Digital image encryption scheme based on generalized Mandelbrot-Julia set

Abstract With the rapid development of quantum computer, the encryption schemes in low key space are facing a huge security threat. The chaotic-based image encryption schemes use the initial values of the systems as the key, so the key spaces are often unchanged, which provide a way for the cracker to perform an exhaustive attack. This paper proposes an image encryption scheme based on generalized Mandelbrot-Julia (M-J) set. The key space of the scheme is not only large, but also dynamically changeable. To verify the feasibility of the generalized M-J set in the encryption scheme we use the simplest two rounds XOR encryption algorithm. We get the key by using environmental noise and SHA-512. The use of one-time keys not only improves the security of the algorithm, but also weakens the difficulty of transmitting many secret keys. Simulation results show that the key space of the our scheme can reach to 23250, which is far more than the most schemes. In order to verify the security of the encryption scheme, we have made corresponding security analysis for many attack methods. The results show that all the performance indexes satisfy the image encryption secure performance test standards. Finally, we tested the randomness of the generalized M-J set using the NIST randomness test software. Various analyses show that the encryption scheme is safe, and the generalized M-J set is an excellent system that can be applied in cryptography.