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arXiv · 2509.15047

Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy

Amirhosein Morteza·Remi A. Chou
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Abstract

We study the trade-off between communication rate and privacy for distributed batch matrix multiplication of two independent sequences of matrices $\mathbf{A}$ and $\mathbf{B}$ with uniformly distributed entries. In our setting, $\mathbf{B}$ is publicly accessible by all the servers while $\mathbf{A}$ must remain private. A user is interested in evaluating the product $\mathbf{AB}$ with the responses from the $k$ fastest servers. For a given parameter $\alpha \in [0, 1]$, our privacy constraint must ensure that any set of $\ell$ colluding servers cannot learn more than a fraction $\alpha$ of $\mathbf{A}$. Additionally, we study the trade-off between the amount of local randomness needed at the encoder and privacy. Finally, we establish the optimal trade-offs when the matrices are square and identify a linear relationship between information leakage and communication rate.

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Amirhosein Morteza, Remi A. Chou. 2025-09-18. Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy. https://arxiv.org/abs/2509.15047

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