Highlights:
- Introduces ModularSubsetSelection (MSS), a new algorithm for locally differentially private frequency estimation.
- Uses Residue Number Systems (RNS) to reduce communication cost and improve computational efficiency.
- Achieves comparable accuracy to leading privacy protocols like SubsetSelection (SS) and ProjectiveGeometryResponse (PGR).
- Demonstrates lower reconstruction-attack success rates in practical experiments.
TLDR:
Héber H. Arcolezi’s new algorithm, ModularSubsetSelection (MSS), brings a major advance in locally differentially private data analysis by leveraging Residue Number Systems for faster, more secure, and bandwidth-efficient frequency estimation.
A significant advancement in data privacy has emerged with the introduction of ModularSubsetSelection (MSS), a new algorithm designed for locally differentially private (LDP) frequency estimation. Developed by Héber H. Arcolezi, the method focuses on optimizing the balance between data security, accuracy, and efficiency—critical aspects of preserving user privacy in large-scale digital data systems. By encoding information using a Residue Number System (RNS), MSS allows users to communicate their data in a compact and privacy-preserving form that greatly reduces network load.
Traditional LDP protocols like SubsetSelection (SS) and ProjectiveGeometryResponse (PGR) have been widely used but often demand high communication costs and complex server-side decoding processes. Arcolezi’s ModularSubsetSelection solves these bottlenecks by encoding each user’s input across multiple pairwise-coprime moduli and transmitting only a single perturbed residue and its index. This method cuts the communication cost down to as few as \u27log bits, depending on the moduli used. As a result, it drastically reduces the bandwidth required from each participating device, an important step for scaling privacy-preserving computation in cloud environments and edge devices.
From a computational standpoint, the server-side decoding process of MSS benefits from efficient linear solver iterations derived from LSMR methods, achieving practical runtime complexities that scale as Θ(n + k log k) when moduli are well chosen. This makes MSS significantly faster in reconstructing frequency estimates compared to competing approaches while maintaining worst-case mean squared error (MSE) within a constant factor of state-of-the-art protocols. Beyond performance gains, the algorithm also enhances privacy guarantees—experimental results show it achieves the lowest reconstruction-attack success rates among evaluated LDP methods. MSS thus represents a compelling new direction for secure, efficient analytics in privacy-sensitive domains such as healthcare, social data aggregation, and federated learning.
Technically, MSS innovates through its integration of RNS-based encoding with a statistically optimal SubsetSelection mechanism. Users randomly select an index corresponding to one of the moduli, apply a differential privacy perturbation to the respective residue, and transmit both values to the server. The server aggregates these partial residues across all users and reconstructs the estimated distribution using linear iterative methods. This efficient encoding-decoding pipeline not only simplifies implementation but also achieves high performance without sacrificing security, setting a new benchmark for privacy-preserving computation frameworks.
Source:
Source:
Original research paper: Héber H. Arcolezi, ‘Private Frequency Estimation Via Residue Number Systems’, arXiv:2511.11569 [cs.CR], https://doi.org/10.48550/arXiv.2511.11569