Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Abstract

Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

“…Although Zhou et al considered these maps to be highly sensitive to initial conditions, they did not perform a formal sensitivity analysis. Also, in 2021, Shi and Deng [55] when studying the dynamical degradation of the twodimensional Barker map they found that this chaotic map can have valuable properties when it is used in a PRNG. Another example showing the application of strategies to overcome security disadvantages in PRNGs based on chaotic maps is the work proposed by Murillo-Escobar et al in 2017 [36].…”

An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

“…This method is easy to implement and can make the output of the digital chaotic system not reflect any system characteristics, but it will lead to poor distribution. The third type is coupling [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], which couples the digital chaotic system and the continuous chaotic system one way or two ways. This method cleverly makes use of the complementarity between the digital chaotic system and the continuous chaotic system, but, compared with other methods, this method is more expensive to implement, and the system is more complex.…”

“…They used variable parameters and Lyapunov exponents to improve the performance of logistic digital systems according to the differential median theorem. Deng et al [ 16 ] made further improvements on the basis of the former and proposed a logistic digital system control method (VPCMDP) based on the differential mean theorem and state feedback technology. Both of these two methods are based on error compensation.…”