Indistinguishability Obfuscation for Turing Machines: Constant Overhead and Amortization

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10402)

Abstract

We study the asymptotic efficiency of indistinguishability obfuscation (\(\mathsf {i}\mathcal {O}\)) on two fronts:
  • Obfuscation size: Present constructions of indistinguishability obfuscation (\(\mathsf {i}\mathcal {O}\)) 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 \(\mathsf {i}\mathcal {O}\) 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 (bounded-input) Turing machines \(M_1,\ldots ,M_n\). We ask whether it is possible to obfuscate \(M_1,\ldots ,M_n\) using a single application of an \(\mathsf {i}\mathcal {O}\) scheme for a circuit family where the size of any circuit is independent of n as well the size of any Turing machine \(M_i\).

    In this work, we resolve this question in the affirmative, obtaining a new bootstrapping theorem for obfuscating arbitrarily many Turing machines.

In order to obtain both of these results, we develop a new template for obfuscating Turing machines that is of independent interest and likely to find applications in future. The security of our results rely on the existence of sub-exponentially secure \(\mathsf {i}\mathcal {O}\) for circuits and re-randomizable encryption schemes.

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.University of California Los AngelesLos AngelesUSA
  2. 2.Johns Hopkins UniversityBaltimoreUSA
  3. 3.University of California Los AngelesLos AngelesUSA

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