Simplifying Game-Based Definitions: Indistinguishability up to Correctness and Its Application to Stateful AE

Often the simplest way of specifying game-based cryptographic definitions is apparently barred because the adversary would have some trivial win. Disallowing or invalidating these wins can lead to complex or unconvincing definitions. We suggest a generic way around this difficulty. We call it indistinguishability up to correctness, or IND|C. Given games G and H and a correctness condition C we define an advantage measure Adv_{G,H,C}^indc wherein G/H distinguishing attacks are effaced to the extent that they are inevitable due to C. We formalize this in the language of oracle silencing, an alternative to exclusion-style and penalty-style definitions. We apply our ideas to a domain where game-based definitions have been cumbersome: stateful authenticated-encryption (sAE). We rework existing sAE notions and encompass new ones, like replay-free AE permitting a specified degree of out-of-order message delivery