Abstract
This study proposes a chaos robustness criterion for a kind of 2D piecewise smooth maps (2DPSMs). Using the chaos robustness criterion, one can easily determine the robust chaos parameter regions for some 2DPSMs. Combining 2DPSM with a generalized synchronization (GS) theorem, this study introduces a novel 6-dimensional discrete GS chaotic system. Based on the system, a 216-word chaotic pseudorandom number generator (CPRNG) is designed. The key space of the CPRNG is larger than 2996. Using the FIPS 140-2 test suit/generalized FIPS 140-2 test suit tests the randomness of the 1000 key streams consists of 20,000 bits generated by the CPRNG, the RC4 algorithm, and the ZUC algorithm, respectively. The numerical results show that the three algorithms do not have significant differences. The CPRNG and a stream encryption scheme with avalanche effect (SESAE) are used to encrypt an image. The results demonstrate that the CPRNG is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs. The SESAE with one-time-pad scheme makes any attackers have to use brute attacks to break our cryptographic system.
Highlights
The dynamic behaviors of chaotic systems have some specific features, such as their extreme sensitivity to the variables of initial conditions and system parameters, pseudorandom property, and ergodic and topological transitivity
The numerical results show that the three algorithms do not have significant differences
The results demonstrate that the chaotic pseudorandom number generator (CPRNG) is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs
Summary
The dynamic behaviors of chaotic systems have some specific features, such as their extreme sensitivity to the variables of initial conditions and system parameters, pseudorandom property, and ergodic and topological transitivity. As early as in the last seventies, Feigin published his pioneering work on the analysis of C-bifurcations in ndimensional PWS systems (e.g., see [5,6,7]), which proposed the classification of the piecewise linear normal form for twoand three-dimensional piecewise smooth continuous maps. It makes it possible to follow closely the process of emergence of complex structures due to parameter variation. Based on one theorem proposed by Banerjee and Grebogi, this paper introduces a chaos robustness criterion for a kind of 2-dimensional piecewise smooth maps (2DPSMs) and constructs a 2DPSM with robust chaos feature.
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