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.
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Funding
The research was supported by Mediterranea Universiti of Reggio Calabria (UNIRC) Research Grant (UPM/INSPEM/700-3/1/GERAN ANTARABA NGSA/6380071-10065). The present research was partially supported by the Putra Grant with Project Number GP-IPS/2018/9657300.
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Nitaj, A., Ariffin, M.R.K., Adenan, N.N.H. et al. Exponential increment of RSA attack range via lattice based cryptanalysis. Multimed Tools Appl 81, 36607–36622 (2022). https://doi.org/10.1007/s11042-021-11335-8
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DOI: https://doi.org/10.1007/s11042-021-11335-8