In the problem of reliable multiparty computation (RC), there are @math parties, each with an individual input, and the parties want to jointly compute a function @math over @math inputs. The problem is complicated by the fact that an omniscient adversary controls a hidden fraction of the parties. We describe a self-healing algorithm for this problem. In particular, for a fixed function @math , with @math parties and @math gates, we describe how to perform RC repeatedly as the inputs to @math change. Our algorithm maintains the following properties, even when an adversary controls up to @math parties, for any constant @math . First, our algorithm performs each reliable computation with the following amortized resource costs: @math messages, @math computational operations, and @math latency, where @math is the depth of the circuit that computes @math . Second, the expected total number of corruptions is @math , after which the adversarially controlled parties are effectively quarantined so that they cause no more corruptions.
This paper particularly builds on @cite_8 . That paper describes self-healing algorithms that provide reliable communication, with a minimum of corruptions, even when a Byzantine adversary can take over a constant fraction of the nodes in a network. While our attack model is similar to @cite_8 , reliable is more challenging than reliable communication, and hence this paper requires a significantly different technical approach. Additionally, we improve the fraction of bad parties that can be tolerated from @math to @math .
@cite_8
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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 '—' e)n nodes, for any non-negative e. 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 bandwidth cost by up to a factor of 70.