Abstract: The notion of hash proof system was first proposed by Cramer and Shoup in Eurocrypt 2002. Inhere arc lots of research results about hash proof system since the notion was proposed, nowadays, some revisited versions were pre- sented. "Projective" and "smoothness" are two important prosperities of hash proof system It is found that hash proof system is used several contexts except used as a means to build efficient chosen-ciphertext secure publi}kcy encryption schemes, such as password-based authenticated key exchange, oblivious transfer, deniable authentication, zero-knowledge proof, commitment, ctc. We addressed the definitions of hash proof system, analyzed the derivation relations and security level among variations,and discussed the applications of hash proof system in cryptography.

Key words: Hash proof system, Subset member problem, CCA secure, Key exchange, OT protocol, Deniable authentica tion protocol,Zero-knowledge proof protocol,Commitment protocol