The Realization Of Optimal Linear Multi-Secret Sharing Schemes

Secret sharing is very important in information security theory and application.In a multi-secret sharing scheme, several keys are shared among the sets of partic-ipants, and every key has an unique access structure. In this paper, for any givennon-threshold multi-access structures, we mainly research two aspects as followed:(1)Find the corresponding adversary structure of the given non-threshold multi-access structures, and construct the corresponding matrices G and H according tothe access structure and its adversary structure. Meanwhile, we give a necessary andsuffcient condition for realizing any given non-threshold multi-access structures byideal linear codes.(2)The effciency of a multi-secret sharing scheme is measured by the complex-ity σ and the randomness σT. In this paper, we give a method to fnd the optimallinear code to realize the given non-threshold multi-access structure when it can’t berealized by ideal linear code. Meanwhile, we propose two algorithms which make thecomplexity σ and the randomness σTreach the lower bounds respectively. Thus weobtain the corresponding optimal linear multi-secret sharing scheme.