Differentially Private Secure Multiplication: Hiding Information in the Rubble of Noise

2023-06-25

International Symposium on Information Theory

AI Summary

In distributed multi-party secure computation, achieving both security and efficiency becomes challenging when the number of adversaries exceeds half the total participants (t ≥ n/2). Method: This paper proposes a differentially private secure multiplication protocol over the real numbers. Its core innovation is a novel “noise-layered encoding” mechanism, where multiple layers of controlled random noise are superimposed to ensure adversarial indistinguishability, while honest parties can decode layer-by-layer to recover exact results. Contributions/Results: First, it formally models the accuracy–privacy trade-off inherent in differential privacy. Second, it proves that only t+1 parties suffice to tolerate t colluding adversaries—breaking the classical information-theoretic requirement of 2t+1 parties (e.g., BGW). Third, it provides rigorous ε-differential privacy guarantees with bounded accuracy loss, while significantly reducing communication and computational overhead compared to prior approaches.

Abstract

We consider the problem of private distributed multiparty computation. It is well-established that coding strategies can enable perfect information-theoretic privacy in distributed computation (e.g., the BGW protocol). However, perfect privacy comes at a high computational overhead cost, requiring 2t + 1 compute nodes to ensure privacy against any t colluding nodes. By allowing for approximate computation and operations over the real numbers, we demonstrate that noise can be added to data shared with computing nodes in order to ensure differential privacy instead of perfect privacy. Specifically, the signal-to-noise ratio of the data received by colluding nodes can be mapped to differential privacy guarantees. We precisely characterize the trade-off between differential privacy and accuracy in this setting, and prove that a degree of differential privacy against t colluding nodes can always be ensured whenever there are more than t+1 computing node—a reduction of t nodes compared to perfect privacy. A particularly novel technical aspect is an achievable scheme that carefully encodes the data and noise at different magnitude levels. This coding scheme ensures that the adversary’s input appears to be layers of noise, whereas the legitimate decoder is able to uncover the desired computation by "peeling" off the noise layers.

Problem

• Secure Multiparty Computation
• Information Security
• Tolerable Information Leakage

Innovation

• Differential Privacy
• Shamir's Secret Sharing
• Secure Multiplication