The All-or-Nothing Nature of Two-Party Secure Computation

A function f is computationally securely computable if two computationally-bounded parties Alice, having a secret input x, and Bob, having a secret input y, can talk back and forth so that (even if one of them is malicious) (1) Bob learns essentially only f(x,y) while (2) Alice learns essentially nothing.We prove that, if any non-trivial function can be so computed, then so can every function. Consequently, the complexity assumptions sufficient and/or required for computationally securely computing f are the same for every non-trivial function f.