Construct And Generalize On The Small Parameter Separate Hash Families

Hash function is an essential aspect of cryptography.which plays an important role in insuring the security of information. The construction of Hash families is mainly studied in this paper. The results of the research are given as follows:In the first chapter, separating hash families theory is chiefly introduced.Detailed analysis of the development is carried out，and some concepts are given.In the second chapter, the construction of the Hash function with small parameter is analyzed. Based on the previous results.we have accomplished the constructions of6-SHF,and then,the necessary conditions for the existence of6-SHF are given.Finally.the sufficient and necessary condition of{1,ω}-SHF is given.In the third chapter, the generalized SHF is studied. First,we use the use the algorithm of graph theory to study the matrix of SHF,and then use group divisible design and difference matrix to study SHF.Finally.a method for constructing a new SHF by using two SHF is given.Finally, this paper is summarized,and the open problem is given.