A dynamic S-box algorithm based on special supersingular elliptic curve

Abstract

Recent research on substitution boxes (S-boxes) has highlighted the need for improved security and efficiency in cryptographic algorithms. This article addresses the limitations of existing S-box generation methods based on elliptic curves (ECs), which often suffer from inadequate computational efficiency and security vulnerabilities. We present a novel S-box algorithm developed from a special singular EC that overcomes these limitations. The algorithm consists of two main components: first, identifying limitations, and second, mitigating these limitations and creating a secure S-box by introducing novel models within a special supersingular EC framework. The S-box is then generated as a complementary element. We conducted comprehensive metric evaluations to assess the efficacy of the newly devised S-box. The proposed S-box has a generation time of 0.00015 s and shows ideal values regarding NL, LAP, DAP, BIC, and SAC. Additionally, our proposed S-box does not have fixed points or singularities, maintains a linear structure, and has a comparable computational complexity of $O\left(p^2\right)$. Therefore, our proposed work is suitable for real-world applications.