Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs  

作　　者：Ying-pu Deng Li-feng Guo Mu-lan Liu 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China [2]State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100049,China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第1期67-78,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10501049,90304012); 973 Project(No.2004CB318000)

摘　　要：In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.

关 键 词：Anonymous secret sharing schemes Steiner systems group divisible designs difference families relative difference sets 

分 类 号：O22[理学—运筹学与控制论]