秘密共享体制的博弈论分析

Game-Theoretic Analysis for the Secret Sharing Scheme

本文提出理性第三方的概念,在秘密共享中任何理性的局中人都可以充当"可信中心"来分发秘密信息,这样使秘密共享体制更具有普适性.基于博弈论分析秘密分发协议,它被形式化为n个二人博弈.证明在这些博弈中,理性秘密分发者总是选择欺骗各局中人以获得更大的收益,同时提出解决该问题的理性秘密分发机制.最后,基于健忘传输协议提出秘密重构机制,有效解决秘密重构中各局中人的不合作问题.

This paper proposes the concept of rational trusted party.Any rational party can be the TTP to distribute the shares in the secret sharing such that it is to be more suitable for use.As far as we know,that is firstly to analyze distribution of shares with game theory in secret sharing scheme.It is formalized as n tow-person games.It is proven that rational dealer always selects cheating all players to get more payoffs in these games.Simultaneously a rational secret distribution mechanism is proposed to solve this problem.Moreover,we construct a mechanism of reconstruction of secret based on oblivious transfer protocol,which solve the problem of players＇ non-cooperation in reconstruction phase.