The Least Information Set Needed by Privacy Attackers

This article studies privacy-preserving problems focusing on the information that is available to the attacker. For a class of general linear average consensus algorithms, we identify the least information set required by an attacker to infer the initial value of the target node. We then propose a novel algorithm that protects the initial value effectively if the attacker fails to have this least information. Furthermore, we show that the initial value of nodes may be disclosed even if the attacker does not know any information exchanged between the target node and its neighbors. Finally, we propose a novel eavesdropping algorithm if the least information is available. Several numerical examples are given to verify the validity of our results.