一种基于二元多项式的多秘密共享方案  

A MULTI-SECRET SHARING SCHEME BASED ON BIVARIATE POLYNOMIAL

作　　者：韩妍妍[1,2] 谢定邦 郭超 赵洪 Han Yanyan;Xie Dingbang;Guo Chao;Zhao Hong(Department of Communication Engineering,Beijing Electronic Science and Technology Institute,Beijing 100070,China;School of Telecommunications Engineering,Xidian University,Xi an 710071,Shaanxi,China)

机构地区：[1]北京电子科技学院通信工程系,北京100070 [2]西安电子科技大学通信工程学院,陕西西安710071

出　　处：《计算机应用与软件》2023年第4期305-310,349,共7页Computer Applications and Software

基　　金：中央高校基本科研业务费项目(328201911)。

摘　　要：近年来,二元多项式多被用来构造秘密共享方案,但构造的多秘密共享方案不能很好兼顾二元多项式性质与安全性。针对这种情况,提出基于二元非对称多项式的一种新的多秘密共享方案。参与者获得的秘密份额不仅可以用于重建多个秘密,还可用于生成任意参与者之间的会话密钥。会话密钥可以在秘密重建过程中保护重构者间信息交换的安全。方案无需任何密码学假设,是无条件安全的。通过安全性分析,可抵抗内部合谋攻击和重构过程中的外部攻击。该方案在实际环境中不需要额外的密钥协商机制来构建参与者间的安全通道,实现一次并行重构多个秘密,提高了实际运行效率。In recent years,bivariate polynomials have been used to construct secret sharing schemes,but the constructed multi-secret sharing schemes cannot take the properties and security of bivariate polynomials into account.Aimed at this situation,a new multi-secret sharing scheme based on bivariate asymmetric polynomials is proposed.The secret share obtained by the participants could be used not only to reconstruct multiple secrets,but also to generate the session key between any participants.The session key could protect the security of information exchange between reconstructors during the secret reconstruction process.The scheme did not require any cryptographic assumptions and was unconditionally safe.Through the security analysis,it could resist internal collusion attacks and external attacks in the reconstruction process.This scheme did not require an additional key agreement mechanism to construct a secure channel between participants in the actual environment,realized the reconstruction of multi-secret in parallel at one time,and improved the actual operating efficiency.

关 键 词：多秘密共享 二元多项式 会话密钥 无条件安全 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]