Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with excellent performance. The chaotic behavior analysis has verified this coupling system's effectiveness and progress. In particular, we give a specific strategy about selecting an appropriate unit transform function to enhance chaos of generated maps. Besides, a new chaos based pseudo-random number generator, shorted as CBPRNG, is designed to improve the distribution of chaotic sequences. We give a mathematical illustration on the uniformity of CBPRNG, and test the randomness of it. Moreover, based on CBPRNG, an image encryption algorithm is introduced. Simulation results and security analysis indicate that the proposed image encryption scheme is competitive with some advanced existing methods.

中文翻译：

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基于单位变换的耦合混沌系统及其在图像加密中的应用

混沌图对于建立基于混沌的图像加密系统非常重要。本文介绍了一种基于一定单位变换的耦合混沌系统，它可以将任意两个一维混沌映射组合起来，生成一个性能优良的新混沌映射。混沌行为分析验证了该耦合系统的有效性和进步性。特别是，我们给出了一个关于选择合适的单元变换函数来增强生成地图的混沌的具体策略。此外，设计了一种新的基于混沌的伪随机数生成器，简称 CBPRNG，旨在改善混沌序列的分布。我们对CBPRNG的均匀性进行了数学说明，并测试了它的随机性。此外，基于CBPRNG，引入了一种图像加密算法。