Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs

Carmit Hazay

doi:10.1007/978-3-662-46497-7_4

Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs

Carmit Hazay

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

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

30 Scopus citations

Abstract

In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [6] technique (CRYPTO 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulationbased definitions in the presence of malicious adversaries.

Original language	English
Title of host publication	Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings
Editors	Yevgeniy Dodis, Jesper Buus Nielsen
Publisher	Springer Verlag
Pages	90-120
Number of pages	31
ISBN (Electronic)	9783662464960
DOIs	https://doi.org/10.1007/978-3-662-46497-7_4
State	Published - 2015
Event	12th Theory of Cryptography Conference, TCC 2015 - Warsaw, Poland Duration: 23 Mar 2015 → 25 Mar 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9015
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th Theory of Cryptography Conference, TCC 2015
Country/Territory	Poland
City	Warsaw
Period	23/03/15 → 25/03/15

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2015.

Keywords

Committed Oblivious PRF
Efficient Secure Computation
Oblivious Polynomial Evaluation
Secure Set-Intersection

Access to Document

10.1007/978-3-662-46497-7_4

Cite this

Hazay, C. (2015). Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. In Y. Dodis, & J. B. Nielsen (Eds.), Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings (pp. 90-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9015). Springer Verlag. https://doi.org/10.1007/978-3-662-46497-7_4

Hazay, Carmit. / Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings. editor / Yevgeniy Dodis ; Jesper Buus Nielsen. Springer Verlag, 2015. pp. 90-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [6] technique (CRYPTO 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulationbased definitions in the presence of malicious adversaries.",

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Hazay, C 2015, Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. in Y Dodis & JB Nielsen (eds), Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9015, Springer Verlag, pp. 90-120, 12th Theory of Cryptography Conference, TCC 2015, Warsaw, Poland, 23/03/15. https://doi.org/10.1007/978-3-662-46497-7_4

Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. / Hazay, Carmit.
Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings. ed. / Yevgeniy Dodis; Jesper Buus Nielsen. Springer Verlag, 2015. p. 90-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9015).

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

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AB - In this paper we study the two fundamental functionalities oblivious polynomial evaluation in the exponent and set-intersection, and introduce a new technique for designing efficient secure protocols for these problems (and others). Our starting point is the [6] technique (CRYPTO 2011) for verifiable delegation of polynomial evaluations, using algebraic PRFs. We use this tool, that is useful to achieve verifiability in the outsourced setting, in order to achieve privacy in the standard two-party setting. Our results imply new simple and efficient oblivious polynomial evaluation (OPE) protocols. We further show that our OPE protocols are readily used for secure set-intersection, implying much simpler protocols in the plain model. As a side result, we demonstrate the usefulness of algebraic PRFs for various search functionalities, such as keyword search and oblivious transfer with adaptive queries. Our protocols are secure under full simulationbased definitions in the presence of malicious adversaries.

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Hazay C. Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. In Dodis Y, Nielsen JB, editors, Theory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings. Springer Verlag. 2015. p. 90-120. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-46497-7_4

Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

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