On Private Lossy Function Computation

In this paper, the problem of lossy function computation with secrecy and privacy constraints is considered. The considered model consists of two legitimate terminals Alice and Bob, and an eavesdropper Eve. Under a certain distortion constraint, Bob would like to compute a function of two distributed source sequences observed at Bob and Alice respectively. To assist the function computing at Bob's side, Alice is allowed to transmit messages to Bob while satisfying two conditions: 1) the information leakage about Alice's source sequence to Bob is limited, which is denoted as privacy constraint; and 2) Eve will not learn too much information about the Alice's source sequence, which is denoted as secrecy constraint. Under this model, we study the relationship among message rate, privacy constraint, secrecy constraint and the function distortion level. We fully characterized the achievable region of these parameters.