CKKS Fully Homomorphic Encryption Based Comparison and Bitonic Sorting

With the increasing importance of data security, fully homomorphic encryption (FHE) enabling privacy-preserving processing has come to the forefront. This study addresses the privacy-preserving sorting problem using FHE. Due to the nature of FHE, conventional sorting algorithms cannot be directly applied, necessitating the use of data-independent algorithms such as the Bitonic Sort Network. In the literature, Bitonic Sort networks based on CKKS perform the comparison operation through scheme switching. In this study, however, the Bitonic Sort Network comparison operation is implemented and its performance is analyzed analyzed using the CKKS scheme and the OpenFHE library. The challenges of the comparison operation within FHE are discussed, and different comparison methods are examined. The findings obtained will pave the way for the development of new high-performance sorting algorithms based on CKKS.