Cryptology ePrint Archive: Report 2015/1023

Indistinguishability Obfuscation for Turing Machines: Constant Overhead and Amortization

Prabhanjan Ananth and Abhishek Jain and Amit Sahai

Abstract: 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 (bounded-input) Turing machines M_1,...,M_n. We ask whether it is possible to obfuscate M_1,...,M_n 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 M_i.

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].

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Original Publication (with minor differences): IACR-CRYPTO-2017

Date: received 22 Oct 2015, last revised 7 Jun 2017

Contact author: prabhanjan va at gmail com

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Version: 20170607:230545 (All versions of this report)

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