A Note On Game-Hopping Proofs

Game hopping is a method for proving the security of a cryptographic scheme. In a game hopping proof, we observe that an attacker running in a particular attack environment has an unknown probability of success. We then slowly alter the attack environment until the attackers success probability can be computed. We also bound the increase in the attacker’s success probability caused by the changes to the attack environment. Thus, we can deduce a bound for the attacker’s success probability in the original environment. Currently, there are three known “types” of game hop: transitions based on indistinguishability, transitions based on failure events, and bridging steps. This note introduces a fourth type of game hop.