Towards provably secure asymmetric image encryption schemes

• Published in: Information sciences 2023-06, Vol.631, p.164-184
• Main Authors: Azam, Naveed Ahmed, Zhu, Jianshen, Hayat, Umar, Shurbevski, Aleksandar
• Format: Article
• Language: English
• Subjects: Elliptic curves; Image encryption; Integer linear programming; Linear and differential cryptanalysis; S-box analysis
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2023.02.057

Image encryption schemes that use substitution box (S-box) generators, and dynamic S-boxes in particular, have attracted wide research interest recently. Typically, the security of S-box generators is tested empirically, and thus encryption schemes that use them do not have provable security against linear and differential attacks. With this work, we propose an asymmetric image encryption scheme with an S-box generator that has provable security against linear attacks, which is an important first step toward developing such schemes. Our generator is based on an integer linear programming (ILP) formulation that is feasible if and only if there exists an S-box with a given level of nonlinearity. We design a pseudo random number generator based on elliptic curves (ECs) which is used in our scheme to create confusion and diffusion in the cipher-images. Our scheme is highly sensitive to the keys and the plain-images, and hence it offers high security against differential attacks. Furthermore, our scheme allows users to use any size of random numbers and ECs, which makes it more flexible than existing schemes. Finally, we confirm through computational experiments that compared to existing state-of-the-art schemes, our scheme has superior cryptographic properties with low computational complexity, and hence is a good candidate for application in real-time systems.