A novel image encryption scheme based on 3D bit matrix and chaotic map with Markov properties

Abstract

Based on 3D cat map, reverse 3D cat map and an improved class of chaotic maps with Markov properties, an effective bit-level image encryption scheme is proposed. Firstly, we convert the plain-image into binary matrix, and use the sum of all bits in the binary matrix as a part of secret keys to resist chosen-plaintext attack and known-plaintext attack. Secondly, we design a mapping which maps a random bit position to another random bit position rather than using traditional sequential visiting the plain-image. Thirdly, a chaotic map with Markov properties is used in the diffuse process. This kind of chaotic map has good chaotic natures than the Logistic map, which keeps the uniformity and low autocorrelation. The results of simulation and security analysis show that the proposed image encryption scheme is able to resist various attacks and has excellent encryption performance.