Improving the Efficiency of Private Function Evaluation Via Optimized Universal Circuits

Private Function Encryption (PFE) enables two parties, one holding a private input x and the other in possession of a private function f, to compute f(x) in such that each party learns nothing substantial beyond f(x). PFE is typically achieved by evaluating Yao's two-party computation protocol over a universal circuit that encodes the private function into a private input. Thus, the efficiency of the PFE protocol highly relies on the size of the underlying universal circuit. A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size n). In 1976, Valiant provided a recursive construction of universal circuits and gave a theoretical construction of UC of asymptotic (multiplicative) size 4.75 n\log n respectively, which matches the asymptotic lower bound \Omega (n\log n) up to some constant factor. More recently, Kiss et al.(Eurocrypt 2016) validated the practicality of universal circuits in real-world privacy-preserving applications. Subsequent work by Günther et al.(Asiacrypt 2017) and Alhassan et al.(J. Cryptology 2020) enhanced UCs' practicality through hybrid constructions with various optimizations. This work focuses on optimizing the size efficiency of universal circuits. Our contributions are three-fold: We implement the 2-way universal circuits and evaluate their performance against other implementations, confirming our theoretical analysis.