Efficient Secure Three-Party Sorting with Applications to Data Analysis and Heavy Hitters

We present a three-party sorting protocol secure against passive and active adversaries in the honest majority setting. The protocol can be easily combined with other secure protocols which work on shared data, and thus enable different data analysis tasks, such as private set intersection of shared data, deduplication, and the identification of heavy hitters. The new protocol computes a stable sort. It is based on radix sort and is asymptotically better than previous secure sorting protocols. It improves on previous radix sort protocols by not having to shuffle the entire length of the items after each comparison step. We implemented our sorting protocol with different optimizations and achieved concretely fast performance. For example, sorting one million items with 32-bit keys and 32-bit values takes less than 2 seconds with semi-honest security and about 3.5 seconds with malicious security. Finding the heavy hitters among hundreds of thousands of 256-bit values takes only a few seconds, compared to close to an hour in previous work.