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.
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Kong, F., Yu, J., Qin, B., Li, D. (2007). Cryptanalysis of Server-Aided RSA Key Generation Protocols at MADNES 2005. In: Xiao, B., Yang, L.T., Ma, J., Muller-Schloer, C., Hua, Y. (eds) Autonomic and Trusted Computing. ATC 2007. Lecture Notes in Computer Science, vol 4610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73547-2_8
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DOI: https://doi.org/10.1007/978-3-540-73547-2_8
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