The Privacy Blanket of the Shuffle Model (1903.02837v2)

Abstract: This work studies differential privacy in the context of the recently proposed shuffle model. Unlike in the local model, where the server collecting privatized data from users can track back an input to a specific user, in the shuffle model users submit their privatized inputs to a server anonymously. This setup yields a trust model which sits in between the classical curator and local models for differential privacy. The shuffle model is the core idea in the Encode, Shuffle, Analyze (ESA) model introduced by Bittau et al. (SOPS 2017). Recent work by Cheu et al. (EUROCRYPT 2019) analyzes the differential privacy properties of the shuffle model and shows that in some cases shuffled protocols provide strictly better accuracy than local protocols. Additionally, Erlingsson et al. (SODA 2019) provide a privacy amplification bound quantifying the level of curator differential privacy achieved by the shuffle model in terms of the local differential privacy of the randomizer used by each user. In this context, we make three contributions. First, we provide an optimal single message protocol for summation of real numbers in the shuffle model. Our protocol is very simple and has better accuracy and communication than the protocols for this same problem proposed by Cheu et al. Optimality of this protocol follows from our second contribution, a new lower bound for the accuracy of private protocols for summation of real numbers in the shuffle model. The third contribution is a new amplification bound for analyzing the privacy of protocols in the shuffle model in terms of the privacy provided by the corresponding local randomizer. Our amplification bound generalizes the results by Erlingsson et al. to a wider range of parameters, and provides a whole family of methods to analyze privacy amplification in the shuffle model.

• The paper presents an optimal protocol for summing real numbers in the shuffle model that reduces noise from Ω(√n) in LDP protocols to O(n^(1/6)).
• The paper establishes a theoretical lower bound on accuracy for shuffle-model protocols, confirming the intermediate privacy-utility trade-off between curator and local models.
• The paper generalizes privacy amplification results by introducing a 'privacy blanket' framework that significantly extends differential privacy guarantees across broader settings.

The Privacy Blanket of the Shuffle Model: An Expert Synopsis

The paper "The Privacy Blanket of the Shuffle Model" explores differential privacy within the recently formulated shuffle model, which situates itself between the established curator and local models. The shuffle model's central premise is anonymizing user data through a shuffling mechanism, thereby offering an intermediate trust level where the data collector does not have the visibility to link data back to individual users, compared to the local model. This framework was introduced in the Encode, Shuffle, Analyze (ESA) model and has quickly gained traction as a potential solution to the accuracy and privacy trade-offs inherent in local differential privacy (LDP).

Key Contributions

1. Optimal Protocol for Real-Number Summation: The authors present an optimal protocol for summing real numbers within the shuffle model, demonstrating improved accuracy and communication efficiency over previous protocols like those by Cheu et al. An innovative single-message strategy is proposed, utilizing a fixed-point representation and a privacy blanket via randomized rounding, resulting in a significant reduction of noise from the $\Omega(\sqrt{n})$ of LDP protocols to $O(n^{1/6})$.
2. Lower Bound Establishment: A theoretical lower bound on the accuracy of shuffle-model protocols for real number summation is established, reinforcing the optimality of the authors' proposed protocol. This bound highlights the shuffle model's intermediate position between the curator and local models — achieving better accuracy than LDP while acknowledging inherent limitations compared to the curator model's trust level.
3. Privacy Amplification Framework: The authors generalize existing privacy amplification results, stating conditions where privacy is amplified significantly in the shuffle model context. They propose a new framework building on Erlingsson et al.'s work, extending privacy amplification to wider parameter ranges and providing the concept of a 'privacy blanket' as a canonical decomposition of a local randomizer. This results in tighter bounds on the differential privacy of shuffle model protocols.

Implications and Future Directions

The findings and methodologies proposed in this paper have important theoretical and practical ramifications for differential privacy research. By integrating a privacy blanket approach, the shuffle model progresses towards addressing the imbalance between utility and privacy seen in LDP applications. The implications span across distributed computations where data privacy remains paramount but cannot compromise accuracy significantly, such as census operations and large-scale customer data analytics.

For future avenues, the authors speculate on the exploration of computational trade-offs and trust assumptions that different implementations of the shuffling step might entail. Extending the framework to incorporate interactive protocols or dealing with non-uniform distributions can broaden the shuffle model's applicability further. Furthermore, as differential privacy continues to embed itself into real-world applications like those from tech giants such as Google, Apple, and Microsoft, refining and optimizing shuffle models will be crucial to balance the required privacy assurances with practical accuracy and efficiency.

In conclusion, the paper advances the discussion on differential privacy by strategically navigating the strengths of both the curator and local models under the shuffle framework, providing rigorous evidence of its benefits while laying the groundwork for subsequent innovations in privacy-preserving technologies.