A New Cryptosystem of Color Image Using a Dynamic-Chaos Hill Cipher Algorithm

Abstract

The conventional symmetric Hill cipher encryption algorithm, applied for data encryption, presents several disadvantages. However, a drawback of the conventional algorithm is known to be vulnerable to plain-text attack. Another setback, it does not hide all features of the image with homogeneous background and finally, the difficulty of finding the inverse of the key matrix. To overcome these problems, in this paper, we propose an improvement of the Hill cipher algorithm. The principle consists in using an affine transformation provided by a three-order invertible matrix and a dynamic translation vector. This vector is dynamically transformed at each iteration by an affine transformation composed of a chaotic matrix T, not necessarily invertible, and a pseudo random translation vector Y. This improvement overcomes the linearity problem of Hill’s classic method. In addition, computational complexity can be reduced by simplifying the inverse matrix search process at the time of decryption. This inverse lies only in the search for the modular inverse of a single element of the matrix in the ring Z/256Z. The proposed scheme overcomes the disadvantages of the conventional Hill cipher, especially, the images with strong homogenous zones. The proposed algorithm guarantees a better quality of security and encryption.