Remarks on the bounds for cryptanalysis of low private key RSA

被引:0
|
作者
Zhou, Haijian [1 ]
Luo, Ping [2 ]
Wang, Daoshun [1 ]
Dai, Yiqi [1 ]
机构
[1] Tsinghua Univ, Dept Comp Sci & Technol, Beijing 100084, Peoples R China
[2] Tsinghua Univ, Sch Software, Beijing 100084, Peoples R China
关键词
RSA; Cryptanalysis; Low private key; Lattice basis reduction; EXPONENTS; ATTACKS; LLL;
D O I
10.1016/j.pnsc.2008.09.013
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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.
引用
收藏
页码:1327 / 1331
页数:5
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