Function computation with privacy constraints

In this manuscript, the problem of function computation with privacy constraints is considered. The problem consists of two legitimate nodes Alice and Bob, and an eavesdropper Eve. Bob would like to compute a function, and the arguments of the function are two source observation sequences that are distributed over the legitimate nodes respectively. To make the function computable at Bob, Alice is allowed to transmit a message to Bob via a public noiseless channel, which Eve has full access to. Under this model, we study the relationship among message rate, private information leakage to Bob and equivocation of Alice's source observations at Eve, and fully single-letter characterize the region of these achievable parameter tuples.