New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method
Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research, Universiti Putra Malaysia, Selangor 43400, Malaysia
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor 43400, Malaysia
Centre of Foundation Studies for Agriculture Science, Universiti Putra Malaysia, Selangor 43400, Malaysia
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 1 November 2018 / Revised: 14 December 2018 / Accepted: 15 December 2018 / Published: 20 December 2018
This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus
in polynomial time. The paper has two parts. In the first part, we report the usage of the small prime difference method of the form
where the ratio of
is close to
, which yields a bound
from the convergents of the continued fraction expansion of
. The second part of the paper reports four cryptanalytic attacks on t
instances of RSA moduli
where we use
as an approximation of
satisfying generalized key equations of the shape
for unknown positive integers
, where we establish that t
RSA moduli can be simultaneously factored in polynomial time using combinations of simultaneous Diophantine approximations and lattice basis reduction methods. In all the reported attacks, we have found an improved short secret exponent bound, which is considered to be better than some bounds as reported in the literature.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Kamel Ariffin, M.R.; Abubakar, S.I.; Yunos, F.; Asbullah, M.A. New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method. Cryptography 2019, 3, 2.
Kamel Ariffin MR, Abubakar SI, Yunos F, Asbullah MA. New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method. Cryptography. 2019; 3(1):2.
Kamel Ariffin, Muhammad R.; Abubakar, Saidu I.; Yunos, Faridah; Asbullah, Muhammad A. 2019. "New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method." Cryptography 3, no. 1: 2.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.