基于分组的理性秘密共享方案  

Rational Secret Sharing Scheme Based on Group

作　　者：李梦慧[1,2] 田有亮[3,2,4] 

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州大学密码学与数据安全研究所,贵阳550025 [3]贵州大学计算机科学与技术学院,贵阳550025 [4]贵州省公共大数据重点实验室,贵阳550025

出　　处：《密码学报》2017年第3期209-217,共9页Journal of Cryptologic Research

基　　金：国家自然科学基金项目(61363068;61262073);贵州省教育厅科技拔尖人才支持项目(黔教合KY字[2016]060);贵州省科技基金计划项目(黔科合基础[2016]1023);贵州大学研究生创新基金(研理工2016016)

摘　　要：理性秘密共享是博弈论与秘密共享相结合的新兴研究方向,它拓展了博弈理论和传统秘密共享的应用领域,已成为密码学的研究热点.但是多数研究者在构造出理性秘密共享方案的同时忽略了方案的效率问题.理性秘密共享方案的通信轮数是影响方案效率的主要因素.现有的多数方案为了实现均衡等需求都采用未知轮数,即不让理性参与者知道当前重构轮是测试轮还是真秘密所在的轮,此方法造成通信复杂度较高,导致方案效率低下,这在一定的程度上会增加额外的通信开销.针对上述问题,基于不完全信息动态博弈模型,研究门限理性秘密共享方案的完美贝叶斯均衡问题.利用椭圆曲线上双线性对的随机函数设计一个知识承诺方案,该方案为可验证的,以此来检验分发者和参与者的欺骗问题.结合"均匀分组"思想使理性参与者以组为单位进行通信,可降低方案的通信复杂度,进而构造出两轮理性秘密共享方案.分析证明本方案具有可验证性,能够实现秘密重构博弈的完美贝叶斯均衡.并从轮复杂度、通信类型和前提假设三个方面与现有的典型方案进行对比,表明本方案不仅满足安全性需求且执行效率更高.Rational secret sharing is an emerging research direction of the combination of game theory and secret sharing, which extends the application field of game theory and traditional secret sharing, and has become a research hot research of cryptography However, most researchers in the construction of a rational secret sharing scheme while ignoring the scheme efficiency issues. The number of communication round of a rational secret sharing scheme is the main factor that influence the efficiency of the scheme. In order to achieve the equilibrium, most of the existing schemes have unknown number of communication rounds, i.e., rational participants do not know whether the current round is test round or the true secret round. This method has high communication complexity and low efficiency, and to a certain extent can add additional communication expense. According to the above problem, based on the incomplete information dynamic game model, and study on the perfect Bayesian equilibrium problem of threshold rational secret sharing scheme, by using bilinear pairings on elliptic curve random function, this paper designs a knowledge commitment scheme. The scheme is verifiable, it can test the distributor and the participants' cheating. 'Homogeneous grouping' makes rational participants as a group for the unit to communicate, which can reduce the communication complexity of the scheme, and enables the construction of two-round rational secret sharing scheme.Analysis shows that this scheme has the verifiability, can achieve the perfect bayesian equilibrium of reconstructing secret game. The scheme is compared with existing typical schemes with respect to complexity, types of communication and premise assumption, it is shown that the scheme satisfies the security requirements and is more efficient.

关 键 词：理性秘密共享 双线性对 博弈论 完美贝叶斯均衡 

分 类 号：O225[理学—运筹学与控制论] TN918.1[理学—数学]