Cryptanalysis of a chaotic image encryption scheme based on permutation-diffusion structure

Chaos-based image encryption algorithms have been widely studied since the permutation-diffusion structure (PDS) was proposed. However, the PDS is not secure from attacks, which may lead to security vulnerabilities of PDS based chaotic cryptosystems. In this study, the security problems of PDS are investigated. Then, a new PDS based chaotic image encryption scheme is cryptanalyzed. In the original scheme, a 3D bit matrix permutation was used to address the intrinsic deficiencies of traditional pixel/bit level permutation of image encryption. The double random position permutation provides a high security level. However, it is not unattackable. In this study, a novel attack method will be introduced where all the chaotic mappings or parameters which are functionally equivalent to the keys used in the permutation and diffusion stages of the original cryptosystem can fully be revealed. The encrypted images can then be completely recovered without knowing the secret keys. Both mathematical analysis and experimental results are given to illustrate the effectiveness of the proposed method.