Abstract
Considering that a majority of the traditional one-dimensional discrete chaotic maps have disadvantages including a relatively narrow chaotic range, smaller Lyapunov exponents, and excessive periodic windows, a new nonlinearly modulated Logistic map with delay model (NMLD) is proposed. Accordingly, a chaotic map called a first-order Feigenbaum-Logistic NMLD (FL-NMLD) is proposed. Simulation results demonstrate that FL-NMLD has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared with existing chaotic maps. Based on FL-NMLD, we propose a new image encryption algorithm that joins the pixel plane and bit-plane shuffle (JPB). The simulation and test results confirm that JPB has higher security than simple pixel-plane encryption and is faster than simple bit-plane encryption. Moreover, it can resist the majority of attacks including statistical and differential attacks.
Highlights
A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice was proposed by Zhang et al [11], a novel image encryption algorithm based on cycle shift and chaotic system was proposed by Wang et al [4], and an image encryption algorithm using the two-dimensional logistic chaotic map was proposed by Wu et al [1]
nonlinearly modulated Logistic map with delay model (NMLD) (FL-NMLD) based on our model. It has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared to existing chaotic maps
To address the disadvantages of 1D chaotic maps, this paper proposed a new nonlinearly modulated chaotic model with delay
Summary
Because of pseudo-randomness, orbital unpredictability, and sensitivity of the initial values, chaotic maps have been widely applied in the encryption system, especially image encryption [1,2,3,4,5,6,7,8,9,10]. There is a report that Logistic map-based image encryption algorithm proposed in [14] was proved to be not safe [15]. It has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared to existing chaotic maps. We propose a image encryption algorithm that joins pixel-plane and bit-plane shuffle (JPB). This algorithm performs different encryption operations on one or several bit planes according to the amount of information contained in each bit plane.
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