Lossy projective hashing and its applications

Abstract

In this paper, we introduce a primitive called lossy projective hashing. It is unknown before whether smooth projective hashing (Cramer-Shoup, Eurocrypt’02) can be constructed from dual projective hashing (Wee, Eurocrypt’12). The lossy projective hashing builds a bridge between dual projective hashing and smooth projective hashing. We give instantiations of lossy projective hashing from DDH, DCR, QR and general subgroup membership assumptions (including 2k-th residue, p-subgroup and higher residue assumptions). We also show how to construct lossy encryption and fully IND secure deterministic public key encryption from lossy projective hashing. – We give a construction of lossy projective hashing via dual projective hashing. We prove that lossy projective hashing can be converted to smooth projective hashing via pairwise independent hash functions, which in turn yields smooth projective hashing from dual projective hashing. – We propose a direct construction of lossy encryption via lossy projective hashing.Our construction is different from that given by Hemenway et al. (Eurocrypt 2011) via smooth projective hashing. In addition, we give a fully IND secure deterministic public key encryption via lossy projective hashing and one round UCE secure hash functions recently introduced by Bellare et al. (Crypto 2013).