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On an attack on RSA with small CRT-exponents

science China(Information sciences) 2010年第8期53卷 1511-1518页

作者： HAN LiDong 1,2 , WANG XiaoYun 3 & XU GuangWu 3,4 1 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong university, Jinan 250100, China 2 School of Mathematics, Shandong university, Jinan 250100, China 3 Institute for Advanced Study, Tsinghua university, Beijing 100084, China 4 department of electrical engineering and computer science, university of wisconsin-milwaukee, milwaukee, wi 53201, usa 1. Key Laboratory of Cryptologic Technology and Information Security Ministry of Education Shandong University Jinan 250100 China2. School of Mathematics Shandong University Jinan 250100 China3. Institute for Advanced Study Tsinghua University Beijing 100084 China4. Department of Electrical Engineering and Computer Science University of Wisconsin-Milwaukee Milwaukee WI 53201 USA

This paper concerns the RSA system with private CRT-exponents. Since Chinese remainder representation provides efficiency in computation, such system is of some practical significance. In this paper, an existing attack to small private CRT-exponents is analyzed. It is indicated that this attack makes nice use of lattice in RSA analysis, but some argument does not hold in general. Several counterexamples are constructed. Refinements and more precise statements of the attack are given.

关键词： RSA CRT cryptanalysis continued fraction lattice reduction

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Generalization of Some Attacks on RSA with Small Prime Combination and Small Private Exponent

Generalization of Some Attacks on RSA with Small Prime Combi...

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2009 Asia-Pacific Conference on Information Processing

作者： Lidong Han Guangwu Xu Key Lab of Cryptographic Technology and Information Security Ministry of Education Shandong university Jinan 250100 China department of electrical engineering and computer science university of wisconsin-milwaukee milwaukee 53201-0784 usa

In 2002,de Weger proposed an attack on small RSA secret decryption exponent with small prime difference |p q|,which improved the insecure private key bound of wiener and Boneh-Durfee ***,Maitra and Sarkar found new weak keys in another case when 2q p is *** this paper,several results on attacking RSA with small prime differences q p,2p q and small private exponent are *** observation is that when |ip jq| is small for some integers i,j,we can explore new insecure keys in *** of our results also makes some statement in literature more accurate.

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