Succinct garbled RAM from indistinguishablity obfuscation

Abstract

In this thesis, I give the first construction of a succinct garbling scheme for RAM programs. For a program requiring space S and time T to compute, the size of its garbling is Õ(S) instead of poly(T). This construction relies on the existence of indistinguishability obfuscation, as well as the existence of injective one-way functions. As a building block, I introduce and construct a primitive called asymmetrically constrained encryption (ACE). This primitive is an encryption system for which keys can be punctured on succinctly described sets of plaintexts. For programs acting on ACE-encrypted values, I give a natural and general condition for their obfuscations to be indistinguishable, using the fact that the encryption and decryption keys can be separately punctured. This succinct garbling scheme serves as a drop-in replacement for the ubiquitous garbled circuits of Yao, but with better asymptotic parameters. In some cases, these improved parameters allow qualitatively new applications.