Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy

Liu, Chunyuan; Ding, Ling; Ding, Qun

doi:10.3390/e21070663

Cited by 9 publications

(5 citation statements)

References 32 publications

(26 reference statements)

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“…In this paper, nonlinear changes are proposed to enhance the chaotic properties of low-dimensional chaotic systems. In order to overcome the above weakness of the low dimensional discrete-time chaotic map, linear combinations of the output values of existing chaotic systems are proposed to enhance the chaotic characteristics in [23][24][25][26][27]. Because the linear combination cannot change the output value of the original system, only the linear combination of these values, the performance of the presented system is not very good.…”

Section: Introductionmentioning

confidence: 99%

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Yan

Ding

2021

Electronics

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In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.

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Section: Introductionmentioning

confidence: 99%

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Yan

Ding

2021

Electronics

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“…The das suffers from statistical defects, which is a manifest of the system's continuities and autocorrelations due to the system's memory. Another plausible problem is the upper bound limit on entropy which was shown in the works of [44], [45] on chaotic univariate maps. Fortunately, the two works are not concerned with continuous chaotic multivariate systems, and no work disproved the conjecture for this category.…”

Section: Sponge-based Prngmentioning

confidence: 99%

Design and Implementation of a flexible Multi-purpose Cryptographic System on low cost FPGA

Maache

Kalache

2023

Int. j. electr. comput. eng. syst. (Online)

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The design of cryptographic hardware that supports multiple cryptographic primitives is common in literature. In this work, a new design is presented consisting of a multi-purpose cryptographic system featuring both 128-bit pipelined AES-CORE (Advanced Encryption Standard) for high-speed symmetric encryption and a Keccak hash core on a low-cost FPGA. The KECCAK-CORE’s security and performance parameters are tunable in the sense that capacity, bitrate, and the number of rounds can be user-defined. Such flexibility enables the core to suit a large range of security requirements. The structure of Keccak’s sponge construction is exploited to enable different modes of operation. An example application outlined in this work is Pseudo Random Number Generation (PRNG). With few adjustments, the KECCAK-CORE was also operated as a post-processing unit for True Random Number Generation (TRNG) that uses the analog Lorenz chaotic circuit as a physical entropy source. The multi-purpose design was implemented in VHDL targeting an IntelFPGA Cyclone-V FPGA. For AES symmetric encryption, a maximum throughput of 31.1Gbps was achieved and a logic usage of 25146LEs (23% of the FPGA) in the case of the pipelined variant of AES-CORE. For the KECCAK-CORE, maximum throughput figures of 5.81, 8.4, and 11Gbps were achieved for the three SHA-3 variants 512, 384, and 256-bit respectively, with an area usage of 8947LEs (8%). The system as a whole occupies an area of 26909LEs (26%). The random sequences generated by the system operating in PRNG and TRNG post- processing modes successfully passed the National Institute of Standards and Technology (NIST) statistical test suite (NIST SP 800-22). The information entropy analysis performed on the post-processed TRNG sequences indicates an average of 0.935.

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“…These numerical simulations, together with some other calculations, imply that system (2) is indeed hyperchaotic. As explained and visualized in Reference [18], the entropy of time series generated by the financial system (2) exhibits relatively high values when system (2) undergoes the hyperchaos phenomenon; see References [18][19][20][21][22], for instance, for more explanation on the relation between entropy and chaos. This could help us locate accurately chaotic and periodic attractors in the system (2).…”

Section: Introductionmentioning

confidence: 98%

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

Wang¹,

Zhao²,

Zhang

et al. 2023

Entropy

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Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial differential equations supplemented by the homogeneous Neumann boundary condition, which governs a financial system comprising the labor force, the stock, the money, and the production sub-blocks distributed in a certain line segment or planar region. The system derived by removing the terms involved with partial derivatives with respect to space variables from our concerned system was demonstrated to be hyperchaotic. We firstly prove, via Galerkin’s method and establishing a priori inequalities, that the initial-boundary value problem for the concerned partial differential equations is globally well posed in Hadamard’s sense. Secondly, we design controls for the response system to our concerned financial system, prove under some additional conditions that our concerned system and its controlled response system achieve drive-response fixed-time synchronization, and provide an estimate on the settling time. Several modified energy functionals (i.e., Lyapunov functionals) are constructed to demonstrate the global well-posedness and the fixed-time synchronizability. Finally, we perform several numerical simulations to validate our synchronization theoretical results.

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Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy

Cited by 9 publications

References 32 publications

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Design and Implementation of a flexible Multi-purpose Cryptographic System on low cost FPGA

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

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