International Association
for Cryptologic Research

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 plus an additive poly(secp) bits, where secp is the security parameter. Save the additive poly(secp) factor, this is the best one could hope for. In contrast, all previous constructions of even single-use garbled circuits incurred a multiplicative poly(secp) blowup.

Our techniques result in constructions of attribute-based and (single key secure) functional encryption schemes where the secret key of a circuit C consists of C itself, plus poly(secp) 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, plus a poly(secp) factor. This improves on the result of Applebaum, Ishai, Kushilevitz and Waters (CRYPTO 2013)

who showed such a result for single-use garbling. 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 poly(secp) additional bits.