Abstract: A novel four-dimensional discrete-time chaotic system was constructed on the basis of a modified version of Marotto’s theorem.On the basis of this system,a digital image encryption scheme was proposed,in which the 256-bit hash value of plain image is used to generate the initial value of the chaotic sequence.Therefore,the encryption key ge-nerated by the chaotic sequence is related with plain image to enhance the security of the encryption system.Theoretical analysis and simulation experiments show that the key space of the image encryption scheme is as large as 3.4×10¹⁰⁰.The histogram of the encrypted image is close to the uniform distribution.The correlation of pixels is eliminated.The information entropy of encrypted image is close to 8 bit and the encrypted image has no obvious statistical information.The scheme is extremely sensitive to perturbations of the initial conditions of the chaos system.Any perturbations which are larger than 10－15 will make corresponding decryptions impossible.The encrypted image is also very sensitive to the plain image and can resist differential attack.

Key words: Chaos,Image encryption,Marotto’s theorem,SHA-256 hash function,Bitwise XOR operation,Circular shifting operation