Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6875770 | Theoretical Computer Science | 2017 | 8 Pages |
Abstract
Let N=pq be an RSA modulus with unknown factorization. Some variants of the RSA cryptosystem, such as LUC, RSA with Gaussian primes and RSA type schemes based on singular elliptic curves use a public key e and a private key d satisfying an equation of the form edâk(p2â1)(q2â1)=1. In this paper, we consider the general equation exâ(p2â1)(q2â1)y=z and present a new attack that finds the prime factors p and q in the case that x, y and z satisfy a specific condition. The attack combines the continued fraction algorithm and Coppersmith's technique and can be seen as a generalization of the attacks of Wiener and Blömer-May on RSA.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Martin Bunder, Abderrahmane Nitaj, Willy Susilo, Joseph Tonien,