一个可公开验证的多重秘密共享门限方案  

A Publicly Verifiable Multiple Secret Sharing Threshold Scheme

作　　者：蔡兆政 瞿云云[3] 包小敏[1] CAI Zhao-zheng;QU Yun-yun;BAO Xiao-min(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China;Chongqing No.18 Middle School,Chongqing 400020,China;School of Mathematical Science,Guizhou Normal University,Guiyang 550001,China)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]重庆市第十八中学,重庆400020 [3]贵州师范大学数学与计算机科学学院,贵阳550001

出　　处：《西南大学学报（自然科学版）》2021年第7期105-110,共6页Journal of Southwest University(Natural Science Edition)

基　　金：贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]130);贵州省科学技术基金项目(黔科合J字[2014]2125号);国家自然科学基金项目(61462016).

摘　　要：本文设计了一个安全有效的可公开验证的(t,n)多重秘密共享门限方案.该方案下的系统需要一个公告牌(bulletin board),只有秘密分发者(Dealer)可以修改和更新上面的数据,参与者只能下载或浏览.该方案的特点是,Dealer分发给参与者加密的秘密份额可以公开被验证,但是只有指定的参与者能够解密得到子秘密,且子秘密可以重复使用;由参与者提供的解密份额也可以公开验证,这两次公开都是非交互的验证,高效便捷,可以有效防止Dealer欺骗行为和参与者的欺骗行为.方案加密采用ElGamal公钥密码体制,计算的验证参数可以多次利用,Dealer要想共享新的秘密,只需要在公告牌上发布新的数据即可,Dealer的计算量较小,具有广泛的适用性.A secure and effective(t,n)multiple secret sharing threshold scheme is designed in this paper.The system of this scheme requires a bulletin board.Only the Dealer can modify and update the data on it,and the participants can only download or browse it.What is unique for this scheme is that the encrypted secret share distributed by the Dealer to the participants can be verified publicly,but only the designated participant(s)can decrypt the sub-secret and the sub-secret can be re-used.The declassified share provided by the participants can also be verified publicly.Both disclosures are non-interactive verification,which are efficient and convenient and can effectively prevent the Dealer s cheating behavior and the participants cheating behavior.The encryption scheme adopts ElGamal public key cryptography,and the calculated verification parameters can be used many times.If the Dealer wants to share the new secret,he needs onlyto publish the new data on the bulletin board.The Dealer has a small amount of computation and a wide range of applicability.

关 键 词：秘密共享方案 拉格朗日插值多项式 门限方案 非交互身份认证 

分 类 号：O211.4[理学—概率论与数理统计]