Colour image encryption based on cross-coupled chaotic map and fractional order chaotic systems

Abstract

This paper presents a colour image encryption algorithm based on cross-coupled chaotic map and fractional order chaotic systems. Firstly the algorithm employs the cross-coupled chaotic skew tent map to perform the shuffling operation, and then uses the fractional order versions of Lorenz's system and Chen's system to disturb image pixel intensity values. Fractional order extensions of the chaotic systems provides a much larger key-space than their original integer order versions. The encrypted image exhibits uniform histogram and a very high entropy for all the three colour channels. Also, the property of zero correlation is satisfied by the intensity values of adjacent pixels in each channel of the encrypted image. Moreover, the algorithm possesses a key-space which is large enough to resist all possible kinds of statistical attacks. Theoretical analysis and experimental results thus demonstrate that the proposed scheme has an excellent efficiency and satisfactory security attributes. However, solving fractional order differential equations is a computationally heavy process. Some efficient computing techniques are successfully employed to deal with this problem, so that the encryption-decryption process is executed reasonably fast.