Exploiting Circular Shifts for Efficient Chaotic Image Encryption

This work presents a chaotic image encryption algorithm that acts on the binary level of the image for effective permutation, and on the byte level for substitution. The permutation step combines actions of bit level rearranging, and bit shuffling. Circular shift operations are used for bit shuffling, to reduce the execution time. Circular shifts are also applied to shuffle the permutation and substitution rules, effectively increasing security at a very low execution cost. The encryption keys are plaintext dependent, and a key mixing step in included, so that each part of the key affects all the subsequent encryption operations. For the encryption, a new Soboleva hyperbolic tangent based map is first designed. The dynamical behavior of the map is studied and shows robust chaos, and an absence of equilibria, meaning that it can generate hidden attractors. This map is used as an entropy source, along with a chaotic pseudo random number generator (PRNG). The encryption process shows a good performance under a collection of tests, and has also a low execution time, 0.0134 sec for a $256\times 256$ image, 0.0530 sec for a $512\times 512$ image, and 0.2050 sec for a $1024\times 1024$ image. So the proposed algorithm is a viable option for fast, efficient, and secure data encryption.