Efficient key-dependent dynamic S-boxes based on permutated elliptic curves

Abstract

Key-dependent dynamic substitution boxes (S-boxes) are important building blocks of many image encryption schemes, in which a session key controls the construction of dynamic S-boxes. Frequently changing the dynamic S-boxes is necessary to improve security. However, the computational overhead of dynamic S-box construction limits the achievable encryption throughput. Therefore, minimizing the construction time of dynamic S-boxes is required. In this paper, we exploit key-dependent permutations over finite elliptic curves to present a novel computationally efficient method for dynamic S-box construction. Theoretical analysis shows that the proposed S-box construction method is immune to chosen-plaintext attacks. Analysis of an image encryption application using the proposed key-dependent S-box indicates resistance to statistical, related key, and chosen-plaintext attacks. Experimental results show that the proposed method is asymptotically an order-of-magnitude faster than relevant methods. A dynamic S-box with 512-bit key can be generated by the proposed method in 0.76 ms, paving the way to reach 1 GB/s encryption throughput. Results show that the generated S-boxes satisfy the standard S-box security criteria and have a competitive nonlinearity distribution compared with rival methods.