基于重构顺序调整机制的理性秘密共享方案

Rational Secret Sharing Scheme Based on Reconstruction Order Adjustment Mechanism

理性秘密共享的研究目标是通过引入自利的理性参与者,设计适用于现实环境的公平的秘密共享方案.然而,由于要求秘密分发者准确知道理性参与者的各种收益,且未考虑秘密重构博弈的稳定性,导致在现有理性秘密共享方案的执行过程中,不能完全避免出现遵循协议执行的参与者未获得共享秘密、而偏离协议执行的参与者却获得共享秘密的不公平情形.针对上述问题,结合机制设计的激励相容原理,通过让秘密分发者随机选择所需重构轮数,设计了能有效约束理性参与者自利性行为的重构顺序调整机制,构造具有未知重构轮数的理性秘密共享方案.分析表明所提方案能实现秘密重构博弈的子博弈完美均衡,确保秘密重构博弈的稳定性,使得所提方案的公平性得以保证.通过从通信方式、重构轮数和前提假设3个方面与现有典型方案进行对比分析,表明所提方案具有较好的实用性.

Rational secret sharing aims to design the realistic secret sharing scheme and to guarantee its fairness by introducing selfish players.However,due to the requirement that the dealer knows all kinds of players’payoffs accurately,the stability of the reconstruction game is not taken into account.It might cause that,during the execution of the existing rational secret sharing schemes,the players who deviate from the prescribed protocol obtain the secret,whereas the others who follow the prescribed protocol faithfully cannot.To prevent this unfair solution,combined with the incentive compatibility principle of mechanism design,this paper makes use of the method that the number of reconstruction rounds is randomly chosen by the dealer,and devises the reconstruction order adjustment mechanism to effectively restrict the selfishness of rational players.Then,a rational secret sharing scheme with unknown reconstruction rounds is proposed.The analysis shows that the proposed scheme can realize the subgame perfect equilibrium of the reconstruction game and ensure its stability.That is,the fairness of the proposed scheme is achieved.In addition,comparied with several typical schemes in communication type,the number of reconstruction rounds and additional assumption,the results illustrate that the presented scheme is not only fair,but also has better practicality.