Efficient Lossy Trapdoor Functions Based on Subgroup Membership Assumptions

We propose a generic construction of lossy trapdoor function from the subgroup membership assumption. We present three concrete constructions based on the k-DCR assumption over , the extended p-subgroup assumption over , and the decisional RSA subgroup membership assumption over . Our constructions are more efficient than the previous construction from the DCR assumption over (s ≤ 3).