Paper 2025/1282

A Novel Partial Key Exposure Attack on Common Prime RSA

Abstract

We propose a novel partial key exposure attack on common prime RSA by leveraging lattice-based techniques. In common prime RSA, the primes $p$ and $q$ are defined as $p=2ga+1$ and $q=2gb+1$ for a common prime $g$. Recently, Zheng introduced the first partial key exposure attack on this scheme; however, it is limited to instances where $g > N^{1/4}$. In contrast, our work investigates deeper into partial key exposure attacks by presenting a unified generic case that targets one consecutive unknown block of the private key. By employing a lattice-based solving strategy for trivariate integer polynomials, we can effectively identify additional weak private keys that are vulnerable to partial exposure. Extensive numerical experiments validate the correctness and practicality of our proposed attack on common prime RSA.