Cryptanalysis of a cubic Pell variant of RSA with primes sharing least significant bits

Nitaj, Abderrahmane and Kamel Ariffin, Muhammad Rezal and Abu, Nur Azman and Adenan, Nurul Nur Hanisah (2024) Cryptanalysis of a cubic Pell variant of RSA with primes sharing least significant bits. Journal of Information & Optimization Sciences, 45 (5). pp. 1263-1280. ISSN 2169-0103

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Abstract

In this paper, we push further the cryptanalysis of a cryptosystem of the RSA’s variant which utilized a cubic Pell equation with the key equation ed − k(p2 + p + 1)(q2 + q + 1) = 1 where N = pq is an RSA modulus, e, N are publicized, while d, p, q are kept private. We consider the case where the prime factors share an amount of their least significant bits (LSBs), that is p and q satisfy p – q = 2m u where m is known, and u is unknown. Through this work, we show that via Coppermith’s method and lattice basis reduction, it is feasible to retrieve the secret key d and factor N for larger values of d.

Item Type:	Article
Uncontrolled Keywords:	RSA, Factorization, Coppersmith’s method, Lattice basis reduction, Cubic Pell equation
Divisions:	Faculty of Information and Communication Technology
Depositing User:	Sabariah Ismail
Date Deposited:	30 Dec 2025 07:19
Last Modified:	30 Dec 2025 07:19
URI:	http://eprints.utem.edu.my/id/eprint/29228
Statistic Details:	View Download Statistic

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