The Game-Playing Technique

In the game-playing technique, one writes a pseudocode game such that an adversary’s advantage in attacking some cryptographic construction is bounded above by the probability that the game sets a flag bad. This probability is then upper bounded by making stepwise, syntactical refinements to the pseudocode—a chain of games. The approach was first used by Kilian and Rogaway (1996) and has been used repeatedly since, but it has never received a systematic treatment. In this paper we provide one. We develop the foundations for game-playing, formalizing a general framework for doing game-playing proofs and providing general and useful lemmas that justify various kinds of game-refinement steps. We use this to provide simpler and more easily verifiable proofs of some classic existing results, including the security of the basic CBC MAC. We then extend this to prove a significant new result, namely an improved security bound for the basic CBC MAC.