基于二元对称多项式的改进秘密共享方案  

An Improved Secret Sharing Scheme Based on Bivariate Symmetric Polynomial

作　　者：王方正 张艳硕[1] 池亚平[1] WANG Fangzheng;ZHANG Yanshuo;CHI Yaping(Beijing Electronic Science and Technology Institute,Beijing 100070,P.R.China)

机构地区：[1]北京电子科技学院,北京市100070

出　　处：《北京电子科技学院学报》2021年第4期57-69,共13页Journal of Beijing Electronic Science And Technology Institute

基　　金：国家重点研发计划项目(课题编号:2018YFB1004100);“信息安全”国家级一流本科专业建设点项目;2020年教育部新工科项目“新工科背景下数学课程群的教学改革与实践”项目资助;中央高校基本科研业务费项目(项目编号:328201915)资助。

摘　　要：秘密共享方案通过对秘密进行分割,分散了秘密遭到窃取的攻击风险,是现代密码学的研究热点,具有很强的理论意义和实践意义。本文梳理了秘密共享方案的发展沿革,整理了预备的数学和密码学知识,深入研究了禹亮龙等人提出的基于二元对称多项式的方案,针对该方案中冗余的验证参数计算和不可靠的身份验证导致的安全风险,通过调整方案执行流程、添加协商会话密钥、引入国密SM4算法、精简方案参数计算,对方案进行了改进,在保证方案正确性的前提下,提升了方案的安全性和可靠性。As a research focus of modern cryptography, the secret sharing scheme has strong theoretical and practical significance, where a secret is split to disperse the risk of being stolen. In this paper, the history of the secret sharing scheme is sorted out, and relevant preliminary mathematics and cryptography knowledge is organized, and an in-depth study on the bivariate symmetric polynomial based scheme proposed by Lianglong Yu et al is performed. For the issues of redundancy parameter calibration and security risks induced by unreliable identity verification, Yu’s scheme is improved by adjusting the execution process, adding the group key agreement protocol, introducing the SM4 algorithm, and simplifying the parameters calculation. The improved scheme could increase the safety and reliability while ensuring the accuracy.

关 键 词：秘密共享 门限方案 信息安全 二元对称多项式 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]