GOMSS:A Simple Group Oriented(t,m,n)Multi-secret Sharing Scheme  

作　　者：MIAO Fuyou WANG Li JI Yangyang XIONG Yan 

机构地区：[1]School of Computer Science and Technology, University of Science and Technology of China, Hefei 230027,China

出　　处：《Chinese Journal of Electronics》2017年第3期557-563,共7页电子学报（英文版）

基　　金：supported in part by the National Natural Science Foundation of China(No.61572454,No.61472382,No.61572453,No.61520106007);Open Project of Key Laboratory of Cryptologic Technology and Information Security,Ministry of Education,Shandong University

摘　　要：In most(t,n)-Multi-secret sharing((t,n)-MSS)schemes,an illegal participant,even without any valid share,may recover secrets when there are over t participants in secret reconstructions.To address this problem,the paper presents the notion of Group oriented(t,m,n)-multi-secret sharing(or(t,m,n)-GOMSS),in which recovering each secret requires all m(n≥m≥t)participants to have valid shares and actually participate in secret reconstruction.As an example,the paper then proposes a simple(t,m,n)-GOMSS scheme.In the scheme,every shareholder has only one share;to recover a secret,m shareholders construct a Polynomial-based randomized component(PRC)each with the share to form a tightly coupled group,which forces the secret to be recovered only with all m valid PRCs.As a result,the scheme can thwart the above illegal participant attack.The scheme is simple as well as flexible and does not depend on conventional hard problems or one way functions.In most （t, n）-Multi-secret sharing （（t,n）- MSS） schemes, an illegal participant, even without any valid share, may recover secrets when there are over t participants in secret reconstructions. To address this problem, the paper presents the notion of Group oriented （t, m, n）-multi-secret sharing （or （t, m, n）-GOMSS）, in which recovering each secret requires all m （n ≥ m ≥ t） participants to have valid shares and actually participate in secret reconstruction. As an example, the paper then proposes a simple （t, m,n）-GOMSS scheme. In the scheme, every shareholder has only one share; to recover a secret, m shareholders construct a Polynomial-based randomized component （PRC） each with the share to form a tightly coupled group, which forces the secret to be recovered only with all m valid PRCs. As a result, the scheme can thwart the above illegal participant attack. The scheme is simple as well as flexible and does not depend on conventional hard problems or one way functions.

关 键 词：Multi-secret sharing Shamirs scheme Tightly coupled group Polynomial-based randomized component(PRC) 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]