September 18, 2021

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Classical Attacks on a Variant of the RSA Cryptosystem, by Abderrahmane Nitaj and Muhammad Rezal Kamel Ariffin and Nurul Nur Hanisah Adenan and Nur Azman Abu

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