New vulnerability of RSA modulus type N = p2q - Nek Abd Rahman, Normahirah; Kamel Ariffin, Muhammad Rezal (Institute for Mathematical Research, Universiti Putra Malaysia, 2017)
This paper proposes new attacks on modulus of type N = p2q. Given k moduli of the form Ni = p2iqi for k ≥ 2 and i = 1, …, k, the attack works when k public keys (Ni, ei) are such that there exist k relations of the shape eix – Niyi = zi – (ap2i + bq2i)yi or of the shape eixi – Niy = zi – (ap2i + bq2i)y where the parameters x, xi, y, yi and zi are suitably small in terms of the prime factors of the moduli. The proposed attacks utilizing the LLL algorithm enables one to factor the k moduli Ni simultaneously.