Security Versus Privacy

TL;DR

This paper explores the fundamental trade-off between privacy and security in linear query systems, showing that increasing privacy inherently weakens security guarantees, with formal optimization and differential privacy analysis.

Contribution

It introduces an optimization framework that balances privacy and security in linear query responses, revealing their inverse relationship and extending results to differential privacy.

Findings

Privacy and security levels are inversely proportional.

Optimal privacy-security trade-off is characterized by a constant product.

Results apply to both Fisher information and differential privacy frameworks.

Abstract

Linear queries can be submitted to a server containing private data. The server provides a response to the queries systematically corrupted using an additive noise to preserve the privacy of those whose data is stored on the server. The measure of privacy is inversely proportional to the trace of the Fisher information matrix. It is assumed that an adversary can inject a false bias to the responses. The measure of the security, capturing the ease of detecting the presence of the false data injection, is the sensitivity of the Kullback-Leiber divergence to the additive bias. An optimization problem for balancing privacy and security is proposed and subsequently solved. It is shown that the level of guaranteed privacy times the level of security equals a constant. Therefore, by increasing the level of privacy, the security guarantees can only be weakened and vice versa. Similar results are developed under the differential privacy framework.