Impossibility of VBB obfuscation with ideal constant-degree graded encodings

Rafael Pass; Abhi Shelat

doi:10.1007/978-3-662-49096-9_1

Impossibility of VBB obfuscation with ideal constant-degree graded encodings

Rafael Pass^*
, Abhi Shelat

^*Corresponding author for this work

Cornell University
University of Virginia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Scopus citations

Abstract

A celebrated result by Barak et al. (Crypto’01) shows the impossibility of general-purpose virtual black-box (VBB) obfuscation in the plain model. A recent work by Canetti, Kalai, and Paneth (TCC’15) extends this impossibility result to the random oracle model (assuming trapdoor permutations). In contrast, Brakerski-Rothblum (TCC’14) and Barak et al. (Euro- Crypt’14) show that in idealized graded encoding models, general-purpose VBB obfuscation indeed is possible; these constructions require graded encoding schemes that enable evaluating high-degree (polynomial in the size of the circuit to be obfuscated) polynomials on encodings. We show a complementary impossibility of general-purpose VBB obfuscation in idealized graded encoding models that enable only evaluation of constant-degree polynomials (assuming trapdoor permutations).

Original language	English
Title of host publication	Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings
Editors	Eyal Kushilevitz, Tal Malkin
Publisher	Springer Verlag
Pages	3-17
Number of pages	15
ISBN (Print)	9783662490952
DOIs	https://doi.org/10.1007/978-3-662-49096-9_1
State	Published - 2016
Externally published	Yes
Event	13th International Conference on Theory of Cryptography, TCC 2016 - Tel Aviv, Israel Duration: 10 Jan 2016 → 13 Jan 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9562
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Conference on Theory of Cryptography, TCC 2016
Country/Territory	Israel
City	Tel Aviv
Period	10/01/16 → 13/01/16

Funding

Funders	Funder number
Microsoft Faculty Fellowship
National Science Foundation	CCF-1214844, 0939718, 1111781, CNS-1217821, 0845811
Air Force Office of Scientific Research	FA9550-15-1-0262
Defense Advanced Research Projects Agency
Microsoft
Air Force Research Laboratory	FA8750-11-2-0211, FA8750-11-C-0080
Google

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10.1007/978-3-662-49096-9_1

Cite this

Pass, R., & Shelat, A. (2016). Impossibility of VBB obfuscation with ideal constant-degree graded encodings. In E. Kushilevitz, & T. Malkin (Eds.), Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings (pp. 3-17). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9562). Springer Verlag. https://doi.org/10.1007/978-3-662-49096-9_1

Pass, Rafael ; Shelat, Abhi. / Impossibility of VBB obfuscation with ideal constant-degree graded encodings. Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. editor / Eyal Kushilevitz ; Tal Malkin. Springer Verlag, 2016. pp. 3-17 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A celebrated result by Barak et al. (Crypto{\textquoteright}01) shows the impossibility of general-purpose virtual black-box (VBB) obfuscation in the plain model. A recent work by Canetti, Kalai, and Paneth (TCC{\textquoteright}15) extends this impossibility result to the random oracle model (assuming trapdoor permutations). In contrast, Brakerski-Rothblum (TCC{\textquoteright}14) and Barak et al. (Euro- Crypt{\textquoteright}14) show that in idealized graded encoding models, general-purpose VBB obfuscation indeed is possible; these constructions require graded encoding schemes that enable evaluating high-degree (polynomial in the size of the circuit to be obfuscated) polynomials on encodings. We show a complementary impossibility of general-purpose VBB obfuscation in idealized graded encoding models that enable only evaluation of constant-degree polynomials (assuming trapdoor permutations).",

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Pass, R & Shelat, A 2016, Impossibility of VBB obfuscation with ideal constant-degree graded encodings. in E Kushilevitz & T Malkin (eds), Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9562, Springer Verlag, pp. 3-17, 13th International Conference on Theory of Cryptography, TCC 2016, Tel Aviv, Israel, 10/01/16. https://doi.org/10.1007/978-3-662-49096-9_1

Impossibility of VBB obfuscation with ideal constant-degree graded encodings. / Pass, Rafael; Shelat, Abhi.
Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. ed. / Eyal Kushilevitz; Tal Malkin. Springer Verlag, 2016. p. 3-17 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9562).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Pass R, Shelat A. Impossibility of VBB obfuscation with ideal constant-degree graded encodings. In Kushilevitz E, Malkin T, editors, Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. Springer Verlag. 2016. p. 3-17. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-49096-9_1

Impossibility of VBB obfuscation with ideal constant-degree graded encodings

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