Randomized Shellsort: a simple oblivious sorting algorithm

In this paper, we describe a randomized Shellsort algorithm. This algorithm is a simple, randomized, data-oblivious ver-sion of the Shellsort algorithm that always runs inO(n log n) time and succeeds in sorting any given input permutation with very high probability. 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 con-version of this Monte Carlo algorithm to its Las Vegas equiv-alent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability. 1