理性密钥共享的扩展博弈模型

理性密钥共享体制通过引入惩罚策略使得参与者不会偏离协议,常采用的惩罚是一旦发现有人偏离就立即终止协议.这种惩罚策略有时导致惩罚人自身利益严格受损,从而降低了对被惩罚人的威慑.为了克服这一弱点,本文以扩展博弈为模型分析了理性密钥共享体制.首先给出(2,2)门限的理性密钥共享体制,证明了所给的协议是该博弈的一个序贯均衡,即经过任何历史之后坚持原协议仍然是每一个参与者的最优选择.特别地,在发现有人偏离后,协议所给出的惩罚策略既可以有效惩罚偏离者又能够完全维护惩罚人的利益.这是本文对前人设计的理性密钥共享体制的一个重要改进.然后针对将协议扩展到(t,n)门限情形,实现密钥分发人离线,达到计算的均衡等相关问题给出了一般的解决方案.

Rational secret sharing as extensive games

The threat that comes from previously used punishment strategies in rational secret sharing is weakened because the punishment somtimes also causes loss to the punisher himself.In this paper,we first model 2-out-of-2 rational secret sharing in an extensive game with imperfect information,and then provide a strategy for achieving secret recovery in this game.Moreover,we prove that the strategy is a sequential equilibrium which means after any history of the game no player can benefit from deviations so long as the other players stick to the strategy.In particular,when a deviation is detected,the punishment executed by the punisher is still his optimaloption.Therefor,by considering rational secret sharing as an extensive game,we design punishment strategies that effectively punish the deviants and meanwhile guarantee punishers’ benefit.Hence,these punishments are more credible than previous ones.Except assuming the existence of simultaneous channels,our scheme can have dealer off-line and extend to the t-out-of-n setting,and also satisfies computational equilibria in some sense.