Several Typical Function Secret Sharing Schemes And Their Application Research

Function secret sharing(FSS)refers to the shared secret is a function instead of a value in the secret sharing.It is an extension of secret sharing.It has also become one of the important means of information security.It has a wide of applications in secure multi-party computation and electronic commerce,and other fields.This paper mainly research on point function secret sharing(PFSS),interval function secret sharing(IFSS)and comparison function secret sharing(CFSS)these three typical FSS schemes and their application.Because these three kinds of typical FSS schemes can well solve the privacy security problems of the private information retrieval(PIR),security electronic election,and so on,and And as far as we know,current very little on the study FSS.Therefore,further study of several kind of typical FSS scheme and its application is very meaningful.The main research results are as follows:(1)Focusing on the study of PFSS scheme and its application.First introduces that the Boyle et al.'s PFSS scheme.To solve the privacy problem of the PIR,this paper constructs a PIR protocol based on PFSS with the PFSS scheme.Because of the existing PFSS scheme can't proceed to add operation and no threshold,and in many applications of PFSS scheme need it can addition operation.Therefore,this paper presents two new PFSS schemes,and found that the second PFSS scheme better by the analysis,and was the first threshold PFSS scheme.Finally,To solve the privacy problem of the three application scenarios,this paper constructs a secure weighted electronic voting protocol,a security keywords retrieval protocol and a incremental secret sharing protocol based on PFSS with the second PFSS scheme,respectively.(2)Focusing on the study of CFSS scheme and its application.First introduces that the Boyle et al.'s PFSS scheme.And then,To solve the privacy problem of the two application scenarios,this paper constructs a security comparison keywords retrieval protocol and a incremental interval secret sharing protocol based on CFSS with the second PFSS scheme,respectively.(3)Focusing on the study of IFSS scheme and its application.As far as we know,there is no a IFSS scheme that has been proposed.Therefore,this paper puts forward a IFSS scheme for the first time.To solve the privacy problem of the secure interval keywords search,this paper constructs a secure interval keywords search protocol based on IFSS with the IFSS scheme.