Generalized implicit-key attacks on RSA

Abstract

RSA (Rivest–Shamir–Adleman) is a fundamental algorithm in information security for public key cryptography. Recently, a novel attack scenario of RSA with two implicitly correlated private keys, i.e., implicit-key attack was formulated. The lattice-based cryptanalytic strategy was proposed to factor RSA moduli using given implicit hints referring to known quantities of unknown common bits distributed among unknown private keys. In this paper, we review the simple basic scenario in which two RSA instances share known amounts of MSBs (most significant bits) and LSBs (least significant bits). We extend it to a more complex situation, where the amounts of MSBs and LSBs shared along with a few common blocks of middle bits are known. In addition, based on the above theoretical analyses, we present a generalized implicit-key attack framework. Our results disclose the vulnerability of RSA using correlated private keys with implicit information. Furthermore, numerical computer experiments are conducted to assess the validity of basic and extended implicit-key attacks.