On the correlation intractability of obfuscated pseudorandom functions

Ran Canetti; Yilei Chen; Leonid Reyzin

doi:10.1007/978-3-662-49096-9_17

On the correlation intractability of obfuscated pseudorandom functions

Ran Canetti^*, Yilei Chen, Leonid Reyzin

^*Corresponding author for this work

School of Computer Science

Boston University

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

24 Scopus citations

Abstract

A family of hash functions is called “correlation intractable” if it is hard to find, given a random function in the family, an inputoutput pair that satisfies any “sparse” relation, namely any relation that is hard to satisfy for truly random functions. Indeed, correlation intractability is a strong and natural random-oracle-like property. However, it was widely considered unobtainable. In fact for some parameter settings, unobtainability has been demonstrated [26]. We construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [13].

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	389-415
Number of pages	27
ISBN (Print)	9783662490952
DOIs	https://doi.org/10.1007/978-3-662-49096-9_17
State	Published - 2016
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
Check Point Institute for Information Security
National Science Foundation	1422965, 1012798, 1413920, 1218461, 1012910
Israel Science Foundation	1523/14
Tel Aviv University

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10.1007/978-3-662-49096-9_17

Cite this

Canetti, R., Chen, Y., & Reyzin, L. (2016). On the correlation intractability of obfuscated pseudorandom functions. In E. Kushilevitz, & T. Malkin (Eds.), Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings (pp. 389-415). (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_17

Canetti, Ran ; Chen, Yilei ; Reyzin, Leonid. / On the correlation intractability of obfuscated pseudorandom functions. Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. editor / Eyal Kushilevitz ; Tal Malkin. Springer Verlag, 2016. pp. 389-415 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "On the correlation intractability of obfuscated pseudorandom functions",

abstract = "A family of hash functions is called “correlation intractable” if it is hard to find, given a random function in the family, an inputoutput pair that satisfies any “sparse” relation, namely any relation that is hard to satisfy for truly random functions. Indeed, correlation intractability is a strong and natural random-oracle-like property. However, it was widely considered unobtainable. In fact for some parameter settings, unobtainability has been demonstrated [26]. We construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [13].",

author = "Ran Canetti and Yilei Chen and Leonid Reyzin",

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Canetti, R, Chen, Y & Reyzin, L 2016, On the correlation intractability of obfuscated pseudorandom functions. 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. 389-415, 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_17

On the correlation intractability of obfuscated pseudorandom functions. / Canetti, Ran; Chen, Yilei; Reyzin, Leonid.
Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. ed. / Eyal Kushilevitz; Tal Malkin. Springer Verlag, 2016. p. 389-415 (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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AB - A family of hash functions is called “correlation intractable” if it is hard to find, given a random function in the family, an inputoutput pair that satisfies any “sparse” relation, namely any relation that is hard to satisfy for truly random functions. Indeed, correlation intractability is a strong and natural random-oracle-like property. However, it was widely considered unobtainable. In fact for some parameter settings, unobtainability has been demonstrated [26]. We construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [13].

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Canetti R, Chen Y, Reyzin L. On the correlation intractability of obfuscated pseudorandom functions. In Kushilevitz E, Malkin T, editors, Theory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings. Springer Verlag. 2016. p. 389-415. (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_17

On the correlation intractability of obfuscated pseudorandom functions

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