Construction and application of new high-order polynomial chaotic maps

Zang, Hongyan; Zhao, Xianming; Wei, Xinyuan

doi:10.1007/s11071-021-06982-3

Cited by 10 publications

(6 citation statements)

References 21 publications

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“…These providing numerical evidence for their uniform distribution characteristics. Table 5 presents a comparison of the information entropy with references [2,14,25]. The information entropy of the sequence generated by our proposed PRNG is greater than that of the PRNG currently proposed.…”

Section: Information Entropy Analysismentioning

confidence: 98%

Constructing new high-order polynomial chaotic maps and application in pseudorandom number generator

Wu,

Zhou

2024

Phys. Scr.

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The chaotic map have been widely applied in fields such as pseudorandom number generation(PRNG) and image encryption due to its excellent chaotic performance. In this paper, two classes of high-order polynomial chaotic maps of special form are proposed based on the Li-Yorke theorem. The dynamic behavior of the proposed maps is numerically analyzed, including bifurcation and Lyapunov exponent, and the analysis results prove the validity of the proposed conclusions. The proposed polynomial chaotic maps have a larger parameters and chaotic range, as well as a more stable Lyapunov exponent. Furthermore, based on the coupling chaotic systems, we design a pseudorandom number generator(PRNG), and the number of chaos parameters are expanded through the coupling control parameters in a PRNG. Then the performance of the pseudorandom sequence generated by the PRNG is tested and analysed. The test and analysis results show that the pseudorandom sequence has favorabble security, structural complexity, and randomness. . Especially, the information entropy of 7.9998 and the key space size of 2^208 exceed the recently reported pseudorandom number generators(PRNGs). In comparison with other pseudorandom number generators(PRNGs) based on chaotic maps in the recent literature, this paper provides comprehensive performance test and analysis of the proposed PRNG and demonstrates its potential for cryptographic applications.

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Section: Information Entropy Analysismentioning

confidence: 98%

Constructing new high-order polynomial chaotic maps and application in pseudorandom number generator

Wu,

Zhou

2024

Phys. Scr.

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“…The bifurcation diagram and Lyapunov exponent spectrum of parameter a in system (9) are shown in Figure 4a,b, respectively. Figure 4 shows that system (9) displays chaotic characteristics In proposition 3, set ( ) sin( ) 1 (9) is chaotic. The bifurcation diagram and Lyapunov exponent spectrum of parameter a in system (9) are shown in Figure 4a,b, respectively.…”

Section: Bifurcation Diagrams and Lyapunov Exponent Spectramentioning

confidence: 99%

“…Researchers have been extensively attracted to constructing new chaotic systems in terms of the existing theory [9,10], which involves the discrimination for the existence of chaos in dynamical systems. In 1975, Li and Yorke first defined the term chaos from a mathematical perspective and proposed a criterion for the existence of chaos in onedimensional discrete dynamical systems [11], which is well known as "period three implies chaos".…”

Section: Introductionmentioning

confidence: 99%

Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems

2022

Self Cite

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This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. The system can be distributed uniformly by adjusting the parameters. In this paper, we propose an image encryption scheme based on a uniformly distributed discrete chaotic system and DNA encoding. DNA encoding and decoding rules are determined by plain text. The experimental results demonstrate that our encryption algorithm has a large key space, high key sensitivity, and fast encryption speed and can resist differential and statistical attacks.

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“…e Lyapunov exponent is a measure of the sensitive dependence of the system on initial conditions [33,34]. A positive Lyapunov exponent indicates that the system is in a chaotic state.…”

Section: Lyapunov Exponentsmentioning

confidence: 99%

Novel One‐Dimensional Chaotic System and Its Application in Image Encryption

et al. 2022

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Designing a chaotic system with a simple structure and complex dynamic behavior is one of the main tasks of chaotic cryptography. This paper designs a new 1D chaotic system called 1D two-parameters-sin-cos (1D-TPSC). Compared with high-dimensional chaotic systems, the 1D-TPSC has a simple structure and is easy to implement with software. The Lyapunov exponent analyzes the parameter space of the 1D-TPSC in a chaotic state. Furthermore, using sensitivity analysis, cobweb plot, and bifurcation diagram to verify that the sequence generated by 1D-TPSC has good performance. In addition, the 1D-TPSC has also been applied in chaotic image encryption. Arnold mapping is used to scramble the plaintext, and random XOR is used to diffuse the scrambled image. Simulation experiments show that the method can remarkably resist standard attack methods.

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Construction and application of new high-order polynomial chaotic maps

Cited by 10 publications

References 21 publications

Constructing new high-order polynomial chaotic maps and application in pseudorandom number generator

Constructing new high-order polynomial chaotic maps and application in pseudorandom number generator

Image Encryption Schemes Based on a Class of Uniformly Distributed Chaotic Systems

Novel One‐Dimensional Chaotic System and Its Application in Image Encryption

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