Functional Privacy for Distributed Function Computation

This paper studies the secure source coding for distributed function computation with a functional privacy constraint. In particular, two distributed encoders, named Alice and Bob, observe two correlated sources and independently compress and transmit their observations to a fusion center who wants to compute a function of the two sources. A passive eavesdropper named Eve, with access to the side information, is able to listen the link between Alice and the fusion center. Two privacy constraints are considered. The first one is a functional privacy constraint for Eve, who is interested in a given function of the two sources rather than original sources. The second requirement is that the fusion center is not allowed to learn too much information about the original sources. For the proposed problem, an inner bound on the achievable rate-distortion-leakage region is characterized for the discrete memoryless setting. When the function of interest at Eve degenerates to the source X and the fusion center has access to uncoded source Y , our inner bound is tight.