Welcome to the resource topic for 2021/1630
Title:
Exponential Increment of RSA Attack Range via Lattice Based Cryptanalysis
Authors: Abderahmanne Nitaj, Muhammad Rezal Kamel Ariffin, Nurul Nur Hanisah Adenan, Domenica Stefania Merenda, Ali Ahmadian
Abstract: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 ed-k\phi(N)=1 and e of the same magnitude to N. Their method was applicable for the case of d<N^{0.292} 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 ea-\phi(N)b=c. 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.
ePrint: https://eprint.iacr.org/2021/1630
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