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On the Depth of Oblivious Parallel RAM

  • T.-H. Hubert ChanEmail author
  • Kai-Min Chung
  • Elaine Shi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10624)

Abstract

Oblivious Parallel RAM (OPRAM), first proposed by Boyle, Chung, and Pass, is the natural parallel extension of Oblivious RAM (ORAM). OPRAM provides a powerful cryptographic building block for hiding the access patterns of programs to sensitive data, while preserving the paralellism inherent in the original program. All prior OPRAM schemes adopt a single metric of “simulation overhead” that characterizes the blowup in parallel runtime, assuming that oblivious simulation is constrained to using the same number of CPUs as the original PRAM.

In this paper, we ask whether oblivious simulation of PRAM programs can be further sped up if the OPRAM is allowed to have more CPUs than the original PRAM. We thus initiate a study to understand the true depth of OPRAM schemes (i.e., when the OPRAM may have access to unbounded number of CPUs). On the upper bound front, we construct a new OPRAM scheme that gains a logarithmic factor in depth and without incurring extra blowup in total work in comparison with the state-of-the-art OPRAM scheme. On the lower bound side, we demonstrate fundamental limits on the depth any OPRAM scheme—even when the OPRAM is allowed to have an unbounded number of CPUs and blow up total work arbitrarily. We further show that our upper bound result is optimal in depth for a reasonably large parameter regime that is of particular interest in practice.

Keywords

Oblivious parallel RAM Oblivious RAM Depth complexity 

Notes

Acknowledgments

We thank Rafael Pass for numerous helpful discussions and for being consistently supportive. We thank Feng-Hao Liu and Wei-Kai Lin for helpful conversations regarding the lower bound. This work is supported in part by NSF grants CNS-1314857, CNS-1514261, CNS-1544613, CNS-1561209, CNS-1601879, CNS-1617676, an Office of Naval Research Young Investigator Program Award, a DARPA Safeware grant (subcontract under IBM), a Packard Fellowship, a Sloan Fellowship, Google Faculty Research Awards, a Baidu Research Award, and a VMWare Research Award.

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  1. 1.The University of Hong KongPokfulamHong Kong
  2. 2.Academia SinicaTaipeiTaiwan
  3. 3.Cornell UniversityIthacaUSA

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