  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.
