The classic multiparty computation protocols are defined around " Untrusted parties trying to compute something together".
But is there a cryptographic abstraction for, "Trusted parties trying to compute together in presence of untrusted server"?
Basically, I am looking for something like multi-player homomorphic encryption for cloud based services. Current homomorphic encryption schemes are two player setup (just a client and server), where client wants to outsource her computation to an untrusted server , but this abstraction does not stretch for most of the cloud based applications, say privacy preserving Facebook or tax processing cloud application where multiple people are involved using a cloud server.
There is a surge in research of functional encryption and its variants (IBE,PBE,ABE, etc.), but they reveal the end-result in plain text.