A practical universal circuit construction and secure evaluation of private functions

Abstract

We consider general secure function evaluation (SFE) of private functions (PF-SFE). Recall, privacy of functions is often most efficiently achieved by general SFE [18,19,10] of a Universal Circuit (UC). Our main contribution is a new simple and efficient UC construction. Our circuit UC k , universal for circuits of k gates, has size ~1.5 k log2 k and depth ~k logk. It is up to 50% smaller than the best UC (of Valiant [16], of size ~19klogk) for circuits of size up to ≈∈5000 gates. Our improvement results in corresponding performance improvement of SFE of (small) private functions. Since, due to cost, only small circuits (i.e.