Self-healing Computation

In the problem of reliable multiparty computation (RC), there are n parties, each with an individual input, and the parties want to jointly compute a function f over n 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 f , with n parties and m gates, we describe how to perform RC repeatedly as the inputs to f change. Our algorithm maintains the following properties, even when an adversary controls up to t ≤ ( 1 4 − )n parties, for any constant > 0. First, our algorithm performs each reliable computation with the following amortized resource costs: O(m+ n logn) messages, O(m+ n logn) computational operations, and O(`) latency, where ` is the depth of the circuit that computes f . Second, the expected total number of corruptions is O(t(log∗m)2), after which the adversarially controlled parties are effectively quarantined so that they cause no more corruptions.