## Cryptology ePrint Archive: Report 2020/125

Oblivious Parallel Tight Compaction

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

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 EREW Parallel-RAM model (i.e., 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.

Category / Keywords: cryptographic protocols / oblivious algorithms; information theoretic cryptography

Original Publication (in the same form): Information-Theoretic Cryptography (ITC) 2020

Date: received 5 Feb 2020, last revised 6 Apr 2020

Contact author: Gilad Asharov at biu ac il,ilan komargodski@ntt-research com,wklin@cs cornell edu,enoch@dei unipd it,runting@gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/125

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