Distributed Private Data Analysis: On Simultaneously Solving How and What (1103.2626v1)

Abstract: We examine the combination of two directions in the field of privacy concerning computations over distributed private inputs - secure function evaluation (SFE) and differential privacy. While in both the goal is to privately evaluate some function of the individual inputs, the privacy requirements are significantly different. The general feasibility results for SFE suggest a natural paradigm for implementing differentially private analyses distributively: First choose what to compute, i.e., a differentially private analysis; Then decide how to compute it, i.e., construct an SFE protocol for this analysis. We initiate an examination whether there are advantages to a paradigm where both decisions are made simultaneously. In particular, we investigate under which accuracy requirements it is beneficial to adapt this paradigm for computing a collection of functions including binary sum, gap threshold, and approximate median queries. Our results imply that when computing the binary sum of $n$ distributed inputs then: * When we require that the error is $o(\sqrt{n})$ and the number of rounds is constant, there is no benefit in the new paradigm. * When we allow an error of $O(\sqrt{n})$, the new paradigm yields more efficient protocols when we consider protocols that compute symmetric functions. Our results also yield new separations between the local and global models of computations for private data analysis.

• The paper demonstrates that simultaneous decisions on function selection and protocol design can improve efficiency in distributed private data analysis.
• It analyzes error and efficiency trade-offs, showing that symmetric functions like binary sum benefit from concurrent SFE and differential privacy for error bounds of O(sqrt(n)).
• The research bridges theoretical and practical aspects, paving the way for more secure and efficient privacy-preserving systems in areas like healthcare and finance.

Insights into Distributed Private Data Analysis: Secure Function Evaluation and Differential Privacy

The research paper titled "Distributed Private Data Analysis: On Simultaneously Solving How and What" by Amos Beimel, Kobbi Nissim, and Eran Omri explores the intersection of two critical approaches in privacy-preserving computations over distributed inputs: Secure Function Evaluation (SFE) and Differential Privacy (DP). The paper reevaluates the typical paradigm of first deciding on a differentially private analysis and then constructing an SFE protocol for it, and instead proposes exploring the simultaneous decision-making in both realms.

Secure Function Evaluation (SFE) and Differential Privacy (DP)

The foundation of this paper is laid on two privacy-preserving methodologies. SFE protocols enable parties to compute functions over their collective inputs without leaking additional information beyond the prescribed outcome. Differential Privacy, on the other hand, ensures that the output of a function does not significantly reveal any single individual's contribution to the inputs, thus preserving privacy even in the presence of outcome leaks.

Paradigm Analysis: What and How

The paper investigates when there might be benefits in making "what" (the function to be computed) and "how" (the protocol) decisions concurrently rather than sequentially. This simultaneous paradigm is analyzed through the lens of accuracy and efficiency improvements.

Key Results and Implications

The paper provides a significant observation for specific functions such as binary sum, gap threshold, and approximate median queries. Specifically, for the binary sum function involving n distributed inputs:

• Error and Efficiency Trade-Offs: When the goal is an error less than o(sqrt(n)) with a constant number of rounds, the traditional sequential paradigm holds no efficiency benefits.
• Improvements in Protocol Efficiency: Allowing an error of O(sqrt(n)) enables more efficient protocol designs for symmetric functions, benefiting from the proposed simultaneous paradigm.

Notably, this research delineates clear separations between local and global computational models for private data analysis, shedding light on the computational efficiencies afforded by simultaneous design strategies.

Theoretical and Practical Implications

The paper's theoretical implications highlight a novel approach in reconciling SFE and DP methodologies for distributed computations, potentially leading to improvements in privacy-preserving protocols' efficiency. Practically, this work could influence the design of protocols across fields where privacy is paramount, such as healthcare data analysis, decentralized finance systems, and collaborative machine learning.

Additionally, the work opens avenues for further exploration of computationally efficient differentially private mechanisms that leverage cryptographic techniques. The results suggest significant efficiency gains under computational assumptions, bolstering the case for hybrid models that blend cryptographic security with statistical privacy guarantees.

Future Developments

The exploration of simultaneous decision-making in determining function and protocol design for distributed privacy highlights the rich potential for more granular, efficient privacy-preserving techniques. Future research could focus on developing adaptive algorithms that dynamically balance the trade-offs between computational overhead and privacy guarantees, potentially guided by advances in machine learning and quantum computing.

In conclusion, this paper advances the theoretical understanding of distributed private data analysis and sets the stage for innovative applications of differential privacy intertwined with secure function evaluation strategies. The implications stretch across both the academic discourse and practical implementations, promising to enhance both privacy assurances and computational efficiency in distributed systems.