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

TLDR: A self-healing algorithm for the problem of reliable multiparty computation, in which n parties want to jointly compute a function f over n inputs, that can reduce message cost by a factor of 432 when compared with algorithms that are not self- healing.

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.