Efficient general-adversary multi-party computation

Abstract

Secure multi-party computation (MPC) allows a set of n players to evaluate a function f in presence of an adversary who corrupts a subset of the players. In this paper we consider active, general adversaries, characterized by a so-called adversary structure which enumerates all possible subsets of corrupted players. In particular for small sets of players general adversaries better capture real-world requirements than classical threshold adversaries. Protocols for general adversaries are "efficient" in the sense that they require |Z|O(1) bits of communication. However, as |Z| is usually very large (even exponential in n), the exact exponent is very relevant. In the setting with perfect security, the most efficient protocol known to date communicates O(|Z|3) bits; we present a protocol for this setting which communicates O(|Z|2) bits. In the setting with statistical security, O(|Z|3) bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication O(|Z|2) bits is known); we present a protocol for this setting (without limitations) which communicates O(|Z|1) bits. © 2013 Springer-Verlag.