Cryptanalysis of RSA for a special case with d>e  

作　　者：LUO Ping ZHOU HaiJian WANG DaoShun DAI YiQi 

机构地区：[1]Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology,Tsinghua University, Beijing 100084, China

出　　处：《Science in China(Series F)》2009年第4期609-616,共8页中国科学（F辑英文版）

基　　金：Supported partially by the National Basic Research Program of China (Grant No. 2003CB314805);the National Natural Science Foundationof China (Grant Nos. 90304014 and 60873249);the Project funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua

摘　　要：In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.

关 键 词：RSA CRYPTANALYSIS lattice basis reduction LLL algorithm 

分 类 号：TN918.2[电子电信—通信与信息系统] O156[电子电信—信息与通信工程]