When is a Function Securely Computable?

A subset of a set of terminals that observe correlated signals seek to compute a given function of the signals using public communication. It is required that the value of the function be kept secret from an eavesdropper with access to the communication. We show that the function is securely computable if and only if its entropy is less than the "aided secret key" capacity of an associated secrecy generation model, for which a single-letter characterization is provided.