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. The rational key sharing system makes the participants not deviate from the agreement by introducing the penalty strategy, which is often used to terminate the agreement immediately if any deviation is found. This penalty strategy sometimes leads to severe damage to the punitive’s own interests, Punish people’s deterrence.In order to overcome this weakness, this paper analyzes the rational key sharing system by using the extended game model.Firstly, a (2,2) threshold rational-key sharing system is given, and it is proved that the given protocol is the game Is a sequential equilibrium that insists that the original agreement after any history remains the optimal choice of each participant.Especially when the punishment of someone is found, the penalty strategy given by the agreement can not only effectively punish the deviation but also complete And protect the interests of punishing people.This is an important improvement of the rational key sharing system designed by our predecessors in this paper.Aiming at the problem that the protocol is extended to the (t, n) threshold, the key distributor is offline and the computing equilibrium is achieved Related issues give a general solution.