摘要： 在大多数参与者有权重的秘密共享方案中，各参与者子秘密份额数量的不同会导致秘密重构阶段产生不公平问题。为此，提出一个基于重复博弈的理性秘密共享方案。在参与者原有份额的基础上，为其构造数量差不超过1的有效子秘密份额，利用重复博弈使每个参与者可以获得其他参与者的全部份额，进而重构出秘密。分析结果表明，该方案可以使理性参与者始终遵守协议，完成秘密重构，且具有较高的安全性和良好的可扩展性。

关键词: 秘密共享, 博弈论, 子秘密份额, 中国剩余定理, 重复博弈, 公平性

Abstract: In most secret sharing schemes with weighted participants, different amount of players’ secret subshares can cause unfairness problem in the secret reconstruction phase. This paper proposes a rational secret sharing scheme based on repeated games. On the basis of original subshares, it constructs new subshares for each player, making sure that each two amount of subshares differ by a value at most 1. Through repeated games, every player can get all of other players’ subshares and then reconstruct the secret. Analysis result shows that the scheme can make every rational player follow the secret reconstruction protocol all the time and be able to reconstruct the secret. And it has high security and expandability.

Key words: secret sharing, game theory, secret subshare, Chinese remainder theorem, repeated games, fairness

中图分类号: 

• TP309