基于中国剩余定理的可验证理性秘密共享方案

针对目前理性秘密共享方案不能动态添加和删除参与者的问题，结合博弈论和密码学理论，提出一种动态理性秘密共享方案。方案基于中国剩余定理，在秘密重构过程，可以动态添加和删除参与者，另外方案采用可验证的随机函数，能检验参与者的欺骗行为。参与者不知当前轮是否是测试轮，偏离协议没有遵守协议的收益大，理性的参与者有动机遵守协议，最终每位参与者公平地得到秘密。方案不需要可信者参与，满足弹性均衡，能防止成员间的合谋攻击。

Verifiable rational secret sharing scheme based on Chinese remainder theorem

To address the problem that participant can not be added or deleted dynamically in rational secret sharing scheme so far, this paper proposed a dynamic rational secret sharing scheme which combined game theory with cryptography. The scheme based on Chinese remainder theorem, can add or delete the participant dynamically in the secret reconstruction phase. And it is verifiable by using the verifiable random function, and the cheat of participants cannot work. The participants did not know whether the current round was a testing round. And the gain of following the protocol was more than the gain of deviating, so rational player had an incentive to abide the protocol. Finally, every player could obtain the secret fairly. In addition, the scheme satisfied resilient equilibrium and could withstand the conspiracy attack.