A Practical Universal Circuit Construction and Secure Evaluation of Private Functions

We consider general secure function evaluation (SFE) of private functions (PF-SFE). Recall, privacy of functions is often most efficiently achieved by general SFE [17,18,9] of a Universal Circuit (UC). Our main contribution is a new simple and efficient UC construction. Our circuit UCk, universal for circuits of k gates, has size ∼ 1.5k log k and depth ∼ k log k. It is up to 50% smaller than the best UC (of Valiant [15], of size ∼ 19k log k) 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. < 5000 gates) are practical for PF-SFE, our construction appears to be the best fit for many practical PF-SFE. We implement PF-SFE based on our UC and Fairplay SFE system [10].