Substitution box generator with enhanced cryptographic properties and minimal computation time

Abstract

With the widespread use of digital devices and the internet, implementing advanced security systems is essential to protect confidential information from cyberattacks and unauthorized access. The substitution box (S-box) is an integral part of security systems that confuses confidential data. Randomized or optimized S-box generators are commonly used in these systems. The former aims to generate highly key-dependent dynamical S-boxes, while the latter generates static S-boxes with optimal cryptographic properties. However, the process of generating S-boxes is computationally expensive, which limits the attainable encryption throughput. This highlights the need to develop new S-box generators that can offer optimal security with minimal computational overhead. We utilized the high resistance of elliptic curves against modern cryptanalysis to propose a novel S-box generator capable of generating both randomized and optimized S-boxes in minimal computation time. The proposed generator has three phases. In the first phase, it generates points on an elliptic curve, converts their coordinates into binary form, and merges them. The second phase diffuses the binary sequences to calculate indices for swapping operations. In the final phase, swapping operations are applied to the initial S-box, resulting in a randomized S-box. For optimizing the S-box, a simplified version of the generator is introduced by omitting swapping operations that reduce nonlinearity in the resulting S-box. The dynamic behavior of the proposed generator is analyzed by proving necessary conditions for outputting distinct S-boxes and ensuring that the resultant S-boxes have a uniform probability distribution. Rigorous security analysis reveals that our generator can output S-boxes with strong cryptographic properties. A detailed comparison indicates that our method is at least 10 times faster than the fastest available randomized generator, while maintaining comparable cryptographic properties. Furthermore, the proposed generator achieves higher nonlinearity of 108 compared to the best available optimized S-box generator with minimal computation time. Our theoretical and computational analyses suggest that our S-box generator is a promising candidate for practical applications that can effectively address the modern security threats and computational time demands. Specifically, we demonstrate the application of our S-box generator by integrating it into an image encryption scheme.