Efficient Lossy Trapdoor Functions Based on Subgroup Membership Assumptions

摘要

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 Z_(N~2)~*, the extended p-subgroup assumption over Z_(N~2)~* , and the decisional RSA subgroup membership assumption over Z_N~*. Our constructions are more efficient than the previous construction from the DCR assumption over Z_(N~s)~*(s ≥ 3).