Abstract
Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the linear feedback function and parameter perturbation function. This method is universal for all different digital chaotic maps. Here, two examples are presented: one is 1D logistic map and the other is 2D Baker map. To show the effectiveness of this method, we take some numerical experiments, including trajectory and phase space analysis, correlation analysis, period analysis, and complexity analysis. All the numerical results prove that the method can greatly improve the dynamics of digital chaotic maps and is quite competitive with other proposed methods. Furthermore, a simple pseudorandom bit generator (PRBG) based on digital Baker map is proposed to show its potential application. The proposed PRBG is completely constructed by the digital chaotic map, without any other complex operations. Several numerical results indicate that this PRBG has good randomness and high complexity level.
Highlights
Chaos has been widely used in many different kinds of scientific fields, including physics, biology, economics, and social science
Motivated by the summary above, in this paper, we proposed a novel effective method to reduce the dynamical degradation of digital chaotic maps. is method is composed of linear feedback control and parameter perturbation
When the encryption algorithm based on chaotic map is implemented on the equipment with finite precision, due to truncation error and rounding error, the chaotic map will degenerate dynamically and enter a period which leads to the insecurity of the encryption algorithm
Summary
Chaos has been widely used in many different kinds of scientific fields, including physics, biology, economics, and social science. The randomness and complexity will degrade, which makes the chaotic map not secure anymore To solve this problem, in this paper, we propose a novel method to reduce the dynamical degradation of digital chaotic maps, whose mathematical model can be described as xi+1 FL f h xi− 1, xi− 2, . We use some characteristics to highlight the effectiveness of this method, including trajectory, phase space, autocorrelation function, period, complexity, and state-mapping network [26]. We can conclude that the average length of the orbit of the SMN of improved map is larger than that of the original map, which indicates the effectiveness of our method
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