and behavioral performance of the randomly connected neuronal population of original and proposed neuron model is equal. In general, the main contribution of the paper is in presenting an efficient hardware model, which consumes less hardware resources, follows the behavior of the original model with high accuracy, and has an acceptable performance in image processing applications such as noise removal and edge detection.

Star Memristive Neural Network: Dynamics Analysis, Circuit Implementation, and Application in a Color Cryptosystem

At present, memristive neural networks with various topological structures have been widely studied. However, the memristive neural network with a star structure has not been investigated yet. In order to investigate the dynamic characteristics of neural networks with a star structure, a star memristive neural network (SMNN) model is proposed in this paper. Firstly, an SMNN model is proposed based on a Hopfield neural network and a flux-controlled memristor. Then, its chaotic dynamics are analyzed by using numerical analysis methods including bifurcation diagrams, Lyapunov exponents, phase plots, Poincaré maps, and basins of attraction. The results show that the SMNN can generate complex dynamical behaviors such as chaos, multi-scroll attractors, and initial boosting behavior. The number of multi-scroll attractors can be changed by adjusting the memristor's control parameters. And the position of the coexisting chaotic attractors can be changed by switching the memristor's initial values. Meanwhile, the analog circuit of the SMNN is designed and implemented. The theoretical and numerical results are verified through MULTISIM simulation results. Finally, a color image encryption scheme is designed based on the SMNN. Security performance analysis shows that the designed cryptosystem has good security.

Spiking Neuron Mathematical Models: A Compact Overview

The features of the main models of spiking neurons are discussed in this review. We focus on the dynamical behaviors of five paradigmatic spiking neuron models and present recent literature studies on the topic, classifying the contributions based on the most-studied items. The aim of this review is to provide the reader with fundamental details related to spiking neurons from a dynamical systems point-of-view.

A Novel Color Image Encryption Scheme Based on Hyperchaos and Hopfield Chaotic Neural Network

Problems such as insufficient key space, lack of a one-time pad, and a simple encryption structure may emerge in existing encryption schemes. To solve these problems, and keep sensitive information safe, this paper proposes a plaintext-related color image encryption scheme. Firstly, a new five-dimensional hyperchaotic system is constructed in this paper, and its performance is analyzed. Secondly, this paper applies the Hopfield chaotic neural network together with the novel hyperchaotic system to propose a new encryption algorithm. The plaintext-related keys are generated by image chunking. The pseudo-random sequences iterated by the aforementioned systems are used as key streams. Therefore, the proposed pixel-level scrambling can be completed. Then the chaotic sequences are utilized to dynamically select the rules of DNA operations to complete the diffusion encryption. This paper also presents a series of security analyses of the proposed encryption scheme and compares it with other schemes to evaluate its performance. The results show that the key streams generated by the constructed hyperchaotic system and the Hopfield chaotic neural network improve the key space. The proposed encryption scheme provides a satisfying visual hiding result. Furthermore, it is resistant to a series of attacks and the problem of structural degradation caused by the simplicity of the encryption system's structure.

Dynamics study on the effect of memristive autapse distribution on Hopfield neural network

As the shortest feedback loop of the nervous system, autapse plays an important role in the mode conversion of neurodynamics. In particular, memristive autapses can not only facilitate the adjustment of the dynamical behavior but also enhance the complexity of the nervous system, in view of the fact that the dynamics of the Hopfield neural network has not been investigated and studied in detail from the perspective of memristive autapse. Based on the traditional Hopfield neural network, this paper uses a locally active memristor to replace the ordinary resistive autapse so as to construct a 2 n-dimensional memristive autaptic Hopfield neural network model. The boundedness of the model is proved by introducing the Lyapunov function and the stability of the equilibrium point is analyzed by deriving the Jacobian matrix. In addition, four scenarios are established on a small Hopfield neural network with three neurons, and the influence of the distribution of memristive autapses on the dynamics of this small Hopfield neural network is described by numerical simulation tools. Finally, the Hopfield neural network model in these four situations is designed and implemented on field-programmable gate array by using the fourth-order Runge-Kutta method, which effectively verifies the numerical simulation results.

Optimization of fractional-order chaotic cellular neural networks by metaheuristics

Artificial neural networks have demonstrated to be very useful in solving problems in artificial intelligence. However, in most cases, ANNs are considered integer-order models, limiting the possible applications in recent engineering problems. In addition, when dealing with fractional-order neural networks, almost any work shows cases when varying the fractional order. In this manner, we introduce the optimization of a fractional-order neural network by applying metaheuristics, namely: differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms. The case study is a chaotic cellular neural network (CNN), for which the main goal is generating fractional orders of the neurons whose Kaplan-Yorke dimension is being maximized. We propose a method based on Fourier transform to evaluate if the generated time series is chaotic or not. The solutions that do not have chaotic behavior are not passed to the time series analysis (TISEAN) software, thus saving execution time. We show the best solutions provided by DE and APSO of the attractors of the fractional-order chaotic CNNs.

High-Security Image Encryption Based on a Novel Simple Fractional-Order Memristive Chaotic System with a Single Unstable Equilibrium Point

Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

FPGA Realization of the Parameter-Switching Method in the Chen Oscillator and Application in Image Transmission

In this paper, the parameter-switching technique was applied to control chaos in the Chen oscillator and as a decryption mechanism in a secure transmission system, to transmit RGB and grayscale images. In the past few decades, considerable efforts have been put into the study of the stabilization of chaotic dynamical systems. Most of the well-known chaos control methods, such as Ott, Grebogi, and Yorke (OGY), Pyragas, and open-loop methods, force an unstable periodic orbit into a stable one while distorting the original attractor. On the other hand, the parameter-switching technique is an elegant method that can synthesize an already-existing stable orbit, thereby preserving the underlying attractor. Consequently, the main contributions of this work were the FPGA realizations of the parameter-switching method and a secure image transmission system using a synchronized master and slave topology. The results of the parameter-switching technique and synchronization were verified using phase plots and time series. The chaos-encrypted image from the image transmission system, verified using correlation, showed no relativity with the original image, while the recovery of the decrypted image has no loss of quality. The encryption and decryption system was symmetric, whereby the key was private. In this work, co-simulations were performed in Active-HDL with MATLAB/Simulink, while the target FPGA board was the Xilinx’s Artix-7 AC701.

Security Analysis and Improvement of an Image Encryption Cryptosystem Based on Bit Plane Extraction and Multi Chaos

This paper analyzes the security of image encryption systems based on bit plane extraction and multi chaos. It includes a bit-level permutation for high, 4-bit planes and bit-wise XOR diffusion, and finds that the key streams in the permutation and diffusion phases are independent of the plaintext image. Therefore, the equivalent diffusion key and the equivalent permutation key can be recovered by the chosen-plaintext attack method, in which only two special plaintext images and their corresponding cipher images are used. The effectiveness and feasibility of the proposed attack algorithm is verified by a MATLAB 2015b simulation. In the experiment, all the key streams in the original algorithm are cracked through two special plaintext images and their corresponding ciphertext images. In addition, an improved algorithm is proposed. In the improved algorithm, the generation of a random sequence is related to ciphertext, which makes the encryption algorithm have the encryption effect of a “one time pad”. The encryption effect of the improved algorithm is better than that of the original encryption algorithm in the aspects of information entropy, ciphertext correlation analysis and ciphertext sensitivity analysis.

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

A Multi-User Public Key Encryption with Multi-Keyword Search out of Bilinear Pairings

Internet of Things (IoT) and cloud computing are adopted widely in daily life and industrial production. Sensors of IoT equipment gather personal, sensitive and important data, which is stored in a cloud server. The cloud helps users to save cost and collaborate. However, the privacy of data is also at risk. Public-key encryption with keyword search (PEKS) is convenient for users to use the data without leaking privacy. In this article, we give a scheme of PEKS for a multi-user to realize the multi-keyword search at once and extend it to show a rank based on keywords match. The receiver can finish the search by himself or herself. With private cloud and server cloud, most users' computing can be outsourced. Moreover, the PEKS can be transferred to a multi-user model in which the private cloud is used to manage receivers and outsource. The store cloud and the private cloud both obtain nothing with the keyword information. Then our IoT devices can easily run these protocols. As we do not use any pairing operations, the scheme is under more general assumptions that means the devices do not need to take on the heavy task of calculating pairing.

Blockchain for COVID-19: Review, Opportunities, and a Trusted Tracking System

The sudden development of the COVID-19 pandemic has exposed the limitations in modern healthcare systems to handle public health emergencies. It is evident that adopting innovative technologies such as blockchain can help in effective planning operations and resource deployments. Blockchain technology can play an important role in the healthcare sector, such as improved clinical trial data management by reducing delays in regulatory approvals, and streamline the communication between diverse stakeholders of the supply chain, etc. Moreover, the spread of misinformation has intensely increased during the outbreak, and existing platforms lack the ability to validate the authenticity of data, leading to public panic and irrational behavior. Thus, developing a blockchain-based tracking system is important to ensure that the information received by the public and government agencies is reliable and trustworthy. In this paper, we review various blockchain applications and opportunities in combating the COVID-19 pandemic and develop a tracking system for the COVID-19 data collected from various external sources. We propose, implement, and evaluate a blockchain-based system using Ethereum smart contracts and oracles to track reported data related to the number of new cases, deaths, and recovered cases obtained from trusted sources. We present detailed algorithms that capture the interactions between stakeholders in the network. We present security analysis and the cost incurred by the stakeholders, and we highlight the challenges and future directions of our work. Our work demonstrates that the proposed solution is economically feasible and ensures data integrity, security, transparency, data traceability among stakeholders.

Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

A Methodology to Evaluate Standards and Platforms within Cyber Threat Intelligence

The cyber security landscape is fundamentally changing over the past years. While technology is evolving and new sophisticated applications are being developed, a new threat scenario is emerging in alarming proportions. Sophisticated threats with multi-vectored, multi-staged and polymorphic characteristics are performing complex attacks, making the processes of detection and mitigation far more complicated. Thus, organizations were encouraged to change their traditional defense models and to use and to develop new systems with a proactive approach. Such changes are necessary because the old approaches are not effective anymore to detect advanced attacks. Also, the organizations are encouraged to develop the ability to respond to incidents in real-time using complex threat intelligence platforms. However, since the field is growing rapidly, today Cyber Threat Intelligence concept lacks a consistent definition and a heterogeneous market has emerged, including diverse systems and tools, with different capabilities and goals. This work aims to provide a comprehensive evaluation methodology of threat intelligence standards and cyber threat intelligence platforms. The proposed methodology is based on the selection of the most relevant candidates to establish the evaluation criteria. In addition, this work studies the Cyber Threat Intelligence ecosystem and Threat Intelligence standards and platforms existing in state-of-the-art.

An Efficient Key Management Technique for the Internet of Things

The Internet of Things (IoT) has changed our lives drastically. Customers, regulatory bodies, and industrial partners are driving us to use IoT. Although IoT provides new opportunities, security remains a key concern while providing various services. It is especially challenging how the data generated from IoT devices can be protected from potential security attacks and how to safeguard the exchange of these data while transiting through different nodes and gateways. In this research, we aim to ensure a safe IoT environment by proposing an efficient key management technique that uses a combination of symmetric and asymmetric cryptosystem to obtain the speed of the former as well as the security benefits of the latter. Our proposal considers a set of Smart Objects (SO) capable of key registration, generation and distribution for IoT data transmission. We used the open-source Message Queuing Telemetry Transport (MQTT) protocol to facilitate communications between the source and the destination nodes. The suitability of the proposed approach is measured experimentally and the results are comparable to existing works with respect to key conversion time, algorithm execution time, number of reuse connections, and bandwidth utilization.