一个基于非齐次线性递归的可验证多秘密共享方案  

Verifiable multi secret sharing scheme based on nonhomogeneous linear recursion

作　　者：袁江涛 彭长根[1,2,3,4,5] Yuan Jiangtao;Peng Changgen(College of Computer Science&Technology,Guizhou University,Guiyang 550025,China;Guizhou Provincial Key Laboratory of Public Big Data,Guiyang 550025,China;Institute of Cryptography&Data Security,Guiyang 550025,China;School of Mathematics&Information Science,Guangzhou University,Guangzhou 510006,China;Guangdong Provincial Key Laboratory of Information Security,Guangzhou 510006,China)

机构地区：[1]贵州大学计算机科学与技术学院,贵阳550025 [2]贵州省公共大数据重点实验室,贵阳550025 [3]密码学与数据安全研究所,贵阳550025 [4]广州大学数学与信息科学学院,广州510006 [5]广东省信息安全技术重点实验室,广州510006

出　　处：《计算机应用研究》2018年第5期1530-1533,1539,共5页Application Research of Computers

基　　金：国家自然科学基金资助项目(61662009;61262073;61363068);广东省信息安全技术重点实验室开放课题资助项目(GDXXAQ2016-04);贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]169)

摘　　要：可验证秘密共享方案的难点在于如何设计出高效的验证算法及方式。为了解决可验证秘密共享中存在的问题,基于非齐次线性递归序列和环上椭圆曲线,构造出一个可验证的秘密共享方案。在方案中用环上的椭圆曲线和单调陷门函数对参与者进行验证。方案中的非齐次递归序列在密钥分发时性能优于拉格朗日插值公式。在秘密分发的过程中需要公开的参数比较少。与Hu和Mashhadi的方案相比,此方案不仅具有Hu和Mashhadi方案的验证算法效率高和密钥短的优点,而且参与者可以一次性验证其他的参与者,而无须逐个验证。方案在相同的安全级别下有效率较高的验证算法和验证方式,从而提高了可验证秘密共享方案的效率。The difficulty of verifiable secret sharing scheme is how to design an efficient verification algorithm and method.In order to solve the problem of verifiable secret sharing,based on the nonhomogeneous linear recursive sequence and the elliptic curve over the ring,this paper constructed a verifiable secret sharing(VSS)scheme.In this scheme,it used the elliptic curve over the ring and the trapdoor function to verify participants.In this scheme,the performance of the nonhomogeneous recursion sequence was better than the Lagrange interpolation formula in the key distribution.In the process of secret distribution,it had fewer public value.Comparing to the scheme of Hu and Mashhadi,this scheme not only has the characteristics of high efficiency of verifiable algorithm of Hu and Mashhadi’s scheme,but also has the advantage of short key,and the participants can verify the other participants one time,not one by one to verify.The proposed scheme has higher efficiency of verification algorithm and verification method in the same security level,and thereby improves the efficiency of verifiable secret sharing scheme.

关 键 词：非齐次线性递归 环上椭圆曲线 秘密共享 一次可验证性 

分 类 号：TP393.04[自动化与计算机技术—计算机应用技术]