A Survey of Blind Sorting Techniques: Approaches Using Fully Homomorphic Encryption

With recent advancements in cloud services, the demand for data security during outsourced computations has been increasing. Fully Homomorphic Encryption (FHE) offers a promising solution to this demand by enabling the evaluation of arbitrary functions on encrypted data. Over the years, there have been significant developments in using FHE for various applications. One interesting but still incomplete topic is the sorting of encrypted arrays. This task presents several challenges, including the choice of a base sorting algorithm and the need for efficient private comparison methods. In this paper, we present a comprehensive survey of blind sorting, providing a canonical arrangement of previous works. Furthermore, we review the core ideas from key studies, as well as the main challenges and solutions in developing efficient blind sorting algorithms.