International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 18 July 2014

Abderrahmane Nitaj, Muhammad Rezal Kamel Ariffin, Dieaa I. Nassr, and Hatem M. Bahig
ePrint Report ePrint Report
This paper presents three new attacks on the RSA cryptosystem.

The rst two attacks work when k RSA public keys (Ni, ei)

are such that there exist k relations of the shape eix-yi\\phi(Ni)=zi or of the shape eixi-y\\phi(Ni)=zi where Ni = piqi, \\phi(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 signicant bits (LSBs) in the presence of two decryption exponents

d1 and d2 sharing an amount of their most signicant bits (MSBs). The

three attacks improve the bounds of some former attacks that make RSA

insecure.

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