MMSC-RSA: Miller-Rabin, Montgomery, Sliding Window, and Shamir’s Chinese Remainder Theorem Optimization-based RSA

RSA is still a popular way to encrypt data asymmetrically, although it has performance problems in applications with limited resources. In this paper, we propose an improved version called MMSC-RSA that uses Miller-Rabin, Montgomery multiplication, sliding-window exponentiation, and Shamir's CRT-based modifications to remedy the issue. This better version of RSA is substantially faster and still works on existing infrastructure. Our MMSC-RSA generates keys using segmented sieving and Miller-Rabin testing methods. This feature improves the key generation performance of our MMSC-RSA cryptosystem by 79% for 4096-bit keys. During encryption, when compared to normal RSA and HRM-RSA at 3072-bit lengths, Montgomery multiplication and sliding-window approaches used by MMSC-RSA lower latency by 62.2% and 31.3%, respectively. Our MMSC-RSA efficiency increases from 74.8% up to 85.9% compared to a 4096-bit key RSA and SNA-RSA, attributable to CRT parallelism and Shamir's optimization techniques in decryption. Our MMSC-RSA cryptosystem is basically engineered based on the core functional strengths of conventional RSA, like prime number security, modular exponentiation, and factorization difficulty. We proposed MMSC-RSA for scalability, making it suitable for extensive systems like IoT and blockchain. It also establishes a basis for future integration with systolic hardware or hybrid post-quantum models to enhance protection against quantum threats. The source code is accessible to the public at the Zenodo Repository, facilitating repeatability and additional research.