Reusable Garbled Turing Machines Without FHE

Abstract

Since Yao introduced the garbled circuit concept in 1980s, it has been an open problem to design efficient reusable garbled Turing machines/circuits. Recently, Goldwasser et al. and Garg et al. answered this question affirmatively by designing reusable garbled circuits and reusable garbled Turing machines. Both of these reusable garbling schemes use fully homomorphic encryption (FHE) schemes as required building components. Here, we use multilinear maps to design a reusable Turing machine garbling scheme that will not need any FHE schemes. Though it is not clear whether our multilinear map based garbling approach could be more efficient than FHE based garbling approach, the goal of this paper is to develop alternative techniques for resuable garbling schemes to stimulate further research in this direction.