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This paper proposes three types of one-dimensional piecewise chaotic maps and two types of symmetrical piecewise chaotic maps and presents five theorems. Furthermore, some examples that satisfy the theorems are constructed, and an analysis and model of the dynamic properties are discussed. The construction methods proposed in this paper have a certain generality and provide a theoretical basis for constructing a new discrete chaotic system. In addition, this paper designs a pseudorandom number generator based on piecewise chaotic map and studies its application in cryptography. Performance evaluation shows that the generator can generate high quality random sequences efficiently.

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps