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Cryptanalysis of Server-Aided RSA Key Generation Protocols at MADNES 2005

  • Fanyu Kong
  • Jia Yu
  • Baodong Qin
  • Daxing Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4610)

Abstract

At MADNES 2005, Y. Chen et al. proposed two improved server-aided RSA key generation protocols, which are claimed to be secure against collusion attack. However, at ISPEC 2006, T. Cao et al. presented a collusion attack on Chen’s standard server-aided RSA key generation protocol and can get the plaintext from a ciphertext. In this paper, we propose a full cryptanalysis of Chen’s two server-aided RSA key generation protocols. Firstly, we give a further analysis of Chen’s standard protocol and can recover the factorization of the RSA modulus N with the complexity O(log3(N)). Secondly, we propose two collusion attacks on Chen’s unbalanced RSA key generation protocol. It is proved that we can decrypt any ciphertext with the complexity O(log3(N)) and find the secret prime p with the complexity O(log4(N)). Therefore, neither of Chen’s two server-aided RSA key generation protocols can resist collusion attack.

Keywords

Smart Card Euclidean Algorithm Modular Exponentiation Collusion Attack Extended Euclidean Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Fanyu Kong
    • 1
    • 2
  • Jia Yu
    • 3
  • Baodong Qin
    • 1
    • 2
  • Daxing Li
    • 1
    • 2
  1. 1.Institute of Network Security, Shandong University, 27 Shanda Nanlu Road, Jinan 250100China
  2. 2.Key Laboratory of Cryptographic Technology and Information Security, Ministry of Education, Jinan 250100China
  3. 3.College of Information Engineering, Qingdao University, Qingdao 266071China

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