Private join and compute (PJC) is a paradigm where two parties owing their private database securely join their databases and compute a function over the combined database. Inner product PJC, introduced by Lepoint et al. (Asiacrypt’21), is a class of PJC that has a wide range of applications such as secure analysis of advertising campaigns. In this computation, two parties, each of which has a set of identifier-value pairs, compute the inner product of the values after the (inner) join of their databases with respect to the identifiers. They proposed inner product PJC protocols that are specialized for the unbalanced setting where the input sizes of both parties are significantly different and not suitable for the balanced setting where the sizes of two inputs are relatively close.

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.