Abstract: Iterated rational secret sharing scheme only fits for the case of infinite rounds. But the secret sharing scheme with infinite rounds is not efficient. Combined with finitely repeated game theory, this paper proposes a new (m+1,n) finite iterated rational secret sharing scheme assigning each player a time limit based on Shamir’s secret sharing scheme. Analysis results show that a rational secret sharing scheme within constant rounds can be constructed when the time limit and payoff functions suffice some conditions, where each player can reconstruct the secret.

Key words: game theory, repeated game, rational secret sharing, Nash equilibrium, utility function, cooperation strategy

摘要： 重复理性秘密分享机制仅适用于交互轮数无限的情形，但是无限轮的理性秘密分享机制的效率不高。为此，在(m,n) Shamir秘密分享机制的基础上，结合有限重复博弈，为每个参与者赋予一个参加协议的时限，由此提出一种新的(m+1,n)有限轮理性秘密分享机制。分析结果表明，当时限和参与者的效用函数满足一定条件时，可以得到一个常数轮的理性秘密分享机制，使所有理性参与者可以恢复秘密。

关键词: 博弈论, 重复博弈, 理性秘密分享, 纳什均衡, 效用函数, 合作策略

CLC Number: 

• TP309.2