Trading robustness for correctness and privacy in certain multiparty computations, beyond an honest majority

• Authors: Anne Broadbent;Stacey Jeffery;Samuel Ranellucci;Alain Tapp
• Venue: ICITS'12 Proceedings of the 6th international conference on Information Theoretic Security
• Year: 2012

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(x1, …,xn)=x1+…+xn for xi∈{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.