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Oblivious Parallel Tight Compaction

Authors Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, Elaine Shi

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Author Details

Gilad Asharov
  • Bar-Ilan University, Ramat-Gan, Israel
Ilan Komargodski
  • NTT Research, East Palo Alto, CA, USA
Wei-Kai Lin
  • Cornell University, Ithaca, NY, USA
Enoch Peserico
  • Università degli Studi di Padova, Italy
Elaine Shi
  • Cornell University, Ithaca, NY, USA

Funding

  • Lin, Wei-Kai: Wei-Kai Lin supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant.
  • Shi, Elaine: Elaine Shi supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant.

Acknowledgements

Wei-Kai thanks Jyun-Jie Liao for reminding the similarity between superconcentrators and oblivious tight compaction.

Cite As Get BibTex

Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, and Elaine Shi. Oblivious Parallel Tight Compaction. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ITC.2020.11

Abstract

In tight compaction one is given an array of balls some of which are marked 0 and the rest are marked 1. The output of the procedure is an array that contains all of the original balls except that now the 0-balls appear before the 1-balls. In other words, tight compaction is equivalent to sorting the array according to 1-bit keys (not necessarily maintaining order within same-key balls). Tight compaction is not only an important algorithmic task by itself, but its oblivious version has also played a key role in recent constructions of oblivious RAM compilers.
We present an oblivious deterministic algorithm for tight compaction such that for input arrays of n balls requires O(n) total work and O(log n) depth. Our algorithm is in the Exclusive-Read-Exclusive-Write Parallel-RAM model (i.e., EREW PRAM, the most restrictive PRAM model), and importantly we achieve asymptotical optimality in both total work and depth. To the best of our knowledge no earlier work, even when allowing randomization, can achieve optimality in both total work and depth.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
Keywords
  • Oblivious tight compaction
  • parallel oblivious RAM
  • EREW PRAM

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