Trading Robustness for Correctness and Privacy in Certain Multiparty Computations, beyond an Honest Majority

Abstract

We improve on the classical results in information-theoreti- cally secure multiparty computation among a set of n participants, by considering the special case of the computation of the addition function over binary inputs in the secure channels model with a simultaneous broadcast channel. This simple function is a useful building block for other applications. The classical results in multiparty computation show that in this model, every function can be computed with information-theoretic security if and only if less than n/2 participants are corrupt. In this article we show that, under certain conditions, this bound can be overcome.

More precisely, let t ^(p), t ^(r) and t ^(c) be the privacy, robustness and correctness thresholds; that is, the minimum number of participants that must be actively corrupted in order for privacy, robustness or correctness, respectively, to be compromised. We show a series of novel tradeoffs applicable to the multiparty computation of f(x ₁, …,x _n ) = x ₁ + … + x _n for x _i  ∈ {0,1}, culminating in the most general tradeoff: t ^(p) + t ^(r) = n + 1 and t ^(c) + t ^(r) = n + 1. These tradeoffs are applicable as long as t ^(r) < n/2, which implies that, at the cost of reducing robustness, privacy and correctness are achievable despite a dishonest majority (as an example, setting the robustness threshold to n/3 yields privacy and correctness thresholds of 2n/3 + 1).

We give applications to information-theoretically secure voting and anonymous message transmission, yielding protocols with the same tradeoffs.