Invited Talk: Resilient Distributed Algorithms

Following the immense recent advances in distributed networks, the explosive growth of the Internet, and our increased dependence on these infrastructures, guaranteeing the uninterrupted operation of communication networks has become a major objective in network algorithms. The modern instantiations of distributed networks, such as, the Bitcoin network and cloud computing, introduce in addition, new security challenges that deserve urgent attention in both theory and practice. This extended abstract describes our initial steps towards developing a unified framework for obtaining fast, resilient and secure distributed algorithms for fundamental graph problems. We will be focusing on two main objectives: - Initiating and establishing the theoretical exploration of security in distributed graph algorithms. Such a notion has been addressed before mainly in the context of secure multi-party computation (MPC). The heart of our approach is to develop new graph theoretical infrastructures to provide graphical secure channels between nodes in a communication network of an arbitrary topology. - Developing efficient distributed algorithms against various adversarial settings, such as, node crashes and Byzantine attacks. The main novelty in addressing these objectives is in our approach, which is based on taking a graph theoretic perspective where common notions of resilience requirements will be translated into suitably tailored combinatorial graph structures. We believe that the proposed perspective will deepen the theoretical foundations for resilient distributed computation, strengthen the connections with the areas of fault tolerant network design and information theoretic security, and provide a refreshing perspective on extensively-studied graph theoretical concepts.