Today's world is highly dependent on the integrity of communication systems as the Internet, WiFi, or cellular networks. As networks become more pervasive, they are increasingly being used for communication and storage of critical as well as sensitive data and therefore impose more stringent demands on reliability and security, which must be maintained even under extreme settings such as partial power failures, natural disasters, or, most importantly, adversarial attacks. This research seeks to understand fundamental limits of protecting complex practical networks against adversarial attacks, and how these limits can be achieved by optimal secure strategies, thus bridging the gap between advanced theoretical research and the development of realistic solutions. Further, the project is able to provide a significant transformative impact on many other critical applications employing reliable networked communications, for example in the fields of healthcare, environmental monitoring, finance, etc. It also provides a platform for creating broader technological, societal, research, and educational impact as advancing information technology and its benefits to society through newly established theory and practice, an ambitious education plan, and actively engaging students from underrepresented demographics.
Specifically, the project focuses on aspects (e.g., distributed users, heterogeneity, delay requirements, actions of adversaries described by probability distributions) important in real network systems but poorly understood in current literature, and seeks to elucidate the impact of each such aspect on capacity and code design. This research aims both to characterize features of the problems and solutions (e.g., hardness of computing the rate of communication under adversarial attacks, interaction between redundancy in different network flows, and non-uniform adversarial sets) that are new to the literature, as well as to identify commonalities between the solutions required in each new scenario. These commonalities are then applied to characterize the fundamental tradeoff between security and performance in general adversarial networks. The technique employed here is via reductions, which demonstrate the relationship between two problems by showing that any solution for one can be employed to build a solution for the other. In particular, reductions are derived between noisy networks with a state chosen by the adversary and their corresponding noiseless and stateless versions, for which capacity is much easier to characterize. Further, these results lead to analytical performance guarantees for the designed secure coding strategies, thus providing guidance on specific design approaches and for those cases where capacity bounds are still open.
