Cryptanalysis of short secret exponents modulo RSA primes

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this manuscript, one way to attack on the short secret exponent d q modulo a larger RSA prime q is presented. When dq < (2q3p)1/2 and e < (pq)1/2, dq can be discovered from the continued fraction of epq, where e and pq denote the public exponent and the modulus, correspondingly. Furthermore, the same way to attack on an unbalanced RSA is also discussed. According to cryptanalysis presented in this study, the unbalanced RSA will be resolved if dq < (23) 1/2q4/9.

Original languageEnglish
Pages (from-to)225-233
Number of pages9
JournalInformation sciences
Issue number1-4
StatePublished - 22 Mar 2004


  • Continued fraction method
  • Cryptography
  • RSA (Ron Rivest, Adi Shamir, and Len Adleman) system


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