2008.06-Present School of Mathematics and Physics, University of Science and Technology Beijing Associate professor 2000.06-2008.06 School of Mathematics and Physics, University of Science and Technology Beijing Lecturer 1998.04-2000.06 School of Mathematics and Physics, University of Science and Technology Beijing Assistant

 Proposed generalized chaotic synchronization theorem for uni-directionally coupled array differential equation systems. Proposed the generalized synchronization theorem for discrete chaotic systems. Proposed the generalized chaotic synchronization theorem for unidirectionally coupled discrete array systems. Proposed the generalized chaotic synchronization theorem for dual directional discrete array systems and differential equation systems. These theorems solve the problem of constructing forms of generalized chaotic systems. They provide tools to understand and control the internal relations of complex system dynamics. They also provide a tool to control and design generalized chaotic synchronization systems and generalized stable systems.  Based on period three theory, Marotto’s theorem and other chaotic theories, some discrete chaotic systems, satisfying these theorem conditions, are set up. For instance, cubic and quartic polynomial chaotic systems with special analytical expressions, piecewise linear chaotic systems, chaotic systems with a uniform distribution and so on. Using these chaotic systems, some applications of chaos in cryptography are investigated. Several algorithms of generating S-box are designed as well as some pseudo-random number generators with good properties. Additionally, some encryption schemes with the function of one key at a time are designed. These schemes have characteristics, such as very sensitive to system’s parameters and initial conditions, large key space.  Deduce the sufficient conditions of quadratic polynomial chaotic systems and tent map, then provide a homogenization method for a kind of quadratic polynomial chaotic systems. Furthermore, for cubic or quartic polynomial chaotic systems or some other chaotic systems, the corresponding homogenization methods are also proposed.  With replacing Euclidean distance in Rn by Hamming distance, Lyapunov exponent in chaotic dynamics is transplanted into a test index of s-box in traditional cryptography, and then Lyapunov exponent of s-box is defined.

1 Master students per year

Representative papers 1. Jiu Li, Hongyan Zang* , Xinyuan Wei, On the construction of one-dimensional discrete chaos theory based on the improved version of Marotto’s theorem, Journal of Computational and Applied Mathematics, 2020.12, 380,112952 . 2. Hongyan Zang, Kai Li and Xinyuan Wei, A quartic polynomial chaotic map with its application in S-box generation, Dynamic Systems and Applications ,2020.12, 29(8): 2601 – 2618 3. Wei Xinyuan , Zang Hongyan*, Construction and complexity analysis of new cubic chaotic maps based on spectral entropy alogorithm, Journal of Intelligent & Fuzzy Systems, 2019, 37（4）：4547-4555. 4. Hongyan Zang, Guodong Li, Xuejuan Han, Lele Wang , The Part Research on Bidirectional Generalized Chaos Synchronization, Wireless Personal Communications, 2018, 102(2): 1269-1282. 5. Hongyan Zang *, Hongyu Chai, Homogenization and entropy analysis of a quadratic polynomial chaotic system, Acta Physica Sinca, 2016, 65(3): 030504. 6. Qi Wang, Xiubin Fan, Hongyan Zang *, The Space Complexity Analysis in the General Number Field Sieve Integer Factorization, Theoretical Computer Science, 2016, 630(30): 76-94.

I have supervised a number of master's students, of which 13 have graduated and 3 are in progress