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A Failure-Free and Efficient Discrete Laplace Distribution for Differential Privacy in MPC

Ivan Tjuawinata, Jiabo Wang, Mengmeng Yang, Shanxiang Lyu, Huaxiong Wang, Kwok-Yan Lam

TL;DR

The paper tackles output privacy in MPC-protected distributed computations by designing discrete, bounded noise perturbations with zero failure probability, enabling $(\epsilon,0)$-DP on finite domains. It introduces two Laplace-inspired mechanisms, the Truncated Discrete Laplace (TDL) and Truncated Cumulative Laplace (TCL), and analyzes their DP properties, distance-based privacy, and accuracy. A secure MPC realization is provided, featuring a two-phase workflow with offline noise generation and online perturbation, and implemented via the ABY framework with benchmarks showing circuit complexities comparable to state-of-the-art discrete Gaussian methods. The results demonstrate practical zero-failure output privacy for secure analytics and federated-like settings, with clear paths for offline-online optimization and cryptographic efficiency.

Abstract

In an MPC-protected distributed computation, although the use of MPC assures data privacy during computation, sensitive information may still be inferred by curious MPC participants from the computation output. This can be observed, for instance, in the inference attacks on either federated learning or a more standard statistical computation with distributed inputs. In this work, we address this output privacy issue by proposing a discrete and bounded Laplace-inspired perturbation mechanism along with a secure realization of this mechanism using MPC. The proposed mechanism strictly adheres to a zero failure probability, overcoming the limitation encountered on other existing bounded and discrete variants of Laplace perturbation. We provide analyses of the proposed differential privacy (DP) perturbation in terms of its privacy and utility. Additionally, we designed MPC protocols to implement this mechanism and presented performance benchmarks based on our experimental setup. The MPC realization of the proposed mechanism exhibits a complexity similar to the state-of-the-art discrete Gaussian mechanism, which can be considered an alternative with comparable efficiency while providing stronger differential privacy guarantee. Moreover, efficiency of the proposed scheme can be further enhanced by performing the noise generation offline while leaving the perturbation phase online.

A Failure-Free and Efficient Discrete Laplace Distribution for Differential Privacy in MPC

TL;DR

The paper tackles output privacy in MPC-protected distributed computations by designing discrete, bounded noise perturbations with zero failure probability, enabling -DP on finite domains. It introduces two Laplace-inspired mechanisms, the Truncated Discrete Laplace (TDL) and Truncated Cumulative Laplace (TCL), and analyzes their DP properties, distance-based privacy, and accuracy. A secure MPC realization is provided, featuring a two-phase workflow with offline noise generation and online perturbation, and implemented via the ABY framework with benchmarks showing circuit complexities comparable to state-of-the-art discrete Gaussian methods. The results demonstrate practical zero-failure output privacy for secure analytics and federated-like settings, with clear paths for offline-online optimization and cryptographic efficiency.

Abstract

In an MPC-protected distributed computation, although the use of MPC assures data privacy during computation, sensitive information may still be inferred by curious MPC participants from the computation output. This can be observed, for instance, in the inference attacks on either federated learning or a more standard statistical computation with distributed inputs. In this work, we address this output privacy issue by proposing a discrete and bounded Laplace-inspired perturbation mechanism along with a secure realization of this mechanism using MPC. The proposed mechanism strictly adheres to a zero failure probability, overcoming the limitation encountered on other existing bounded and discrete variants of Laplace perturbation. We provide analyses of the proposed differential privacy (DP) perturbation in terms of its privacy and utility. Additionally, we designed MPC protocols to implement this mechanism and presented performance benchmarks based on our experimental setup. The MPC realization of the proposed mechanism exhibits a complexity similar to the state-of-the-art discrete Gaussian mechanism, which can be considered an alternative with comparable efficiency while providing stronger differential privacy guarantee. Moreover, efficiency of the proposed scheme can be further enhanced by performing the noise generation offline while leaving the perturbation phase online.

Paper Structure

This paper contains 33 sections, 12 theorems, 49 equations, 1 figure, 2 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Preliminaries
  4. Differential Privacy
  5. Secure Multi-Party Computation
  6. Fixed Point Encoding for MPC
  7. Problem Statement
  8. Truncated Laplace Mechanism
  9. Truncation on Laplace Mechanism
  10. Privacy
  11. Accuracy
  12. Truncated Discrete Laplace Mechanism: A Laplace-inspired Perturbation
  13. Definition of the Mechanism
  14. Privacy
  15. Accuracy
  16. ...and 18 more sections

Key Result

Proposition 4.1

For any positive values $L,E,\sigma$ and $x\in [-E,E],$ we have $\lambda^{(\mathtt{Lap})}_{L,E,\sigma}=2\left(\sigma+(E-\sigma)e^{-\frac{L}{\sigma}}\right).$

Figures (1)

  • Figure 1: Distribution of Truncated Discrete Laplace for $E=64$, $L=32$, $\sigma=8$, and precision $p=2$ : Theoretical vs. Experimental

Theorems & Definitions (40)

  • Definition 1: Differential Privacy
  • Definition 2: Laplace Mechanism dwork2006calibrating
  • Definition 3: Discrete Laplace Distribution
  • Proposition 4.1
  • proof
  • Proposition 4.2
  • proof
  • Proposition 4.3
  • proof
  • Definition 4: Truncated Discrete Laplace Mechanism $\mathcal{M}^{(\mathtt{DLap})}_{L,E,\sigma}$
  • ...and 30 more