一种基于STSS的可验证秘密分享方案  

A verifiable secret sharing scheme based on STSS

作　　者：杨景奕 郑明辉 汪玉 黄世成 YANG Jingyi;ZHENG Minghui;WANG Yu;HUANG Shicheng(College of Intelligent Systems Science and Engineering,Hubei Minzu University,Enshi 445000,Hubei,China;School of Cyber Science and Engineering,Sichuan University,Chengdu 437100,China)

机构地区：[1]湖北民族大学智能科学与工程学院,湖北恩施445000 [2]四川大学网络空间安全学院,成都610065

出　　处：《中南民族大学学报（自然科学版）》2024年第4期540-546,共7页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61772181);湖北民族大学研究生科研创新资助项目(MYK2023079)。

摘　　要：针对秘密分享体制下非诚实分发者提供错误份额无法追责的问题,提出了一种基于STSS的可验证秘密分享方案来提升不诚实参与者的检测能力.STSS方案首先让分发者通过Feldman秘密分享方案将主秘密分割成n份,所得子秘密使用SM2算法对其进行签名;其次,所得签名值(r,s)采用TEA算法进行加密得到最终份额;最后,针对秘密分享体制下非诚实分发者提供错误份额无法追责的问题,方案使用双重验证,接收者在收到分享份额后通过对称密钥解密得到签名值,对比分发者公钥,保证其在传输和存储过程中未受到篡改.需要使用主秘密时,t(t<n)位接收者参与验证秘密重构可恢复原始秘密.方案在随机预言机模型下证明了安全性,通过仿真实验表明:该方案在给定门限值和子秘密数量下运算效率较高.A verifiable secret sharing scheme based on STSS is proposed to improve the detection ability of dishonest participants,in response to the problem that dishonest distributors cannot be held accountable for providing incorrect shares under the secret sharing system.The scheme firstly requires the distributor to divide the main secret into n parts using the Feldman secret sharing scheme,and the resulting sub secrets are signed using the SM2 algorithm;Secondly,the obtained signature values(r,s)are encrypted using the TEA algorithm to obtain the final share;Finally,to address the issue of dishonest distribution under the secret sharing system,which cannot be held accountable for providing incorrect shares,the scheme uses double verification.After receiving the shared shares,the receiver decrypts the signature value using a symmetric key,compares it with the distributor's public key,and ensures that it has not been tampered with during transmission and storage.When the master secret needs to be used,t(t<n)receivers participate in verifying the reconstruction of the secret to recover the original secret.The scheme has been proven to be secure under a random oracle model,and simulation experiments have shown that it has high computational efficiency under given threshold values and the number of sub secrets.

关 键 词：秘密分享 秘密重构 可验证性 门限值 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]