Generic applications of multilinear maps

Cryptographic bilinear maps -- i.e. bilinear functions f such that x=f(a,b) can easily be computed, but a cannot readily be computed from x and b, nor b from x and a -- have had a great deal of use in advanced cryptography. Extending these to multilinear maps has long been a wish of cryptographers. New constructions have recently been produced, shot down, strengthened, shot down again, and so on, in a struggle that shows no sign of ending. Hence one important question is what the generic characteristics of these multilinear map candidates are, and what protocols can be designed independent of the specific multilinear map, allowing modular replacement, as has been done in other areas of security