Randomized requantization with local differential privacy

Abstract

In this paper we study how individual sensors can compress their observations in a privacy-preserving manner. We propose a randomized requantization scheme that guarantees local differential privacy, a strong model for privacy in which individual data holders must mask their information before sending it to an untrusted third party. For our approach, the problem becomes an optimization over discrete mem-oryless channels between the sensor observations and their compressed version. We show that for a fixed compression ratio, finding privacy-optimal channel subject to a distortion constraint is a quasiconvex optimization problem that can be solved by the bisection method. Our results indicate interesting tradeoffs between the privacy risk, compression ratio, and utility, or distortion. For example, in the low distortion regime, we can halve the bit rate at little cost in distortion while maintaining the same privacy level. We illustrate our approach for a simple example of privatizing and recompressing lowpass signals and show that it yields better tradeoffs than existing approaches based on noise addition. Our approach may be useful in several privacy-sensitive monitoring applications envisioned for the Internet of Things (IoT).