Group rank for encrypted data

Minje Park, Jae Seon Kim, Sungchul SHIN, Sulgi Kim, Cheolwoo Park, Changdae Oh, Kyungwoo Song, Jaekyeong Jung, Hosik Choi

Keywords: privacy preserving; encrypted data; rank correlation

TL;DR: We propose an efficient method for estimating Spearman rank correlation on homomorphic encrypted data using approximate ranks to reduce computational costs in comparison operations.

Abstract:

Recently, there has been an increasing demand for privacy-preserving techniques in numerous machine learning algorithms, elevating it to a critical concern. One promising solution involves the application of homomorphic encryption (HE). This study focuses on obtaining statistics based on the ranks of HE-encrypted data as a vital tool for robust data analysis. However, computing ranks in HE comes with significant computational costs due to the necessity of comparison operations, and there is currently no efficient method available.
To address this gap, we propose an approximate rank method that exploits pairwise comparisons of data to derive ranks for encrypted information. This method effectively measures the association between two-dimensional ranks. Specifically, by utilizing approximate ranks of two variables, we estimate Spearman rank correlation without relying on perfect sorting and introduce a technique to reduce the number of required comparisons.
Numerical experiments have been conducted to validate our approach, demonstrating that the disparity in values between rank correlation and approximate rank correlation is not substantial. Notably, the processing of one block comprising 32,768 ciphertexts took approximately one minute, exhibiting observed linear complexity dependent on the number of blocks.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 4188