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Cryptanalysis of RSA for a special case with d >e

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Abstract

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.

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Authors and Affiliations

  1. Tsinghua National Laboratory for Information Science and Technology (TNlist), Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Ping Luo, HaiJian Zhou, DaoShun Wang & YiQi Dai

Authors
  1. Ping Luo
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  2. HaiJian Zhou
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  3. DaoShun Wang
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  4. YiQi Dai
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Corresponding author

Correspondence to HaiJian Zhou.

Additional information

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

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Luo, P., Zhou, H., Wang, D. et al. Cryptanalysis of RSA for a special case with d >e . Sci. China Ser. F-Inf. Sci. 52, 609–616 (2009). https://doi.org/10.1007/s11432-009-0014-z

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  • DOI: https://doi.org/10.1007/s11432-009-0014-z

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