Communication-Efficient Laplace Mechanism for Differential Privacy via Random Quantization

TL;DR

This paper introduces a novel communication-efficient Laplace mechanism for differential privacy that uses random quantization, ensuring exact noise addition without utility loss and maintaining privacy against both server and database.

Contribution

The paper presents the first finite-communication Laplace mechanism using random quantization that preserves utility and guarantees privacy against all parties involved.

Findings

Exact Laplace noise added with finite communication

No utility degradation due to quantization

Guarantees privacy against server and database

Abstract

We propose the first method that realizes the Laplace mechanism exactly (i.e., a Laplace noise is added to the data) that requires only a finite amount of communication (whereas the original Laplace mechanism requires the transmission of a real number) while guaranteeing privacy against the server and database. Our mechanism can serve as a drop-in replacement for local or centralized differential privacy applications where the Laplace mechanism is used. Our mechanism is constructed using a random quantization technique. Unlike the simple and prevalent Laplace-mechanism-then-quantize approach, the quantization in our mechanism does not result in any distortion or degradation of utility. Unlike existing dithered quantization and channel simulation schemes for simulating additive Laplacian noise, our mechanism guarantees privacy not only against the database and downstream, but also against the honest but curious server which attempts to decode the data using the dither signals.