Hashing garbled circuits for free

Abstract

We introduce Free Hash, a new approach to generating Garbled Circuit (GC) hash at no extra cost during GC generation. This is in contrast with state-of-the-art approaches, which hash GCs at computational cost of up to 6× of GC generation. GC hashing is at the core of the cut-and-choose technique of GC-based secure function evaluation (SFE). Our main idea is to intertwine hash generation/verification with GC generation and evaluation. While we allow an adversary to generate a GC GC whose hash collides with an honestly generated GC, such a GC w.h.p. will fail evaluation and cheating will be discovered. Our GC hash is simply a (slightly modified) XOR of all the gate table rows of GC. It is compatible with Free XOR and half-gates garbling, and can be made to work with many cut-and-choose SFE protocols. With today’s network speeds being not far behind hardware-assisted fixed-key garbling throughput, eliminating the GC hashing cost will significantly improve SFE performance. Our estimates show substantial cost reduction in typical settings, and up to factor 6 in specialized applications relying on GC hashes. We implemented GC hashing algorithm and report on its performance.