Implicit Related-Key Factorization Problem on the RSA Cryptosystem

Abstract

In this paper, we address the implicit related-key factorization problem on the RSA cryptosystem. Informally, we investigate under what condition it is possible to efficiently factor RSA moduli in polynomial time given the implicit information of related private keys. We propose lattice-based attacks using Coppersmith’s techniques. We first analyze the special case given two RSA instances with known amounts of shared most significant bits (MSBs) and least significant bits (LSBs) of unknown related private keys. Subsequently a generic attack is proposed using a heuristic lattice construction when given more RSA instances. Furthermore, we conduct numerical experiments to verify the validity of the proposed attacks.