Parallelized Common Factor Attack on RSA

In this paper, we present a parallel approach to common factor attack on RSA moduli obtained by mining TLS and SSH certificates from the Internet. Our work generalizes that of Heninger et al. (2012) for a resource constrained environment, where the memory may not be sufficient to create the product tree required for batch-wise GCD computation on the entire dataset. We propose a data-parallel routine to efficiently exploit the batch-wise GCD algorithm in a resource constrained setting, and mount the common factor attack on TLS and SSH certificates to obtain the set of vulnerable RSA moduli with reasonable accuracy.