Exponential increment of RSA attack range via lattice based cryptanalysis

• Main Authors: Nitaj, Abderahmanne, Ariffin, Muhammad Rezal Kamel, Adenan, Nurul Nur Hanisah, Ahmadian, Ali, Merenda, Domenica Stefania
• Format: Article
• Published: Springer 2021
• Online Access: http://psasir.upm.edu.my/id/eprint/97233/; https://link.springer.com/article/10.1007/s11042-021-11335-8?error=cookies_not_supported&code=81fcf9cb-c1e6-4b19-9ff3-ad3379d9d10b

The RSA cryptosystem comprises of two important features that are needed for encryption process known as the public parameter e and the modulus N. In 1999, a cryptanalysis on RSA which was described by Boneh and Durfee focused on the key equation and e of the same magnitude to N. Their method was applicable for the case of via Coppersmith’s technique. In 2012, Kumar et al. presented an improved Boneh-Durfee attack using the same equation which is valid for any e with arbitrary size. In this paper, we present an exponential increment of the two former attacks using the variant equation . The new attack breaks the RSA system when a and |c| are suitably small integers. Moreover, the new attack shows that the Boneh-Durfee attack and the attack of Kumar et al. can be derived using a single attack. We also showed that our bound manage to improve the bounds of Ariffin et al. and Bunder and Tonien.