Succinct Garbling and Indistinguishability Obfuscation for RAM Programs

We show how to construct succinct Indistinguishability Obfuscation (IO) schemes for RAM programs. That is, given a RAM program whose computation requires space S and time T, we generate a RAM program with size and space requirements of ~O(S) and runtime ~O(T). The construction uses non-succinct IO (i.e., IO for circuits) and injective one way functions, both with sub-exponential security. A main component in our scheme is a succinct garbling scheme for RAM programs. Our garbling scheme has the same size, space and runtime parameters as above, and requires only polynomial security of the underlying primitives. This scheme has other qualitatively new applications such as publicly verifiable succinct non-interactive delegation of computation and succinct functional encryption.