Asymptotically tight bounds for composing ORAM with PIR

Ittai Abraham, Christopher W. Fletcher, Kartik Nayak, Benny Pinkas, Ling Ren

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

22 Scopus citations


Oblivious RAM (ORAM) is a cryptographic primitive that allows a trusted client to outsource storage to an untrusted server while hiding the client’s memory access patterns to the server. The last three decades of research on ORAMs have reduced the bandwidth blowup of ORAM schemes from O(√N) to O(1). However, all schemes that achieve a bandwidth blowup smaller than O(logN) use expensive computations such as homomorphic encryptions. In this paper, we achieve a sub-logarithmic bandwidth blowup of O(logd N) (where d is a free parameter) without using expensive computation. We do so by using a d-ary tree and a two server private information retrieval (PIR) protocol based on inexpensive XOR operations at the servers. We also show a Ω(logcD N) lower bound on bandwidth blowup in the modified model involving PIR operations. Here, c is the number of blocks stored by the client and D is the number blocks on which PIR operations are performed. Our construction matches this lower bound implying that the lower bound is tight for certain parameter ranges. Finally, we show that C-ORAM (CCS 15) and CHf-ORAM violate the lower bound. Combined with concrete attacks on C-ORAM/CHf-ORAM, we claim that there exist security flaws in these constructions.

Original languageEnglish
Title of host publicationPublic-Key Cryptography – PKC 2017 - 20th IACR International Conference on Practice and Theory in Public-Key Cryptography, Proceedings
EditorsSerge Fehr
PublisherSpringer Verlag
Number of pages30
ISBN (Print)9783662543641
StatePublished - 2017
Event20th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2017 - Amsterdam, Netherlands
Duration: 28 Mar 201731 Mar 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10174 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th IACR International Conference on Practice and Theory of Public-Key Cryptography, PKC 2017
City Amsterdam

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2017.


We would like to thank authors of C-ORAM (Tarik Moataz, Travis Mayberry and Erik-Oliver Blass) for discussions and inputs on algorithmic details of C-ORAM. We would like to thank Dahlia Malkhi, Jonathan Katz, Elaine Shi, Hubert Chan and Xiao Wang for helpful discussions on this work. This work is funded in part by NSF awards #1111599, #1563722 and a Google Ph.D. Fellowship award.

FundersFunder number
National Science Foundation1563722, 1111599


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