Cryptology ePrint Archive: Report 2021/1160

Classical Attacks on a Variant of the RSA Cryptosystem

Abderrahmane Nitaj and Muhammad Rezal Kamel Ariffin and Nurul Nur Hanisah Adenan and Nur Azman Abu

Abstract: Let N = pq be an RSA modulus with balanced prime factors. In 2018, Murru and Saettone presented a variant of the RSA cryptosystem based on a cubic Pell equation in which the public key (N, e) and the private key (N, d) satisfy ed \equiv 1 mod (p^2+p+1)(q^2+q+1)). They claimed that the classical small private attacks on RSA such as Wiener's continued fraction attack do not apply to their scheme. In this paper, we show that, on the contrary, Wiener's method as well as the small inverse problem technique of Boneh and Durfee can be applied to attack their scheme. More precisely, we show that the proposed variant of RSA can be broken if d < N^{0:5694}. This shows that their scheme is in reality more vulnerable than RSA, where the bound of vulnerability is d < N^{0.292}.

Category / Keywords: public-key cryptography / RSA, Factorization, Continued fractions, Small inverse problem, Coppersmith's method

Date: received 10 Sep 2021

Contact author: rezal at upm edu my

Available format(s): PDF | BibTeX Citation

Version: 20210914:175332 (All versions of this report)

Short URL:

[ Cryptology ePrint archive ]