(2,2)贝叶斯理性秘密共享方案

The(2,2)Bayesian Rational Secret Sharing Scheme

在理性秘密共享协议中,自利性目标可能会驱使理性参与者偏离协议,从而影响协议的公平性.在(t,n)门限理性秘密共享方案中,其特殊情形(2,2)理性秘密共享方案的公平性较难实现.在同时考虑理性参与者的眼前利益和长远利益的基础上,基于不完全信息动态博弈模型,通过分析理性参与者在(2,2)秘密重构阶段可能采取的策略和信念系统,引入理性参与者的期望收益,研究了(2,2)理性秘密共享重构阶段的完美贝叶斯均衡问题.进一步结合机制设计理论中的VCG(Vickrey-Clarke-Groves)机制,设计激励相容的交互记录机制来约束理性参与者的行为,在不需要秘密分发者保持在线的情形下,提出一个适用于异步通信的公平的(2,2)理性秘密共享方案.

The rational secret sharing is an intersection direction between the traditional secret sharing and game theory .In the rational secret sharing scheme,the selfishness maybe impels rational players to deviate from the protocols so as to influence the fairness of scheme .In the existing threshold rational secret sharing schemes,the fairness of （2,2）rational secret sharing scheme, which is a special case,is hard to be realized,especially implementing on the asynchronous communication channel .To achieve fair-ness of （2,2）rational secret sharing over the asynchronous communication channel,this paper firstly analyzes rational players’utili-ty by simultaneously discussing their short-term interest and long-term interest .Then through illustrating rational players’available actions and belief systems,and computing their expected utilities with the dynamic games of incomplete information,the perfect Bayesian equilibrium for reconstruction phase of （2,2）rational secret sharing is studied.Furthermore,combining with the VCG （Vickrey-Clarke-Groves）mechanism of design theory,the incentive compatibility mechanism,which is named recording interaction, is designed to restrict the behavior of rational players.Consequently,the fair （2,2）rational secret sharing scheme is presented, which does not need the dealer to keep on-line over the asynchronous communication channel .