Summary
This research work reports the finding of a new 4‐D hyperchaotic two‐scroll system having three second‐order nonlinear terms. It is detailed that the system does not have any rest point for ...non‐zero values of the system parameters. Thus, we deduce that the new hyperchaotic system has a hidden attractor. The main findings of the new hyperchaotic system include a detailed bifurcation analysis, coexisting attractors, and offset‐boosting control. The new 4‐D hyperchaotic two‐scroll system with hidden attractor is prototyped using the field‐programmable gate array (FPGA) Zybo Z7‐20 development board, Xilinx Vivado tool, and the hardware description by VHDL. It is highlighted that the simulation of the circuit design, and the experimental results from the FPGA synthesis, all of them are in good agreement with theoretical simulations.
Artificial neurons are quite useful to generate chaotic behavior, and they can be implemented on embedded systems like Raspberry Pi that include WiFi network connectivity. In this manner, this paper ...shows the use of some artificial neurons to generate chaotic binary sequences whose randomness is enhanced by post-processing approaches and measured by performing statistical NIST SP 800-22 tests. The chaotic neurons are synchronized by different methods and each neuron is implemented on a Raspberry Pi, which allows connectivity to a machine-to-machine (M2M) broker. This wireless connectivity advantage is exploited herein to develop a lightweight cryptographic application under the message queueing telemetry transport (MQTT) for Internet of Things (IoT) protocol. The synchronized neurons have a topology in which one Raspberry Pi works as publisher and can send encrypted information to multiple subscribers. Due to the chaotic behavior of the neurons, the Raspberry Pi acting as subscriber can recover the encrypted information if and only if it has the right key, i.e., the correct random binary sequence generated by the publisher. To augment the security against attacks, the chaotic neurons have different initial conditions before M2M synchronization is accomplished, and the color image encryption under MQTT for IoT is evaluated by performing correlation, histogram, variance, entropy, and NPCR tests.
Fractional-order chaotic systems have many applications in science and engineering. This work describes a new fractional-order 3-D jerk chaotic system with no equilibrium point. The proposed ...fractional order chaotic system exhibits a hidden attractor since it does not have any equilibrium point. We carry out a detailed bifurcation analysis for the fractional-order jerk system with respect to its parameters. In this research work, we use the Grünwald-Letnikov method (GL) to solve the fractional order jerk system with the short memory principle, and provide a detailed bifurcation analysis and the Lyapunov spectrum.
This paper shows the use of four sets of coefficient values of the 2D chaotic map to generate pseudo-random number generators. We demonstrate that the generated sequences are random by applying NIST ...suite 800-22-a and TestU01 tests. The generated random sequences are used to implement a stream cipher and are applied to encrypt images. To detect if the images have been modified, we propose to use the random sequences as keys for a hash function based on the pseudo-dot product. This hash can be used as a message authentication code in the images to detect if the stored information has been compromised. The proposed schemes can be used to encrypt and authenticate any digital data not only images. The random sequences generator is probed also in a high-performance microcontroller STM32F746ZG obtaining a throughput of 173.35 Kbit/s.
We show the usefulness of bifurcation diagrams to implement a pseudo-random number generator (PRNG) based on chaotic maps. We provide details on the selection of the best parameter values to obtain ...high entropy and positive Lyapunov exponent from the bifurcation diagram of four chaotic maps, namely: Bernoulli shift map, tent, zigzag, and Borujeni maps. The binary sequences obtained from these maps are analyzed to implement a PRNG both in software and in hardware. The software implementation is realized using 32 and 64 bits microprocessor architectures, and with floating point and fixed point computer arithmetic. The hardware implementation is done by using a field-programmable gate array (FPGA) architecture. We developed a serial communication interface between the PRNG on the FPGA and a personal computer to obtain the generated sequences. We validate the randomness of the generated binary sequences with the NIST test suite 800-22-a both in floating point and fixed point arithmetic. At the end, we show that those chaotic maps are suitable to implement a PRNG but according to the hardware resources, the one based on the Bernoulli shift map is better. In addition, another advantage is that the required initial value for the sequences can be within the whole interval
-
1
,
1
, including its bounds.
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.
A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic ...model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.
Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the ...Hindmarsh-Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan-Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh-Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.
PDF
