In secret sharing we are asked to split a secret into several shares in such a way that a minimum number of shares is necessary and sufficient to reconstruct the secret. Rational secret sharing considers secret sharing in the context of adversarial players who want to learn the secret but, secondarily, want to prevent other players from learning the secret. We present protocols, and bounds on the effectiveness of any protocol, for recombining secret shares in the presence of players who do not want others to learn the secret (rationality), may not want to learn the secret themselves (maliciousness), may be colluding, may have unbounded computational capacity, may be able to synchronize sends (asynchronous/synchronous broadcast), and/or may be able to recognize the secret independently (conspicuousness). We propose four protocols and analyze their security against players and coalitions who are each rational or malicious. We also prove three results that show protocols using only asynchronous broadcast are less secure than what can be achieved by protocols using synchronous broadcast.

This thesis considers the problem of finitely iterated rational secret sharing. We describe how to evaluate this problem using game theory and finitely iterated prisoner’s dilemma. The players each have a private horizon that the other player does not know. The only thing that a player knows about their opponent’s private horizon is a common upper bound. The description of a synchronous and asynchronous finitely iterated secret sharing protocol with private information is followed by a game theoretic proof of the viability of such protocols. / Graduate