Indistinguishability Obfuscation for Turing Machines: Constant Overhead and Amortization

We study the asymptotic efficiency of indistinguishability obfuscation (iO) on two fronts: • Obfuscation size: Present constructions of indistinguishability obfuscation (iO) create obfuscated programs where the size of the obfuscated program is at least a multiplicative factor of security parameter larger than the size of the original program. In this work, we construct the first iO scheme for (bounded-input) Turing machines that achieves only a constant multiplicative overhead in size. The constant in our scheme is, in fact, 2. • Amortization: Suppose we want to obfuscate an arbitrary polynomial number of (boundedinput) Turing machinesM1, . . . ,Mn. We ask whether it is possible to obfuscateM1, . . . ,Mn using a single application of an iO scheme for a circuit family where the size of any circuit is independent of n as well the size of any Turing machine Mi. In this work, we resolve this question in the affirmative, obtaining a new bootstrapping theorem for obfuscating arbitrarily many Turing machines. Our results rely on the existence of sub-exponentially secure iO for circuits and re-randomizable encryption schemes. In order to obtain these results, we develop a new template for obfuscating Turing machines that is of independent interest and has recently found application in subsequent work on patchable obfuscation [Ananth et al, EUROCRYPT’17]. University of California Los Angeles. Email: [email protected]. This work was partially supported by grant #360584 from the Simons Foundation and the grants listed under Amit Sahai. Johns Hopkins University. Email: [email protected]. Supported in part by a DARPA/ARL Safeware Grant W911NF-15-C-0213 and NSF CNS-1414023. University of California Los Angeles. Email: [email protected] Research supported in part from a DARPA/ARL SAFEWARE award, NSF Frontier Award 1413955, NSF grants 1619348, 1228984, 1136174, and 1065276, BSF grant 2012378, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through the ARL under Contract W911NF-15-C-0205. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.