A Generalized Attack on Some Variants of the RSA Cryptosystem

Authors

Abderrahmane Nitaj, Universite de Caen
Yanbin Pan, Chinese Academy Of Sciences
Joseph Tonien, University of WollongongFollow

RIS ID

133083

Publication Details

Nitaj, A., Pan, Y. & Tonien, J. (2019). A Generalized Attack on Some Variants of the RSA Cryptosystem. Lecture Notes in Computer Science, 11349 421-433.

Abstract

Let N=pq be an RSA modulus with unknown factorization. The RSA cryptosystem can be attacked by using the key equation ed−k(p−1)(q−1)=1 . Similarly, some variants of RSA, such as RSA combined with singular elliptic curves, LUC and RSA with Gaussian primes can be attacked by using the key equation ed−k(p2−1)(q2−1)=1 . In this paper, we consider the more general equation eu−(p2−1)(q2−1)v=w and present a new attack that finds the prime factors p and q in the case that u, v and w satisfy some specific conditions. The attack is based on Coppersmith's technique and improves the former attacks.