Circuit Optimizations and Constructions

Abstract

The complexity of many cryptographic protocols, including today’s most efficient Secure Function Evaluation (SFE) protocols, depends linearly on the size of the boolean circuit representation of the function to be evaluated. In this chapter we show how to optimize boolean circuits for cryptographic protocols and give efficient circuit constructions. We first motivate protocols that allow “free” evaluation of XOR gates: (SFE), Homomorphic Encryption (HE), and zero-knowledge (Introduction). Afterwards, we give optimization algorithms that reduce the size of boolean circuits in particular when XOR gates can be evaluated “for free” in circuit optimizations. In circuit constructions we show how our optimizations allow one to construct more efficient circuits for standard functionalities such as integer comparison. We also give efficient circuit constructions for computing minima (or maxima) and for fast multiplication. As applications we consider efficient protocols for secure comparison and first-price auctions in applications: secure comparison auctions.