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.
- Continued fraction method
- RSA (Ron Rivest, Adi Shamir, and Len Adleman) system