Practically Efficient Secure Computation of Rank-based Statistics Over Distributed Datasets

TL;DR

This paper introduces a practical, secure, and efficient method for computing rank-based statistics over distributed datasets in a malicious setting, avoiding privacy leaks and improving efficiency over previous solutions.

Contribution

It presents a novel, modular protocol for secure rank-based statistics computation with optimized rounds, stronger security, and no privacy-accuracy trade-off, applicable with homomorphic encryption or secret-sharing.

Findings

Achieves $O(N ext{log}||R||)$ time complexity, outperforming previous $O(N^2 ext{log}||R||)$ solutions.

Provides a UC-secure instantiation using threshold Paillier cryptosystem.

Offers protocols with at most $ ext{log}||R||$ rounds, optimized for efficiency and security.

Abstract

In this paper, we propose a practically efficient model for securely computing rank-based statistics, e.g., median, percentiles and quartiles, over distributed datasets in the malicious setting without leaking individual data privacy. Based on the binary search technique of Aggarwal et al. (EUROCRYPT \textquotesingle 04), we respectively present an interactive protocol and a non-interactive protocol, involving at most $\log ||R||$ rounds, where $||R||$ is the range size of the dataset elements. Besides, we introduce a series of optimisation techniques to reduce the round complexity. Our computing model is modular and can be instantiated with either homomorphic encryption or secret-sharing schemes. Compared to the state-of-the-art solutions, it provides stronger security and privacy while maintaining high efficiency and accuracy. Unlike differential-privacy-based solutions, it does not suffer a trade-off between accuracy and privacy. On the other hand, it only involves $O(N \log ||R||)$ time complexity, which is far more efficient than those bitwise-comparison-based solutions with $O(N^2\log ||R||)$ time complexity, where $N$ is the dataset size. Finally, we provide a UC-secure instantiation with the threshold Paillier cryptosystem and $\Sigma$-protocol zero-knowledge proofs of knowledge.