Cryptanalysis and improvement of two hyper-chaos-based image encryption schemes

•Two image encryption schemes suffer from the problem of low security-sensitivity.•An improvement is proposed to fix the weakness found.•Confusion and diffusion are enhanced such that attacks are turned infeasible.

As chaos-based image encryption developed, its security relies on two operations, permutation and diffusion. Some existing schemes in the literature are broken due to the failed design of either permutation or diffusion. An image encryption scheme based on hyper-chaos, proposed by Gao and Chen has undergone the scrutiny from research community and security weaknesses found. Its improvement by Rhouma and Belghith needs to be carefully examined. This paper points out that both of them suffer from the problem of low security-sensitivity to plain-image change. Thus, attackers can predict the order of permutation and the security of the cryptosystem only relies on the diffusion operation. This implies that security level is potentially degraded. In this paper, an improvement of the hyper-chaos-based image encryption scheme is proposed to fix the weakness in not only Gao and Chen׳s but also that in Rhouma and Belghith׳s modified approaches.