Limitation Exploration and Optimization Verification of RSA Encryption: using Digital Signature as an example

Abstract

This dissertation investigates the limitations of RSA encryption and evaluates optimization schemes using digital signatures as the main application example. RSA remains a core asymmetric cryptographic algorithm, but its practical use is constrained by computational cost, key-management complexity, and possible attacks on weak parameter choices. The study combines a literature review of traditional RSA, multi-prime RSA, replaced-modulus RSA, and multi-exponent RSA with a controlled Python experiment. Four algorithms were implemented under the same hardware and software environment, and ten trials were conducted for each algorithm across five stages: key generation, encryption, decryption, signing, and verification. A total of 200 timing data points were analyzed using normalized execution time, acceleration ratios, standard deviation, and box plots. The results show that theoretical optimization does not always translate into practical acceleration. Multi-prime RSA performed worse than the basic algorithm in all stages, with key generation 5.39 times slower and high variability. Replaced-modulus RSA remained close to the baseline while offering potential security advantages, and multi-exponent RSA produced slight improvements in key generation, encryption, and decryption with stable performance. The study concludes that RSA optimization should be evaluated through both security reasoning and empirical performance testing, especially when applied to digital signature systems.