New Attacks on the RSA Cryptosystem

Abderrahmane Nitaj (1) , Muhammad Rezal Kamel Ariffin (2) , Dieaa I Nassr (3) , Hatem M Bahig (3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Universiti Putra Malaysia
3 Faculty of Science [ASU]

This paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix − yiφ(Ni) = zi or of the shape eixi − yφ(Ni) = zi where Ni = piqi, φ(Ni) = (pi − 1)(qi − 1) and the parameters x, xi, y, yi, zi are suitably small in terms of the prime factors of the moduli. We show that our attacks enable us to simultaneously factor the k RSA moduli Ni. The third attack works when the prime factors p and q of the modulus N = pq share an amount of their least significant bits (LSBs) in the presence of two decryption exponents d1 and d2 sharing an amount of their most significant bits (MSBs). The three attacks improve the bounds of some former attacks that make RSA insecure.

Mots clés: RSA; Cryptanalysis; Factorization; LLL algorithm; Simultaneous diophantine approximations; Coppersmith's method

Domaines: Cryptographie et sécurité [cs.CR]

Abderrahmane Nitaj, Muhammad Rezal Kamel Ariffin, Dieaa I Nassr, Hatem M Bahig. New Attacks on the RSA Cryptosystem. in D. Pointcheval and D. Vergnaud (Eds.): AFRICACRYPT 2014, LNCS 8469, pp. 178–198, 2014. Springer 2014, 2014, Marrakesh, Morocco. ⟨hal-02330228⟩