The Research On Bounds For FP Code

Frameproof codes were first introduced by Boneh and Shaw, In order to protect copyrighted material, FP codes were designed to prevent a small of coalition of legitimate users from constructing a copy of fingeprint of another user. Since an (N, n,q) ω-FP code exists if and only if an SHF(N;n,q,{1,ω}) exists, We will give the bounds for (N,n,q),q<ω ω -FP code in terms of separating hash families. By the knowledge of matrix and coding theory, we generalized the bound that Chuan Guo et al got for binary ω-FP codes, where parameter N, ω were positive integers such that ω+1< N< 3ω,ω> 3. This paper generalized the result on parameter N and parameter q respectively. This paper consists of the following three parts:In the first chapter, a survey of digital fingerprint code and the concepts of FP codes and separating hash family are introduced, the matrix representation of an SHF(N; n, q,{1, ω}) is given, some notations and main result are also given.In the second chapter, we mainly study the bound for (ω+1,n,3)ω-FP code. The sufficient and necessary condition for the existence of an (ω,n,q) ω-FP code is given. Based on the result, we get the bound for (ω+1, n,3)ω-FP code, where ω is a positive integer such that ω≥ 4.In the third chapter, we mainly study the bound for (3ω+1, n,2)ω-FP code. First of all, we give the sufficient and necessary condition for the existence of an binary ω-FP codes, where parameter N, ω were positive integers such that ω+1≤N<≤3ω,ω> 3. Second, We give the upper bound and lower bound for (3ω+1, n,2)ω-FP code, the difference between the two bounds is 2. At last, we give the bound for (3ω+2,n,2)ω-FP code.