A novel deterministic substitution box generator over elliptic curves for real-time applications

Abstract

Recently, highly dynamic substitution box (S-box) generators are widely used in cryptosystems to improve the security against modern computational attacks. However, generating S-boxes is computationally costly, and frequently generating them slows down the encryption process and hence limits the encryption throughput. This fact necessitates developing new S-box generators that can provide optimal security with minimum computation cost. We propose a novel S-box generator based on a deterministic algorithm over elliptic curves to generate highly dynamic and secure S-boxes with low computation cost. Experimental results show that our generator is i times, i∈[6.720,1.3×105] faster than the fastest available S-box generator to generate S-boxes of an input size 2m,m=4,6,8,10,12,14,16 over large ECs. This fact allows us to attain significantly higher throughput as compared to the state-of-the-art schemes. Furthermore, our generator can generate highly dynamic, key-sensitive, and cryptographically secure S-boxes. As a sample application, we used our generator in an image encryption scheme. Experimental results reveal that our encryption scheme has high resistance against differential and statistical attacks, and key attacks. Furthermore, with the new S-box generator, the running time of the modified scheme reduced by two orders of magnitude.

Keywords

• Elliptic curve
• Group law
• Substitution box
• Image encryption