# Efficient General-Adversary Multi-Party Computation

**Efficient General-Adversary Multi-Party Computation**

*Advances in Cryptology - ASIACRYPT 2013 - 19th International Conference on the Theory and Application of Cryptology and Information Security, Bengaluru, India, December 1-5, 2013, Proceedings, Part II*, pp. 181–200, Springer, 2013.

**Abstract.** Secure multi-party computation (MPC) allows a set P 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 Z 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 |Z|^3 bits; we present a protocol for this setting which communicates |Z|^2 bits. In the setting with statistical security, |Z|^3 bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication |Z|^2 bits is known); we present a protocol for this setting (without limitations) which communicates |Z|^1 bits.