A generalized attack on RSA type cryptosystems

Martin Bunder , Abderrahmane Nitaj (1) , Willy Susilo (2) , Joseph Tonien (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 University of Wollongong [Australia]

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 ed − k (p^2 − 1)(q^2 − 1) = 1. In this paper, we consider the general equation ex − (p^2 − 1)(q^2 − 1) 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.

Domains: Computer Science [cs]; Cryptography and Security [cs.CR]

Martin Bunder, Abderrahmane Nitaj, Willy Susilo, Joseph Tonien. A generalized attack on RSA type cryptosystems. Theoretical Computer Science, 2017, ⟨10.1016/j.tcs.2017.09.009⟩. ⟨hal-02320917⟩