A practical analysis of oblivious sorting algorithms for secure multi-party computation

Abstract

Cryptographic secure computing methods like secure multiparty computation, circuit garbling and homomorphic encryption are becoming practical enough to be usable in applications. Such applications need special data-independent sorting algorithms to preserve privacy. In this paper, we describe the design and implementation of four different oblivious sorting algorithms. We improve two earlier designs based on sorting networks and quicksort with the capability of sorting matrices. We also propose two new designs—a naive comparison-based sort with a low round count and an oblivious radix sort algorithm that does not require any private comparisons. For all these algorithms, we present thorough complexity and performance analysis including detailed breakdown of running-time, network and memory usage.