Efficient Ranking, Order Statistics, and Sorting under CKKS
Federico Mazzone, Maarten Everts, Florian Hahn, Andreas Peter

TL;DR
This paper introduces a highly parallelizable method for ranking, order statistics, and sorting under CKKS FHE, significantly reducing comparison depth and enabling efficient encrypted data processing.
Contribution
It shifts from swap-based techniques to SIMD-based parallel comparisons, achieving a constant comparison depth of up to 2, enhancing efficiency and hardware acceleration potential.
Findings
Ranks 128-element vector in ~5.76 seconds
Computes argmin/argmax in ~12.83 seconds
Sorts 128 elements in ~78.64 seconds
Abstract
Fully Homomorphic Encryption (FHE) enables operations on encrypted data, making it extremely useful for privacy-preserving applications, especially in cloud computing environments. In such contexts, operations like ranking, order statistics, and sorting are fundamental functionalities often required for database queries or as building blocks of larger protocols. However, the high computational overhead and limited native operations of FHE pose significant challenges for an efficient implementation of these tasks. These challenges are exacerbated by the fact that all these functionalities are based on comparing elements, which is a severely expensive operation under encryption. Previous solutions have typically based their designs on swap-based techniques, where two elements are conditionally swapped based on the results of their comparison. These methods aim to reduce the primary…
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Taxonomy
TopicsData Management and Algorithms · Bayesian Modeling and Causal Inference · Game Theory and Voting Systems
