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Title:
Generalized Cryptanalysis of Cubic Pell RSA
Authors: Hao Kang, Mengce Zheng
Abstract:The RSA (Rivest-Shamir-Adleman) cryptosystem is a fundamental algorithm of public key cryptography and is widely used across various information domains. For an RSA modulus represented as N = pq, with its factorization remaining unknown, security vulnerabilities arise when attackers exploit the key equation ed-k(p-1)(q-1)=1. To enhance the security, Murru and Saettone introduced cubic Pell RSA — a variant of RSA based on the cubic Pell equation, where the key equation becomes ed-k(p^2+p+1)(q^2+q+1)=1. In this paper, we further investigate the security implications surrounding the generalized key equation eu-(p^2+p+1)(q^2+q+1)v=w. We present a novel attack strategy aimed at recovering the prime factors p and q under specific conditions satisfied by u, v, and w. Our generalized attack employs lattice-based Coppersmith’s techniques and extends several previous attack scenarios, thus deepening the understanding of mathematical cryptanalysis.
ePrint: https://eprint.iacr.org/2024/2081
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