Private Sum Computation: Trade-Offs between Communication, Randomness, and Privacy

2026-02-05

IEEE Transactions on Information Theory

AI Summary

This work addresses the problem of privacy-preserving summation of bit sequences over a one-way public channel in a multi-user setting with a fusion center, where privacy is defined by requiring that the mutual information between any coalition of users (possibly colluding with the fusion center) and the data of other users does not exceed a threshold δ. Employing an information-theoretic approach combined with secret sharing mechanisms, the paper proposes a privacy protocol and establishes, for the first time, tight theoretical lower bounds on both communication overhead and local randomness requirements for arbitrary δ ≥ 0. Furthermore, it rigorously proves that secret sharing is not merely sufficient but necessary for achieving private summation, thereby uncovering a fundamental connection between this task and the theory of secret sharing.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

Consider multiple users and a fusion center. Each user possesses a sequence of bits and can communicate with the fusion center through a one-way public channel. The fusion center's task is to compute the sum of all the sequences under the privacy requirement that a set of colluding users, along with the fusion center, cannot gain more than a predetermined amount $\delta$ of information, measured through mutual information, about the sequences of other users. Our first contribution is to characterize the minimum amount of necessary communication between the users and the fusion center, as well as the minimum amount of necessary randomness at the users. Our second contribution is to establish a connection between private sum computation and secret sharing by showing that secret sharing is necessary to generate the local randomness needed for private sum computation, and prove that it holds true for any $\delta \geq 0$.

Problem

• private sum computation
• privacy
• communication
• randomness
• mutual information

Innovation

• Private Sum Computation
• Communication-Randomness Trade-off
• Information-Theoretic Privacy
• Secret Sharing
• Mutual Information