Analyzing user data while protecting the privacy of individuals remains a big challenge. Trusted execution environments (TEEs) are a possible solution as they protect processes and Virtual Machines (VMs) against malicious hosts. However, TEEs can leak access patterns to code and to the data being processed. Furthermore, when data is stored in a TEE database, the data volume required to answer a query is another unwanted side channel that contains sensitive information. Both types of information leaks, access patterns and volume patterns, allow for database reconstruction attacks.

The problem of finding the kth Ranked Element (KRE) is of particular interest in collaborative studies for financial and medical agencies alike. Many of the applications of KRE deal with sensitive information that needs to be protected. The protocol by Chandran et al. (SECRYPT'22) considers a model where multiple parties hold datasets with many elements and wish to compute the kth element of their joint dataset. In their model, all participating parties interact with a central party in a star network topology. However, they leak some intermediate information to the central party.