Refine
Document Type
Keywords
- Anonymity (1)
- DHT (1)
- Node lookup (1)
- Onion routing (1)
- Tor (1)
- infinite horizon (1)
- necessary optimality conditions (1)
- vector-valued optimal control (1)
Institute
Node discovery is a fundamental service for any overlay network. It is a particular challenge to provide unbiased discovery in untrustworthy environments, e.g., anonymization networks. Although a major line of research focused on solving this problem, proposed methods have been shown to be vulnerable either to active attacks or to leak routing information, both threatening the anonymity of users. In response, we propose GuardedGossip—a novel gossip-based node discovery protocol—that achieves an unbiased random node discovery in a fully-decentralized and highly-scalable fashion. It is built on top of a Chord distributed hash table (DHT) and relies on witness nodes and bound checks to resist active attacks. To limit routing information leakages, GuardedGossip uses gossiping to create uncertainty in the process of node discovery. By incorporating the principles of DHTs with the unstructured nature of gossiping in a subtle way, we profit from the strengths of both techniques while carefully mitigating their shortcomings. We show that GuardedGossip provides a sufficient level of security for users even if 20% of the participating nodes are malicious. Concurrently, our system scales gracefully and provides an adequate overhead for its security and privacy benefits.
We consider a class of infinite horizon optimal control problems with vector-valued states and controls involving the Lebesgue integral in the objective and a linear dynamics. The key idea is to show that the solutions of the state-equation belong to a weighted Hilbert space, due to a natural growth condition. This allows to introduce the weighted Sobolev space as the state space and the weighted Lebesgue space as the control space in the problem setting. We answer the fundamental question of how one can choose the weight function in dependence of the system dynamics. In the setting of Hilbert spaces, we show a Pontryagin-type maximum principle. Therefore, we use techniques from earlier publications of the authors. In contrast to these publications, we deal with vector-valued states and controls, here. These vector-valued problems arise in many applications. The maximum principle also includes a transversality condition which makes the difference to related publications in the field of necessary optimality conditions. This condition brings advantages for the numerical calculations of the solution by indirect methods, like a pseudospectral method.