Revisiting Small Private Key Attacks on Common Prime RSA

This paper revisits small private key attacks on common prime RSA, with a focus on critically analyzing the most recent Mumtaz-Luo’s attack and rectifying its flaws. Through a detailed examination of relevant parameters while solving a specific trivariate integer polynomial equation, we present a refined and enhanced small private key attack. Extensive numerical computer experiments validate the proposed method, confirming its accuracy and efficiency. Additionally, our simulated attacks successfully break common prime RSA instances that employ small private keys, enabling the rapid factorization of a given modulus. Our work not only corrects significant shortcomings in previous cryptanalysis but also offers a synthesized attack illustration of small private key attacks on common prime RSA. Moreover, the findings emphasize the importance of robust parameter selection in cryptographic implementations.