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On Extractability Obfuscation

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 8349)

Abstract

We initiate the study of extractability obfuscation, a notion first suggested by Barak et al. (JACM 2012): An extractability obfuscator \(e{\mathcal{O}}\) for a class of algorithms \(\mathcal{M}\) guarantees that if an efficient attacker \(\mathcal{A}\) can distinguish between obfuscations \(e{\mathcal O}(M_1), e{\mathcal O}(M_2)\) of two algorithms \(M_1,M_2 \in{\mathcal{M}}\), then \(\mathcal{A}\) can efficiently recover (given M 1 and M 2) an input on which M 1 and M 2 provide different outputs.

  • We rely on the recent candidate virtual black-box obfuscation constructions to provide candidate constructions of extractability obfuscators for NC 1; next, following the blueprint of Garg et al. (FOCS 2013), we show how to bootstrap the obfuscator for NC 1 to an obfuscator for all non-uniform polynomial-time Turing machines. In contrast to the construction of Garg et al., which relies on indistinguishability obfuscation for NC 1, our construction enables succinctly obfuscating non-uniform Turing machines (as opposed to circuits), without turning running-time into description size.

  • We introduce a new notion of functional witness encryption, which enables encrypting a message m with respect to an instance x, language L, and function f, such that anyone (and only those) who holds a witness w for x ∈ L can compute f(m,w) on the message and particular known witness. We show that functional witness encryption is, in fact, equivalent to extractability obfuscation.

  • We demonstrate other applications of extractability extraction, including the first construction of fully (adaptive-message) indistinguishability-secure functional encryption for an unbounded number of key queries and unbounded message spaces.

  • We finally relate indistinguishability obfuscation and extractability obfuscation and show special cases when indistinguishability obfuscation can be turned into extractability obfuscation.

Keywords

  • Encryption Scheme
  • Signature Scheme
  • Turing Machine
  • Homomorphic Encryption
  • Message Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2014 International Association for Cryptologic Research

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Boyle, E., Chung, KM., Pass, R. (2014). On Extractability Obfuscation. In: Lindell, Y. (eds) Theory of Cryptography. TCC 2014. Lecture Notes in Computer Science, vol 8349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54242-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-54242-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

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