基于线性码上无可信第三方的多秘密共享方案

刘荣香1,2， 赖红2

(1. 青岛理工大学 通信与电子工程学院，山东 青岛 266520；2. 北京邮电大学 理学院，北京 100876)

摘要： 为了避免秘密共享方案中第三方的不诚实行为造成的威胁，利用Massey线性码上的秘密共享体制，提出了一个无可信第三方的多秘密共享方案。该方案的重构算法满足加法同态性，其中每个参与方既是参与者也是分发者。同时方案实现了非门限结构上的无分发者的秘密共享，适用于更广泛的存取结构。证明了方案的正确性和安全性，并通过效率分析表明该方案只需较小的存储空间。此外，基于方案中重构算法的同态性给出了一种设计安全多方计算协议的方法。

关键词： 无可信第三方的秘密共享； 加法同态性； 安全多方计算

 中图分类号： TP 309.7       文献标志码： A

Multisecret Sharing Scheme Without a Trusted Third Party Based on Linear Codes

 LIU Rongxiang1,2, LAI Hong2

(1. School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, China;

2. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China)

Abstract: To avoid the collapse caused by a dishonest third party, this paper presents a dynamic multisecret sharing scheme without a trusted third party based on Massey secret sharing scheme using linear codes. The secret reconstruction algorithm meets the property of additive homomorphism, where each participant also plays a role as a dealer. Meanwhile, the new proposal achieves nonthreshold access structure secret sharing that can be widely used. The correctness and security are proved. Analysis on the efficiency shows that the scheme needs small data storage space. Furthermore, on the basis of the homomorphism property of the reconstruction algorithm, a method for constructing secure multiparty computation protocols is given.

Key words: secret sharing scheme without a trusted third party; additive homomorphism; secure multiparty computation

收稿日期： 20140221

作者简介： 刘荣香(1977—)，女，博士研究生.