Not sure I understand precisely what you're asking. 'Generic composition' is a tricky term, because it tends to hide the assumptions underlying what we're actua

Not sure I understand precisely what you're asking. 'Generic composition' is a tricky term, because it tends to hide the assumptions underlying what we're actually composing together. Bellare and Namprempre's paper, which is the most usually cited in this sort of discussion, takes a probabilistic encryption scheme (read: something that takes a random IV) and a MAC, and results in a probabilistic AE scheme. This is obviously not the only way to model encryption and authentication schemes (SIV above transforms those same primitives into a nonce-based AE scheme instead, or DAE with a fixed nonce), but this tends to be overlooked from GC discussions. In some models, MtE and friends is OK. But the truth is that EtM is safe in the widest range of assumptions, while the other ones are more brittle.