$$\mathsf {Free\ }{} \mathtt{IF} $$ : How to Omit Inactive Branches and Implement $$\mathcal {S}$$ -Universal Garbled Circuit (Almost) for Free

Abstract

Two-party Secure Function Evaluation (SFE) allows two parties to evaluate a function known to both parties on their private inputs. In some settings, the input of one of the parties is the definition of the computed function, and requires protection as well. The standard solution for SFE of private functions (PF-SFE) is to rely on Universal Circuits (UC), which can be programmed to implement any circuit of size \(s \). Recent UC optimizations report the cost of UC for \(s \)-gate Boolean circuits is \(\approx 5 s \log s \).