Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908545862074368 |
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| author | Morteza, Amirhosein Chou, Remi A. |
| author_facet | Morteza, Amirhosein Chou, Remi A. |
| contents | 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 $α\in [0, 1]$, our privacy constraint must ensure that any set of $\ell$ colluding servers cannot learn more than a fraction $α$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15047 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy Morteza, Amirhosein Chou, Remi A. Information Theory Cryptography and Security 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 $α\in [0, 1]$, our privacy constraint must ensure that any set of $\ell$ colluding servers cannot learn more than a fraction $α$ 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. |
| title | Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy |
| topic | Information Theory Cryptography and Security |
| url | https://arxiv.org/abs/2509.15047 |