无条件安全并可识别欺骗者多秘密共享方案  

Unconditionally Secure Multi-secret Sharing Scheme with Identifiable Cheaters

作　　者：陈振华[1] 李顺东[1] 王文涛[2] 谭示崇[3] 

机构地区：[1]陕西师范大学计算机科学学院,西安710062 [2]西安建筑科技大学土木工程学院,西安710055 [3]西安电子科技大学综合业务网理论与关键技术国家重点实验室,西安710067

出　　处：《小型微型计算机系统》2014年第3期488-492,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61070189;61272435)资助;中央高校基本科研业务费专项资金项目(K5051201027;GK261001206)资助

摘　　要：(k,n)门限的多秘密共享方案是秘密被分割成n个份额,任何≥k个份额都能重构出秘密,但任何<k个份额不能得到秘密的任何信息.已公开的可识别欺骗者的门限多秘密共享方案大都是基于计算性安全,如大整数分解、离散对数或者Hash函数等,若当敌手计算能力无界时,则方案的安全性得不到保障.针对以上问题,当欺骗者的个数t≤(k-1)/3时,本文给出一种新的无条件安全的可识别欺骗者(k,n)的多秘密共享方案,利用RS纠错码和Shamir秘密共享方案之间的关系构造门限多项式充当消息验证码进行份额的验证,此方案不但能觉察到欺骗者的存在,而且能识别出谁是欺骗者.由于在所有的用户中采用单一密钥的消息验证码,并且通信成本不会随着参与者的增加而线性增长,方案设计简单,计算量小,安全性能良好,因而具有较高的效率.In a threshold multi-secret sharing scheme, the secrets are divided into n pieces （called shares） in such a way that the se- crets can be reconstructed with any more than k shares but less shares k reveal no information about the secrets. Existing threshold multi-secret sharing schemes with identifiable cheaters are mostly based on computational assumptions such as large integer factor, discrete logarithm and Hash function etc. The secrecy of scheme cannot be guaranteed for unbounded adversary. To overcome the problems in existed schemes, we propose a novel t cheaters identifiable （ k, n } multi-secret sharing scheme with unconditional security where t ~〈 { k - 1 ）/3. The scheme constructs a threshold polynomial, which is based on the relation between the RS error correcting code and the Shamir＇s scheme, to be used as message authentication code to verify the validity of shares. Our scheme can detect the existence of cheaters and identify who provide the forged shares, simultaneously. Since all participants share a single key in this scheme and the communication overhead will not linearly increase with the number of participants, which makes the scheme simple, secure and efficient.

关 键 词：无条件安全 可识别的多秘密共享 RS码 消息验证码 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]