On the Asymptotic Capacity of Information-Theoretic Privacy-Preserving Epidemiological Data Collection

Area of Science:

• Information Theory
• Cryptography
• Data Privacy
• Epidemiological Studies

Background:

• Current data-sharing systems, especially in epidemiology, collect excessive personal data, leading to privacy intrusions.
• Existing cryptographic and information theory advancements aim to enhance data privacy but require novel approaches for distributed systems.

Purpose of the Study:

• To formulate and analyze a new distributed multiparty computation problem: privacy-preserving epidemiological data collection.
• To determine the optimal data collection rate under strict privacy constraints for users, servers, and data collectors.
• To establish theoretical limits for secure data collection in untrusted environments.

Main Methods:

• Formulation of a novel distributed multiparty computation problem for privacy-preserving data collection.
• Development of an asymptotic capacity-achieving scheme using cross-subspace alignment for E < N-1.
• Proof of an upper bound for the asymptotic rate and analysis of conditions where positive capacity is not achievable (E ≥ N-1).

Main Results:

• An optimal data collection rate was defined and an achievable scheme was proposed for E < N-1.
• A theoretical upper bound on the achievable rate was proven, meeting the achievable scheme as the number of users approaches infinity.
• It was demonstrated that a positive asymptotic capacity is unattainable when E ≥ N-1.

Conclusions:

• The study establishes the asymptotic capacity for privacy-preserving epidemiological data collection, providing the best achievable performance.
• The findings advance research in information theory and data privacy, offering a framework for secure collection of sensitive health data.
• The proposed methods and theoretical bounds are crucial for designing more secure and efficient epidemiological studies.