基于矩阵特征值的可验证无可信中心门限方案  

Verifiable Threshold Scheme without Trusted Center Based on Matrix Eigenvalue

作　　者：张艳硕 王泽豪 杜耀刚 王志强 ZHANG Yanshuo;WANG Zehao;DU Yaogang;WANG Zhiqiang(Department of Cryptology Science and Technology.Beijing Electronic Science&Technology Institute,Beijing 100070,China;State Key Laboratory of Cryptology,Beijing 100878,China;Data Communication Science and Technology Research Institute,Beijing 100191,China;Xingtang Telecommunications Technology Co.Ltd.,Beijing 100191,China)

机构地区：[1]北京电子科技学院密码科学与技术系,北京100070 [2]密码科学技术国家重点实验室,北京100878 [3]数据通信科学技术研究所,北京100191 [4]兴唐通信科技有限公司,北京100191

出　　处：《武汉大学学报（理学版）》2020年第2期135-140,共6页Journal of Wuhan University:Natural Science Edition

基　　金：国家重点研发计划(2018YFB1004101);中央高校基本科研业务费项目(328201902)。

摘　　要：传统的门限(秘密共享)方案大多存在一个可信中心,可信中心负责秘密份额的产生、分配以及秘密的恢复,这会影响系统的安全性、鲁棒性和可用性,本文利用矩阵特征值的特点,设计了一个可验证无可信中心门限方案。在本文方案中,所有参与者提供相同秘密份额的值给黑盒子,构成一个2n维的可逆方阵P,该可逆方阵P和对角矩阵L生成一个矩阵A,将矩阵A的特征向量标准正交化,作为子密钥分发给各参与者。每个参与者各分得两个子密钥,这两个子密钥满足两个条件:正交和所对应的特征值相同。在子密钥生成和主密钥恢复的过程中,均可以利用这两个条件保证方案安全实施。分析表明,该方案是正确且安全的,信息率为1/2。通过实例说明了方案的可行性。Mostly,there is a trusted center in traditional secret sharing(threshold)schemes,and the trusted center is responsible for the generation and distribution of secret shares and the recovery of secrets, which may affect the security, robustness and usability of the system.In this paper, we use the eigenvalues of matrices to design a verifiable untrusted central threshold scheme. In this scheme, all participants provide the same value of secret share equally to the black box, forming a 2 n-dimensional matrix P of invertible matrix. A matrix A is generated for the reversible matrix P and the diagonal matrix L, and the standard orthogonalization of the eigenvector of the matrix A is distributed as a sub-key to each participant. Each participant is divided into two subkeys, which satisfies two conditions: orthogonality and the corresponding eigenvalues are the same. In the process of subkey generation and master key recovery, these two conditions can be used to ensure the security implementation of the scheme. The analysis results show that the scheme is correct and safe, and the information rate is 1/2. At the end of the article, examples are used to illustrate the feasibility of the implementation of the program.

关 键 词：门限 秘密共享 可信 可验证 黑盒子 特征向量 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]