Paper 2013/687 Original: eprint.iacr.org/2013/687 ↗

How to Compress (Reusable) Garbled Circuits

Abstract

A fundamental question about (reusable) circuit garbling schemes is: how small can the garbled circuit be? Our main result is a reusable garbling scheme which produces garbled circuits that are the same size as the original circuit {\em plus} an additive $\mathsf{poly}(\secp,d)$ bits, where $\secp$ is the security parameter and $d$ is the circuit depth. Save the additive $\mathsf{poly}(\secp,d)$ factor, this is the best one could hope for. In contrast, all previous constructions of even single-use garbled circuits incurred a {\em multiplicative} $\mathsf{poly}(\secp)$ blowup. Our techniques result in constructions of attribute-based and (single key secure) functional encryption schemes where the secret key of a depth $d$ circuit $C$ consists of $C$ itself, {\em plus} $\mathsf{poly}(\secp,d)$ additional bits. All of these constructions are based on the subexponential hardness of the learning with errors problem. We also study the dual question of how short the garbled inputs can be, relative to the original input. We demonstrate a (different) reusable circuit garbling scheme, based on multilinear maps, where the size of the garbled input is the same as that of the original input, {\em plus} a $\mathsf{poly}(\secp,d)$ factor. Similar to the above, this also results in attribute-based and (single key secure) functional encryption schemes where the size of the ciphertext encrypting an input $x$ is the same as that of $x$, plus $\mathsf{poly}(\secp,d)$ additional bits.