Randomized Shellsort: A Simple Oblivious Sorting Algorithm

TL;DR

This paper introduces a randomized, data-oblivious version of Shellsort that is simple, efficient, and suitable for privacy-preserving computations, with high-probability guarantees on sorting performance.

Contribution

It presents the first randomized Shellsort algorithm that is both simple and provably runs in O(n log n) time with high probability, enhancing privacy-preserving applications.

Findings

Runs in O(n log n) time with high probability

Data-oblivious and suitable for secure multi-party computation

First provably efficient randomized Shellsort implementation

Abstract

In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high probability. Thus, randomized Shellsort is simultaneously simple, time-optimal, and data-oblivious. Taken together, these properties imply applications in the design of new efficient privacy-preserving computations based on the secure multi-party computation (SMC) paradigm. In addition, by a trivial conversion of this Monte Carlo algorithm to its Las Vegas equivalent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability.