Cryptanalysis Of The Rsa Variant Based On Cubic Pell Equation

RSA (Rivest-Shamir-Adleman) cryptosystem is the most popular asymmetric key cryptographic algorithm used in computer science and information security. Recently, an RSA-like cryptosystem was proposed using a novel product that arises from a cubic field connected to the cubic Pell equation. The relevant key equationis ed = 1 mod(p(2)+ p+ 1)(q(2)+ q+ 1) with N = pq. This RSA variant is claimed to be robust against the Wiener's attack and hence the bit-size of the private key could be shorter, namely d < N-1/4. In this paper, we explore the further security analysis and investigate the potential small private exponent attack. We show that such RSA variant is particularly vulnerable to the lattice-based method. To be specific, we can carry out the lattice-based small private exponent attack if d < N2-root 2 , which is less secure than the standard RSA. Furthermore, we conduct numerical experiments to verify the validity of the proposed attack. (C) 2021 Elsevier B.V. All rights reserved.