Abstract.

A program obfuscator takes a program and outputs a “scrambled” version of it, where the goal is that the obfuscated program will not reveal much about its structure beyond what is apparent from executing it. There are several ways of formalizing this goal. Specifically, in indistinguishability obfuscation, first defined by Barak et al. [Advances in Cryptology - CRYPTO, 2001, Lect. Notes Comput. Sci. 2139, Springer, Berlin, Heidelberg, pp. 1–18], the requirement is that the results of obfuscating any two functionally equivalent programs (circuits) will be computationally indistinguishable. In 2013, a fascinating candidate construction for indistinguishability obfuscation was proposed by Garg et al. [Proceedings of the Symposium on Theory of Computing Conference, STOC, ACM, 2013, pp. 467–476]. This has led to a flurry of discovery of intriguing constructions of primitives and protocols whose existence was not previously known (for instance, fully deniable encryption by Sahai and Waters [Proceedings of the Symposium on Theory of Computing, 2014, STOC, pp. 475–484]). Most of them explicitly rely on additional hardness assumptions, such as one-way functions. Our goal is to get rid of this extra assumption. We cannot argue that indistinguishability obfuscation of all polynomial-time circuits implies the existence of one-way functions, since if \(\mathsf{P} = \mathsf{NP}\) , then program obfuscation (under the indistinguishability notion) is possible. Instead, the ultimate goal is to argue that if \(\mathsf{P} \neq \mathsf{NP}\) and program obfuscation is possible, then one-way functions exist. Our main result is that if \(\mathsf{NP} \not \subseteq \mathsf{io\textsf{-}BPP}\) and there is an efficient (even imperfect) indistinguishability obfuscator, then there are one-way functions. In addition, we show that the existence of an indistinguishability obfuscator implies (unconditionally) the existence of SZK-arguments for \(\mathsf{NP}\) . This, in turn, provides an alternative version of our main result, based on the assumption of hard-on-the-average \(\mathsf{NP}\) problems. To get some of our results we need obfuscators for simple programs such as \(3\mathsf{CNF}\) circuits.

Keywords

  1. obfuscation
  2. one-way functions
  3. indistinguishability obfuscation
  4. virtual black-box

MSC codes

  1. 68Q15
  2. 94A60

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1769 - 1795
ISSN (online): 1095-7111

History

Submitted: 16 November 2015
Accepted: 2 August 2022
Published online: 20 December 2022

Keywords

  1. obfuscation
  2. one-way functions
  3. indistinguishability obfuscation
  4. virtual black-box

MSC codes

  1. 68Q15
  2. 94A60

Authors

Affiliations

Ilan Komargodski Contact the author
Hebrew University of Jerusalem, Jerusalem, Israel, and NTT Research, Sunnyvale, CA 94085 USA.
Tal Moran
Reichman University, Herzliya, Israel 4610101.
Moni Naor
Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel.
Rafael Pass
Department of Computer Science, Cornell University, Ithaca, NY 14853 USA.
Alon Rosen
Bocconi University, Milan 47010, Italy, and Reichman University, Herzliya 46150, Israel.
Eylon Yogev
Computer Science, Bar-Ilan University, Ramat-Gan 5290002, Israel.

Funding Information

Israel Science Foundation (ISF): 1774/20
BSF-NSF: 2020643
European Union Seventh Framework Programme: FP7/2007-2013, 293843
BSF
IMOS
Microsoft New Faculty Fellowship
National Science Foundation (NSF): CNS-1217821, CCF-0746990, CCF-1214844
Seventh Framework Programme: FP/2007-2013
European Research Council (ERC): 101019547
Israel Science Foundation (ISF): 1399/17
PROMETHEUS: 780701
BIU
Funding: The first author is the incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University, supported in part by an Alon Young Faculty Fellowship, by a grant from the Israel Science Foundation (ISF grant 1774/20), and by a grant from the U.S.-Israel Binational Science Foundation and the U.S. National Science Foundation (BSF-NSF grant 2020643). Most of this work was done while the first author was at the Weizmann Institute. The second author is supported by ISF grant 1790/13 and by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement 293843. The third author is supported in part by a grant from the I-CORE Program of the Planning and Budgeting Committee, the Israel Science Foundation, BSF, IMOS, and the Citi Foundation. The third author is the incumbent of the Judith Kleeman Professorial Chair. The fourth author is supported in part by an Alfred P. Sloan Fellowship, Microsoft New Faculty Fellowship, NSF Award CNS- 1217821, NSF CAREER Award CCF-0746990, NSF Award CCF-1214844, AFOSR YIP Award FA9550-10-1-0093, and DARPA and AFRL under contract FA8750-11-2-0211. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the U.S. Government. The fifth author was originally supported by ISF grant 1255/12 and by the ERC under the EU’s Seventh Framework Programme (FP/2007-2013) ERC grant agreement 307952. Currently, the fifth author is supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 101019547), by ISF grant 1399/17, and by project PROMETHEUS (grant 780701). The sixth author is supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, and by the Alter Family Foundation. Most of this work was done while the sixth author was at the Weizmann Institute.

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