New vulnerability on system of Ni = p²iqi using good approximation of Φ(N)

This paper proposes new vulnerability in m moduli of the form Ni = p2iqi for m ≥ 2 and i = 1, ...,m. The attack works when m public keys (Ni, ei) there exist m relations of the form eid − kΦ (Ni) = 1 or eidi − kiΦ (Ni) = 1 with the parameters d, di, k and ki are suitably small. By using the term N − 2N2/3 − N1/3 as a good approximation of Φ(N) applying the LLL algorithm enables one to factor m moduli of the form Ni = p2iqi simultaneously