Cryptanalysis of large RSA exponent by using the LLL algorithm

Chien Yuan Chen, Cheng-Yuan Ku*, David C. Yen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The study of paper "Cryptanalysis of RSA with Private Key d less than N0.292' [IEEE Trans. Information Theory, 46 (2000) 1339], which Boneh and Durfee published in IEEE Transactions on Information Theory in July 2000, supported that when d < N0.292, the RSA system can be cracked by using the LLL algorithm. In this paper, we find ways to utilize the LLL algorithm to break the RSA system even when the value of d is large. According to the proposed cryptanalysis, if d satisfies |λ - d| < N 0.25, the RSA system will be possible to be resolved computationally.

Original languageEnglish
Pages (from-to)516-525
Number of pages10
JournalApplied Mathematics and Computation
Issue number1
StatePublished - 1 Oct 2005


  • Cryptanalysis
  • LLL algorithm
  • Public key encryption
  • RSA exponent
  • RSA system


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