On Information-theoretic Measures for Quantifying Privacy Protection of Time-series Data

Privacy protection of time-series data, such as traces of household electricity usage reported by smart meters, is of much practical importance. Solutions are available to improve data privacy by perturbing clear traces to produce noisy versions visible to adversaries, e.g., in battery-based load hiding (BLH) against non-intrusive load monitoring (NILM). A foundational task for research progress in the area is the definition of privacy measures that can truly evaluate the effectiveness of proposed protection methods. It is a difficult problem since resilience against any attack algorithms known to the designer is inconclusive, given that adversaries could discover or indeed already know stronger algorithms for attacks. A more basic measure is information-theoretic in nature, which quantifies the inherent information available for exploitation by an adversary, independent of how the adversary exploits it or indeed any assumed computational limitations of the adversary. In this paper, we analyze information-theoretic measures for privacy protection and apply them to several existing protection methods against NILM. We argue that although these measures abstract away the details of attacks, the kind of information the adversary considers plays a key role in the evaluation, and that a new measure of offline conditional entropy is better suited for evaluating the privacy of perturbed real-world time-series data, compared with other existing measures.