On the Security of Permutation-Only Image Encryption Schemes

Permutation is a commonly used primitive in multimedia (image/video) encryption schemes, and many permutation-only algorithms have been proposed in recent years for the protection of multimedia data. In permutation-only image ciphers, the entries of the image matrix are scrambled using a permutation mapping matrix which is built by a pseudo-random number generator. The literature on the cryptanalysis of image ciphers indicates that the permutation-only image ciphers are insecure against ciphertext-only attacks and/or known/chosen-plaintext attacks. However, the previous studies have not been able to ensure the correct retrieval of the complete plaintext elements. In this paper, we revisited the previous works on cryptanalysis of permutation-only image encryption schemes and made the cryptanalysis work on chosen-plaintext attacks complete and more efficient. We proved that in all permutation-only image ciphers, regardless of the cipher structure, the correct permutation mapping is recovered completely by a chosen-plaintext attack. To the best of our knowledge, for the first time, this paper gives a chosen-plaintext attack that completely determines the correct plaintext elements using a deterministic method. When the plain-images are of size ${M}times {N}$ and with ${L}$ different color intensities, the number ${n}$ of required chosen plain-images to break the permutation-only image encryption algorithm is ${n}=lceil log _{L}$ (MN) $rceil $ . The complexity of the proposed attack is $O$ ( $n,cdot , {M N}$ ) which indicates its feasibility in a polynomial amount of computation time. To validate the performance of the proposed chosen-plaintext attack, numerous experiments were performed on two recently proposed permutation-only image/video ciphers. Both theoretical and experimental results showed that the proposed attack outperforms the state-of-the-art cryptanalytic methods.