A uniform chaotic system with extended parameter range for image encryption

Abstract

Chaotic maps are found to be a promising external entropy source for image encryption. However, many existing chaotic systems have relatively narrow parameter space and cannot generate uniformly distributed sequences, which may reduce the reliability of cryptosystem. In this paper, a novel chaotification model named as UCS is proposed to improve the statistical property and expand the parameter range of existing maps. The new chaotic maps generated from UCS exhibit more complex chaotic behaviors than seed maps, and the two independent parameters can take almost any value in $$\mathbf {R}^2$$ . Moreover, the iterated chaotic sequences are approximately uniformly distributed and thus have better randomness. Based on the improved chaotic maps, a new image encryption algorithm is designed, which encodes digital images by derangement-based confusion, row–column bidirectional diffusion and 2D zigzag diffusion. Experimental results indicate the high performance of the proposed image encryption scheme, since it has obtained excellent results in various tests when compared with several existing methods.