Remarks on the bounds for cryptanalysis of low private key RSA

Boneh and Durfee have developed a cryptanalytic algorithm on low private key RSA. The algorithm is based on lattice basis reduction and breaks RSA with private key d < N-0.292. Later on, an improved version by Blomer and May enhanced the efficiency, while reaching approximately this same upper bound. Unfortunately, in both the algorithms, there is a critical error in theoretical analysis, leading to the overestimated upper bound N-0.292. In this paper we present a more precise analytical model, with which the theoretical upper bound on d is modified to approximately d < N-0.277 for ordinary RSA systems with a 1024-bit public key (N,e). (C) 2009 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.