A perturbation method to the tent map based on Lyapunov exponent and its application

Abstract

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.

A Novel Image Encryption Scheme Based on Self-Synchronous Chaotic Stream Cipher and Wavelet Transform

“…The parameters of MPE have embedding dimension m, delay factor τ, and scale factor s. For the choice of the parameter values of the multi-scale permutation entropy with the purpose of calculating the complexity of chaotic binary sequences, Sun et al [22] and Xu et al [23] give the recommended parameter range in order to obtain more accurate entropy values. On the basis of the theoretical research of the above references, in this experiment, we set m = 3, τ = 2, and s ∈ [3,7], respectively. The experimental results are shown in Table 1.…”

“…In recent years, in order to better solve the security transmission of digital images, some scholars have put forward a series of image security encryption schemes based on the chaotic system and the inherent characteristics of digital images [6][7][8][9]. For example, Ping et al [10] proposed a permutation-substitution image encryption scheme with the Henon map, which can resist a chosen-plaintext attack and known-plaintext attack.…”

An Efficient Chaotic Map-Based Authentication Scheme with Mutual Anonymity

“…Though there are some other types of chaos systems, only the extended Chebyshev chaotic map has the semigroup property and satisfies the requirements stated above. In addition, the Chebyshev map has good chaotic properties with mixture and ergodicity, and the chaotic sequences generated by the Chebyshev map have good statistical distribution characteristics as the mean is 0 [35]. Wang et al [7,8] pointed out that low dimension chaotic maps have degradation of dynamics in finite precision computations in computers; however, this issue can be addressed using appropriate implementation; for example, Liu et al [36] proposed an analogue-digital mixed method to solve the dynamical degradation of digital chaotic system.…”

Effects of Limited Computational Precision on the Discrete Chaotic Sequences and the Design of Related Solutions

“…Deng et al [17] designed an analogue-digital mixed method for enhancing the performance of chaotic sequences. Cao et al [18] came up with a 2 Complexity new perturbation method based on Lyapunov exponent to improve random distribution of chaotic sequences.…”