A subexponential construction of graph coloring for multiparty computation

Abstract

Abstract. We show the first deterministic construction of an unconditionally secure multiparty computation (MPC) protocol in the passive adversarial model over black-box non-Abelian groups which is both optimal and has subexponential complexity of construction. More specifically, following the result of that the problem of MPC over non-Abelian groups can be reduced to finding a t-reliable n-coloring of planar graphs, we show the construction of such a graph which allows a path from the input nodes to the output nodes when any t-party subset is in the possession of the adversary. Unlike the (deterministic) constructions from our construction is subexponential and optimal at the same time, i.e., it is secure for any t < n 2 .