The Optimal Linear Secret Sharing Scheme For Non-Threshold Access Structure

At present, the research on group cryptography protocol is basically thresh-old. Because of non-threshold access structures is complex, the realization of non-threshold group cryptography is very difficult. In this paper, we do some works thatconstruct the optimal liner secret sharing scheme for non-threshold access structure.This paper mainly does the following areas:1. In secret sharing scheme, the access structureΓand the adversary structure (?)are decided each other. Therefore, given access structureΓ, we provide a algorithm tofind the adversary structure (?).2. We construct the corresponding generating matrix G and check matrix Haccording to the access structureΓand the adversary structure (?) respectively. Andwe prove that there exists linear code with length n + 1 (namely ideal secret sharingscheme) that can realize the given access structure is equivalent that the equationGHT = 0 has solution. If linear equation GHT = 0 has solution, there is a linearcode of length n + 1 to realize the given access structure. Otherwise, it does not exist.3. If there is no ideal linear code to realize given access structure, then we give aalgorithm to find the optimal linear code (the maximum information rate) to realize it.4. Adversary structure that found by 1) is more complex. Therefore we putforward another algorithm that finding real adversary structure by using linear codetheory.