基于马尔可夫决策的理性秘密共享方案

基于马尔可夫决策理论研究理性密码共享系统模型和秘密重构方法。首先利用马尔可夫决策方法，提出适合于理性秘密共享的系统模型，该模型包括参与者集合、状态集合、风险偏好函数、状态转移函数、回报函数等。在模型中，引入秘密重构中的参与者的风险偏好函数刻画秘密共享模型的状态集合和状态转移函数。其次，基于所提出的系统模型构造相应的理性秘密共享方案，基于马尔可夫策略解决各理性参与者在秘密共享方案中的秘密重构问题。最后对方案进行理论分析证明，给出理性秘密重构方案中折扣因子、回报函数、参与者风险偏好函数间的函数关系，其结果表明所提系统模型方法的合理性和有效性。

Rational secret sharing scheme based on Markov decision

The reconstruction methods of a rational secret sharing based on the Markov decision was studied. Firstly, a rational secret sharing system model was proposed using the Markov decision process, which included the players set, the states set, the risk preference function, the state transfer function, the return function, etc. The risk preference function was introduced in order to depict the state set and the state transfer function in this model. Secondly, a rational secret sharing scheme was constructed based on the proposed system model, which was able to solve the secret reconstruction problems according to the Markov strategy. Finally, the functional relations of among the discount factor, the return function and the risk preference function was proposed in this scheme. The analysis results show that the proposed model and scheme are rationality and validity.