Recent years have seen significant interest in designing networks that are self-healing in the sense that they can automatically recover from adversarial attacks. Previous work shows that it is possible for a network to automatically recover, even when an adversary repeatedly deletes nodes in the network. However, there have not yet been any algorithms that self-heal in the case where an adversary takes over nodes in the network. In this paper, we address this gap. In particular, we describe a communication network over n nodes that ensures the following properties, even when an adversary controls up to t <= (1 8 - )n nodes, for any non-negative . First, the network provides a point-to-point communication with bandwidth and latency costs that are asymptotically optimal. Second, the expected total number of message corruptions is O(t(log* n)^2) before the adversarially controlled nodes are effectively quarantined so that they cause no more corruptions. Empirical results show that our algorithm can reduce the bandwidth cost by up to a factor of 70.
Our results are also similar in spirit to those of Saia and Young @cite_9 and @cite_18 , which both show how to reduce message complexity when transmitting a message across a quorum path of length @math . The first result, @cite_9 , achieves expected message complexity of @math by use of bipartite expanders. However, this result is impractical due to high hidden constants and high setup costs. The second result, @cite_18 , achieves expected message complexity of @math . However, this second result requires the sender to iteratively contact a member of each quorum in the quorum path.
@cite_9 @cite_18
1971843894 2116910210
Several recent research results describe how to design Distributed Hash Tables (DHTs) that are robust to adversarial attack via Byzantine faults. Unfortunately, all of these results require a significant blowup in communication costs over standard DHTs. For example, to perform a lookup operation, all such robust DHTs of which we are aware require sending O(log^3n) messages while standard DHTs require sending only O(logn), where n is the number of nodes in the network. In this paper, we describe protocols to reduce the communication costs of all such robust DHTs. In particular, we give a protocol to reduce the number of messages sent to perform a lookup operation from O(log^3n) to O(log^2n) in expectation. Moreover, we also give a protocol for sending a large (i.e. containing @W(log^4n) bits) message securely through a robust DHT that requires, in expectation, only a constant blowup in the total number of bits sent compared with performing the same operation in a standard DHT. This is an improvement over the O(log^2n) bit blowup that is required to perform such an operation in all current robust DHTs. Both of our protocols are robust against an adaptive adversary. There are several analytical results on distributed hash tables (DHTs) that can tolerate Byzantine faults. Unfortunately, in such systems, operations such as data retrieval and message sending incur significant communication costs. For example, a simple scheme used in many Byzantine fault-tolerant DHT constructions of @math nodes requires @math messages, this is likely impractical for real-world applications. The previous best known message complexity is @math in expectation , however, the corresponding protocol suffers from prohibitive costs owing to hidden constants in the asymptotic notation and setup costs. In this paper, we focus on reducing the communication costs against a computationally bounded adversary. We employ threshold cryptography and distributed key generation to define two protocols both of which are more efficient than existing solutions. In comparison, our first protocol is deterministic with @math message complexity and our second protocol is randomized with expected @math message complexity. Further, both the hidden constants and setup costs for our protocols are small and no trusted third party is required. Finally, we present results from micro benchmarks conducted over PlanetLab showing that our protocols are practical for deployment under significant levels of churn and adversarial behaviour.