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基于多项式插值的门限函数秘密分享方案

罗景龙^1,2, 林昌露^1,2, 李朝珍^1,2, 张剑^1,2

(1.福建师范大学数学与信息学院, 福州 350117;2.
福建师范大学福建省网络安全与密码技术重点实验室, 福州 350007)

Threshold Function Secret Sharing Scheme Based on Polynomial Interpolation

LUO Jing-Long^1,2, LIN Chang-Lu^1,2, LI Chao-Zhen^1,2, ZHANG Jian^1,2

(1.College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China;2.
Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China)

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本文已被：浏览 1179次下载 1720次
Received:September 28, 2019 Revised:October 29, 2019

中文摘要: 针对现存的函数秘密分享方案在重构的过程中需要所有的参与者全部参与，不能灵活地适用于现实场景的问题，本文运用多项式技术构造了含有门限的函数秘密分享方案.按照函数秘密分享的安全模型证明了新构造的方案具有信息论意义下的安全性.此外本文分析了Yuan等学者提出的函数秘密分享方案，阐述了其方案不满足函数秘密分享方案安全性的原因.最后将本文构造的方案与现有的函数秘密分享方案进行了比较，发现其具有更高级别的安全性和更高的效率.

中文关键词: 秘密分享函数秘密分享私密信息恢复多项式插值安全性分析

Abstract:Since the existing function secret sharing schemes require all participants to join in the reconstruction phase. Therefore, it cannot be flexibly applied to real-world scenarios. A function secret sharing scheme with thresholds is constructed in this study using polynomial techniques. According to the security model of function secret sharing, we proved that the proposed scheme has security in the sense of information theory. In addition, this study analyzes the function secret sharing scheme proposed by Yuan et al., and expounds the reason why their scheme does not satisfy the security of function secret sharing. Finally, a comprehensive comparison between the newly constructed scheme and the existing function secret sharing scheme is found. We note that the newly constructed scheme has higher level of security and higher efficiency through the comprehensive comparison.

keywords: secret sharing function secret sharing private information retrieval polynomial interpolation security analysis

文章编号： 中图分类号： 文献标志码：

基金项目:国家自然科学基金（U1705264，61572132）；福建省自然科学基金（2019J01275）

Author Name	Affiliation	E-mail
LUO Jing-Long	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China
LIN Chang-Lu	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China	cllin@fjnu.edu.cn
LI Chao-Zhen	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China
ZHANG Jian	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China

Author Name	Affiliation	E-mail
LUO Jing-Long	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China
LIN Chang-Lu	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China	cllin@fjnu.edu.cn
LI Chao-Zhen	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China
ZHANG Jian	College of Mathematics and informatics, Fujian Normal University, Fuzhou 350117, China Fujian Provincial Key Lab of Network Security & Cryptology, Fujian Normal University, Fuzhou 350007, China

引用文本：
罗景龙,林昌露,李朝珍,张剑.基于多项式插值的门限函数秘密分享方案.计算机系统应用,2020,29(5):29-35
LUO Jing-Long,LIN Chang-Lu,LI Chao-Zhen,ZHANG Jian.Threshold Function Secret Sharing Scheme Based on Polynomial Interpolation.COMPUTER SYSTEMS APPLICATIONS,2020,29(5):29-35