A novel pseudo-random coupled LP spatiotemporal chaos and its application in image encryption**Project supported by the National Natural Science Foundation of China (Grant Nos. 61672124, 61370145, and 61173183), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund, China (Grant No. MMJJ20170203), the Program for New Century Excellent Talents in Fujian Province University, and the Natural Science

Abstract

In this paper, first, we investigate a novel one-dimensional logistic-PWLCM (LP) modulation map which is derived from the logistic and PWLCM maps. Second, we propose a novel PCLML spatiotemporal chaos in pseudo-random coupling method that can accelerate the system behavior of the fully spatial chaos. Here, because the better chaotic properties include a wide range of parameter settings and better ergodicity than a logistic map, the LP is used in PCLML as f(x). The Kolmogorov–Sinai entropy density and universality and the bifurcation diagram are employed to investigate the chaotic behaviors of the proposed PCLML model. Finally, we apply the LP and PCLML chaotic systems to image encryption to improve the effectiveness and security of the encryption scheme. By combining self-generating matrix model M and dynamic substitution box (S-Box) methods, we design a new image encryption algorithm. Numerical simulations and security analysis have been carried out to demonstrate that the proposed algorithm has a high security level and can efficiently encrypt several different kinds of images into random-like images.