Application of 8-dimensional Generalized Synchronization System in Pseudorandom Number Generator
HAN Dandan① MIN Lequan② ZHAO Geng③
①(School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China) ②(School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China) ③(Beijing Electronic Science and Technology Institute, Beijing 100070, China)
This paper proposes a class of 4-Dimensional Discrete Systems (4DDSs). Using the eigenvalues of Jacobian matrix of the system at the equilibrium, the?stability of the system at the equilibrium is analyzed. A theorem is set up, which is used to determine whether the class systems are periodic or chaotic. Based on the theorem, a 4DDS is constructed. The 4DDS has positive Lyapunov exponent. Numerical simulations show that the dynamic behaviors of the 4DDS have chaotic attractor characteristics as they expects. Combining the 4DDS with Generalized Synchronization (GS) theorem, an 8-Dimensional GS Chaotic System (8DGSCS) is designed. Using this system, this paper designs a 16 bit string Chaotic Pseudo Random Number Generator (CPRNG). Theoretically the key space of the CPRNG is larger than 21245. The FIPS 140-2 test suit/Generalized FIPS 140-2 test suit are used to test the randomness of the 1000-key streams consisting of 20000 bit generated by the CPRNG, Narendra RBG, RC4 PRNG and ZUC PRNG, respectively. The results show that there are 100%/99%, 100%/ 82.9%, 99.9%/98.8% and 100%/97.9% key streams passing the FIPS 140-2 test suit/Generalized FIPS 140-2 test suit, respectively. Numerical simulations show that the different key-streams have 50.004% different codes. The results show that the generated CPRNG has good randomness properties, can better resist the brute attack. The designed CPRNG provides a novel tool for the research and development of cryptography.
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HAN Dandan, MIN Lequan, ZHAO Geng. Application of 8-dimensional Generalized Synchronization System in Pseudorandom Number Generator. JEIT, 2016, 38(5): 1158-1165.
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