Determining accurate Lyapunov exponents of a multiscroll chaotic attractor based on SNFS

Carbajal-Gomez, Victor Hugo; Sánchez–López, C.

doi:10.1007/s11071-019-05288-9

Cited by 19 publications

(3 citation statements)

References 26 publications

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“…Lyapunov Exponent (LE) is a significant tool commonly applied to analyze the dynamics of a nonlinear system and to evaluate the sensitivity of a chaotic system statistically. 16 A negative value of LE indicates contracting in the time state of the system. Whereas, a positive value indicates an expanding in time state of the system.…”

Section: Prngmentioning

confidence: 99%

Hardware implementation of a strong pseudorandom number generator based block‐cipher system for color image encryption and decryption

Gafsi

Amdouni

Hajjaji

et al. 2022

Circuit Theory & Apps

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Summary This paper proposed a hardware architecture of a strong block‐cipher system dedicated to digital image encryption and decryption. On the one hand, a pseudorandom number generator (PRNG) based on two 3D chaotic systems is created to produce strong keys. On the other hand, a robust algorithm is proposed to ensure high‐level security and low computational complexity of image encryption. The algorithm performs image encryption mainly through three processes: pixel values hiding by applying the XOR operation with a key, pixel positions hiding by operating random permutation, and pixel substitution using the S‐box method. To increase the complexity, R rounds of encryption could be accomplished in a loop. Then as a final step, using the Xilinx Vivado/system generator tool, the hardware cryptosystem is developed, implemented, and evaluated on an FPGA‐Zynq evaluation board. According to the synthesis results, the suggested hardware system performs on a reduced FPGA area and gives a good frequency of 156.813 MHz with a high throughput of 20,072.064 Mbps. Several tools and tests utilizing various images are used to evaluate and analyze the hardware cryptosystem. The experimental results show that the hardware implementation has higher performance compared to other recent works.

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Section: Prngmentioning

confidence: 99%

Hardware implementation of a strong pseudorandom number generator based block‐cipher system for color image encryption and decryption

Gafsi

Amdouni

Hajjaji

et al. 2022

Circuit Theory & Apps

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“…In the last decade, the study of synchronization phenomena in a group of coupled Piece-Wise Linear (PWL) in the context of nonlinear systems theory has attracted considerable attention due to its wide application in fields such as physics, biology, and engineering, among others (Muñoz-Pacheco et al 2012;Anzo-Hernández et al 2019;Carbajal-Gómez and Sánchez-López 2019;Ruiz-Silva et al 2021;Echenausía-Monroy et al 2021;Ruiz-Silva et al 2022).…”

Section: Introductionmentioning

confidence: 99%

Multi-scroll Systems Synchronization on Strongly Connected Digraphs

MARTÍNEZ¹,

Echenausía-Monroy

Ruiz-Silva

2022

Chaos Theory and Applications

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In this paper, we study the synchronization problem in complex dynamic networks of Piece Wise Linear (PWL) systems. PWL systems exhibit multi-scrolls and belong to a special class of Unstable Dissipative Systems (UDS). We consider strongly connected digraphs and linear diffusive couplings. The synchronization regions are computed using the concept of disagreement vectors, generalized algebraic connectivity of the network topology, and Lyapunov functions, which provide lower bounds on the coupling gain of the network. Then, different combinations of linear diffusive coupling are explored by changing the observed and measured variables to illustrate the contribution of our results. The theoretical results are validated by numerical simulations.

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“…Como se menciona anteriormente, este tipo de sistemas no contiene productos de sus variables de estado en el modelo, es decir, estos presentan una función no lineal que genera los enrollamientos. En la literatura se ha reportado modelos caóticos de múltiple enrollamiento con un término no lineal conformado por funciones lineales por partes (PWL, por su sigla en inglés "piecewise linear") (Carbajal-Gómez y Sánchez-López, 2019;Tlelo-Cuautle et al, 2015), por formas especiales de una función seno (SFSF, por su sigla en inglés special form of a sine function), funciones hiperbólicas (Chen et al, 2017;Signing et al, 2019), entre otras, (Ding y Feng, 2020;Li y Zeng, 2023).…”

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Sincronización de sistemas caóticos de múltiple enrollamiento mediante observador de estado extendido

Aldrete-Maldonado,

Prieto-Entenza,

Plata-Ante

et al. 2023

ICBI

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Este artículo presenta el diseño de un observador para resolver el problema de sincronización de sistemas caóticos de múltiple enrollamiento. La propuesta consiste en el diseño de un observador de estado extendido para estimar la no linealidad que genera el múltiple enrollamiento en la dinámica del sistema caótico. Además, se presenta un análisis de estabilidad bajos los criterios de Lyapunov para demostrar que las soluciones se mantienen acotadas de manera uniforme. Finalmente, se muestran resultados de simulación para ilustrar la efectividad del observador propuesto.

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Determining accurate Lyapunov exponents of a multiscroll chaotic attractor based on SNFS

Cited by 19 publications

References 26 publications

Hardware implementation of a strong pseudorandom number generator based block‐cipher system for color image encryption and decryption

Hardware implementation of a strong pseudorandom number generator based block‐cipher system for color image encryption and decryption

Multi-scroll Systems Synchronization on Strongly Connected Digraphs

Sincronización de sistemas caóticos de múltiple enrollamiento mediante observador de estado extendido

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