Cryptanalysis of multi-prime Φ -hiding assumption

In Crypto 2010, Kiltz, O’Neill and Smith used m -prime RSA modulus N with m ≥ 3 for constructing lossy RSA. The security of the proposal is based on the Multi-Prime Φ -Hiding Assumption. In this paper, we propose a heuristic algorithm based on the Herrmann-May lat- tice method (Asiacrypt 2008) to solve the Multi-Prime Φ -Hiding Problem when prime e > N2/3M. Further, by combining with mixed lattice tech- niques, we give an improved heuristic algorithm to solve this problem when prime e > N2/3M-1/4m2. These two results are verified by our experiments. Our bounds are better than the existing works.