Fast Software Cryptography. Such an object is easier to use than a stream cipher, yet more amenable than a block cipher, it seems, for achieving extreme software speeds than a block cipher. After SEAL we now knew how to encrypt messages faster than we knew how to authenticate them. Secure Function Evaluation. They wish to evaluate some function on these private inputs in a way that reveals only the correctly-computed answer.
Voting is a standard example.
In the presence of a trusted party, each player could send his input to the trusted party, who would compute the function and return the answers. The other direction on SFE I have followed is to look at the efficiency of SFE protocols. I haven't been doing much in complexity theory of late, but perhaps I will return to it. Compared to what came later, the techniques here are very simple. To Rogaway's home page.