A theoretical and empirical evaluation of an algorithm for self-healing computation

Abstract

In the problem of reliable multiparty computation (RMC), there are n parties, each with an individual input, and the parties want to jointly compute a function f over n inputs; note that it is not required to keep the inputs private. 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 RMC repeatedly as the inputs to f change. Our algorithm maintains the following properties, even when an adversary controls up to $t \le (\frac{1}{4} - \epsilon ) n$ parties, for any constant $\epsilon >0$. First, our algorithm performs each reliable computation with the following amortized resource costs: $O(m + n \log n)$ messages, $O(m + n \log n)$ computational operations, and $O(\ell )$ latency, where $\ell$ 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. Empirical results show that our algorithm can reduce message cost by a factor of 432 when compared with algorithms that are not self-healing.