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Security Analysis of an RSA Key Generation Algorithm with a Large Private Key

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Information Security (ISC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7001))

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Abstract

In 2003, L. H. Encinas, J. M. Masqué and A. Q. Dios proposed an algorithm for generating the RSA modulus N with a large private key d, which was claimed secure. In this paper, we propose an attack on Encinas-Masqué-Dios algorithm and find its security flaw. Firstly, we prove that Encinas-Masqué-Dios algorithm is totally insecure when the public exponent e is larger than the sum of the two primes p and q. Secondly, we show that when e is larger than \(N^{\frac{1}{4}}\), Encinas-Masqué-Dios algorithm leaks sufficient secret information and then everyone can recover the factorization of the RSA modulus N in polynomial time.

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Author information

Authors and Affiliations

  1. Institute of Network Security, Shandong University, Jinan, 250100, China

    Fanyu Kong

  2. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Jinan, 250100, China

    Fanyu Kong

  3. College of Information Engineering, Qingdao University, Qingdao, 266071, China

    Jia Yu

  4. School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

    Lei Wu

Authors
  1. Fanyu Kong
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  2. Jia Yu
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  3. Lei Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, 200240, Min Hang Shanghai, China

    Xuejia Lai

  2. Cryptography and Security Department, Institute for Infocomm Research, Singapore

    Jianying Zhou

  3. Key Laboratory of Computer Networks and Information, Security Xidian University, 2 South Taibai Road, Xi’an, 710071, Shaanxi, China

    Hui Li

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© 2011 Springer-Verlag Berlin Heidelberg

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Kong, F., Yu, J., Wu, L. (2011). Security Analysis of an RSA Key Generation Algorithm with a Large Private Key. In: Lai, X., Zhou, J., Li, H. (eds) Information Security. ISC 2011. Lecture Notes in Computer Science, vol 7001. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24861-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-24861-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24860-3

  • Online ISBN: 978-3-642-24861-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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