Calculus of Cooperation and Game-Based Reasoning about Protocol Privacy

The article introduces a new formal system, the calculus of cooperation, for reasoning about coalitions of players in a certain class of games. The calculus is an extension of the propositional intuitionistic logic that adds a coalition parameter to intuitionistic implication. The system is shown to be sound and complete with respect to a game semantics. One intended application of the calculus of cooperation is the verification of privacy properties in multiparty computation protocols. The article argues that such properties can be established by providing a set of strategies for a non-zero-sum, perfect information game based on the protocol. It concludes with several examples of such verifications formalized in the calculus of cooperation.