Bayesian mechanism for rational secret sharing scheme

We consider the cooperation of rational parties in secret sharing. We present a new methodology for rational secret sharing both in two-party and multi-party settings based on Bayesian game. Our approach can resolve the impossible solutions to a rational secret sharing model. First, we analyze the 2-out-of-2 rational secret sharing using Bayesian game, which makes us able to consider different classes of the protocol player (for "good" and "bad" players) and model attributes such as any other parties' preferences and beliefs that may affect the outcome of the game. Thus, the new model makes us able to reason rational secret sharing from the perspective of Bayesian rationality, a notion that may be in some scenarios more appropriate than that defined as per pure rational. According to these analyses, we propose a Bayesian rational protocol of 2-out-of-2 secret sharing. Also, our techniques can be extended to the case of t-out-of-n Bayesian rational secret sharing easily. Our protocol is adopted only by the parties in their decision-making according to beliefs and Bayes rule, without requiring simultaneous channels and can be run over asynchronous networks.