摘要： 由于网络信息不能同步传输，直接将需要面对面同步进行的传统游戏构建在网络中将无法保证游戏的公平性。针对该问题，采用基于合数高阶剩余的公钥系统中比特承诺的思想，设计传统的石头、剪刀、布游戏的双人和可计数多人游戏方案。在多人游戏协议中利用系统的同态性实现计数功能，从而隐藏出拳失败者的出拳信息，同时降低网络开销，并在协议设计中根据算法博弈论的原理，引入保证所有参与者都不可能偏离协议的机制。分析结果表明，采用以上思想设计传统的石头、剪刀、布游戏，能够实现在网络应用中的公平性和有效性。

关键词: 比特承诺, 游戏, 网络信息, 同态性, 算法博弈论

Abstract: It becomes difficult to play the games that need face-to-face mechanism to ensure the fairness on Internet. Bit Commitment(BC) can solve this problem. This paper, using public-key cryptosystem based on high degree composite residuosity classes, proposes a new bit commitment scheme, and then, using this BC scheme as building block, designs two protocols to implement the traditional rock, paper and scissors game for multi-players. These protocols use the homomorphism of the public-key cryptosystems to perform the counting function, to hide the information of the fail player’s promise, and to reduce the network overhead meanwhile. In design of these protocols, algorithmic game theory is introduced to guarantee that all players will loyally follow the prescribed game protocols. Analysis result shows that the traditional rock, paper and scissors game designed by the idea mentioned above can be achieved fairly and effectively in network.

Key words: Bit Commitment(BC), game, network information, homomorphism, algorithmic game theory

中图分类号: 

• TP393