) Martin Hirt 1 , Ueli Maurer 1 , and Bartosz Przydatek 2?? 1 ETH Zurich, Switzerland, fhirt,maurerg@inf.ethz.ch 2 Carnegie Mellon University, USA, bartosz@cs.cmu.edu Asiacrypt 2000 Abstract. Since the introduction of secure multi-party computation, all proposed protocols that provide security against cheating players suer from very high communication complexities. The most ecient unconditionally secure protocols among n players, tolerating cheating by up to t < n=3 of them, require communicating O(n 6 ) eld elements for each multiplication of two elements, even if only one player cheats. In this paper, we propose a perfectly secure multi-party protocol which requires communicating O(n 3 ) eld elements per multiplication. In this protocol, the number of invocations of the broadcast primitive is independent of the size of the circuit to be computed. The proposed techniques are generic and apply to other protocols for robust distributed computations. Furthe...