Statistically-secure ORAM with Õ(log2 n) overhead

Kai Min Chung; Zhenming Liu; Rafael Pass

doi:10.1007/978-3-662-45608-8_4

Statistically-secure ORAM with Õ(log² n) overhead

Kai Min Chung, Zhenming Liu, Rafael Pass

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

Abstract

We demonstrate a simple, statistically secure, ORAM with computational overhead Õ(log² n); previous ORAM protocols achieve only computational security (under computational assumptions) or require Ω(log³ n) overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware.

Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a “supermarket” problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of “upset” customers in the “supermarket” problem.

Original language	English
Title of host publication	Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II
Editors	Palash Sarkar, Tetsu Iwata
Publisher	Springer Verlag
Pages	62-81
Number of pages	20
ISBN (Electronic)	9783662456071
DOIs	https://doi.org/10.1007/978-3-662-45608-8_4
State	Published - 2014
Externally published	Yes
Event	20th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2014 - Kaoshiung, Taiwan, Province of China Duration: 7 Dec 2014 → 11 Dec 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8874

Conference

Conference	20th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2014
Country/Territory	Taiwan, Province of China
City	Kaoshiung
Period	7/12/14 → 11/12/14

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-45608-8_4

Cite this

Chung, K. M., Liu, Z., & Pass, R. (2014). Statistically-secure ORAM with Õ(log² n) overhead. In P. Sarkar, & T. Iwata (Eds.), Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II (pp. 62-81). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8874). Springer Verlag. https://doi.org/10.1007/978-3-662-45608-8_4

Chung, Kai Min ; Liu, Zhenming ; Pass, Rafael. / Statistically-secure ORAM with Õ(log² n) overhead. Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II. editor / Palash Sarkar ; Tetsu Iwata. Springer Verlag, 2014. pp. 62-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We demonstrate a simple, statistically secure, ORAM with computational overhead {\~O}(log2 n); previous ORAM protocols achieve only computational security (under computational assumptions) or require Ω(log3 n) overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware.Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a “supermarket” problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of “upset” customers in the “supermarket” problem.",

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Chung, KM, Liu, Z & Pass, R 2014, Statistically-secure ORAM with Õ(log² n) overhead. in P Sarkar & T Iwata (eds), Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8874, Springer Verlag, pp. 62-81, 20th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2014, Kaoshiung, Taiwan, Province of China, 7/12/14. https://doi.org/10.1007/978-3-662-45608-8_4

Statistically-secure ORAM with Õ(log² n) overhead. / Chung, Kai Min; Liu, Zhenming; Pass, Rafael.
Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II. ed. / Palash Sarkar; Tetsu Iwata. Springer Verlag, 2014. p. 62-81 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8874).

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

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AB - We demonstrate a simple, statistically secure, ORAM with computational overhead Õ(log2 n); previous ORAM protocols achieve only computational security (under computational assumptions) or require Ω(log3 n) overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware.Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a “supermarket” problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of “upset” customers in the “supermarket” problem.

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Chung KM, Liu Z, Pass R. Statistically-secure ORAM with Õ(log² n) overhead. In Sarkar P, Iwata T, editors, Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II. Springer Verlag. 2014. p. 62-81. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-45608-8_4