Private Summation in the Multi-Message Shuffle Model (2002.00817v3)

Abstract: The shuffle model of differential privacy (Erlingsson et al. SODA 2019; Cheu et al. EUROCRYPT 2019) and its close relative encode-shuffle-analyze (Bittau et al. SOSP 2017) provide a fertile middle ground between the well-known local and central models. Similarly to the local model, the shuffle model assumes an untrusted data collector who receives privatized messages from users, but in this case a secure shuffler is used to transmit messages from users to the collector in a way that hides which messages came from which user. An interesting feature of the shuffle model is that increasing the amount of messages sent by each user can lead to protocols with accuracies comparable to the ones achievable in the central model. In particular, for the problem of privately computing the sum of $n$ bounded real values held by $n$ different users, Cheu et al. showed that $O(\sqrt{n})$ messages per user suffice to achieve $O(1)$ error (the optimal rate in the central model), while Balle et al. (CRYPTO 2019) recently showed that a single message per user leads to $\Theta(n^{1/3})$ MSE (mean squared error), a rate strictly in-between what is achievable in the local and central models. This paper introduces two new protocols for summation in the shuffle model with improved accuracy and communication trade-offs. Our first contribution is a recursive construction based on the protocol from Balle et al. mentioned above, providing $\mathrm{poly}(\log \log n)$ error with $O(\log \log n)$ messages per user. The second contribution is a protocol with $O(1)$ error and $O(1)$ messages per user based on a novel analysis of the reduction from secure summation to shuffling introduced by Ishai et al. (FOCS 2006) (the original reduction required $O(\log n)$ messages per user).

• The paper presents a recursive protocol for real summation that reduces error using logarithmic messages per user and achieves a poly-log-log performance improvement.
• It refines secure summation methods to ensure constant mean squared error with constant messages per user, addressing practical communication constraints.
• The work enhances privacy-accuracy trade-offs in the shuffle model, bridging theoretical insights with applications in privacy-preserving data analytics.

Overview of "Private Summation in the Multi-Message Shuffle Model"

The paper "Private Summation in the Multi-Message Shuffle Model" explores the shuffle model of differential privacy, focusing on the development and enhancement of protocols for real summation. The shuffle model has gained attention as it bridges the gap between the local and central models of differential privacy, leveraging a secure shuffler to anonymize messages while allowing the computation of accurate statistics on privatized data. This work is set against the backdrop of existing protocols, notably those presented by Cheu et al. and Balle et al., and introduces improved multi-message protocols that enhance the trade-offs between the accuracy and communication complexity in the shuffle model.

Key Contributions

1. Recursive Protocol for Real Summation: The authors present a protocol that recursively utilizes the protocol from Balle et al., achieving a poly-log-log error with logarithmic messages per user. Their recursive construction addresses the balance between accuracy and privacy loss incurred with additional messages. This advancement allows for reduced MSE compared to single-message protocols without requiring the high message overhead encountered in other approaches.
2. Simplified Secure Summation Protocol: By refining the multi-message secure summation protocol proposed by Ishai et al., the paper demonstrates how constant messages per user can achieve an MSE constant in nature. The authors improve the protocol's analysis, reducing the required messages significantly, and allow practical implementations that were previously infeasible due to communication constraints.
3. Enhanced Privacy-Accuracy Trade-off: The paper bridges the theoretical insights of summation capabilities in the shuffle model with improvements in efficiency. The recursive algorithm's improved communication-to-accuracy ratio and the IKOS protocol's enhanced security analysis cater to practical deployment scenarios where message overhead is a critical bottleneck.

Practical Implications and Considerations

The practical implications of these results are significant:

• Accuracy Improvements in a Real-World Setting: By reducing the error to grow sub-linearly with respect to user count and message size, the shuffle model becomes viable for more applications requiring privacy, from standard statistics to machine learning models trained on aggregated data.
• Communication Efficiency: As communication constraints are a central limiting factor for implementing secure protocols at scale, improvements in efficiency ensure the protocols are deployable in systems where bandwidth or computational requests are a concern.
• Robustness Against Adversaries: While the analysis primarily focuses on honest but curious adversary models, attention to adversarial robustness is recognized as an avenue for further innovation, helping solidify the shuffle model as a staple in privacy-preserving analytics.

Speculation on Future Developments

The paper's insights suggest several directions for future research:

• Exploring Further Reductions in Communication Complexity: Continued advancements in reducing message sizes and counts while maintaining or improving accuracy can further optimize these protocols for various deployment contexts.
• Adversarial Robustness and Generalization: Expanding the proposed methods to handle adversarial behaviors directly, possibly by incorporating robust noise mechanisms or blockchain-based validations, could extend their applicability.
• Real-World Deployments and Empirical Analysis: As these theoretical models become established, collaboration with industry partners to test these mechanisms in real-world infrastructure would enhance their robustness and reveal novel applications.

In conclusion, the paper advances the state of differential privacy in distributed models. Its contributions toward efficient and accurate summation protocols lay the groundwork for broader adoption of differential privacy beyond theoretical contexts, aligning well with the practical needs of industries invested in secure, privacy-aware data analytics.