{"ID":2869403,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.15047","arxiv_id":"2509.15047","title":"Distributed Batch Matrix Multiplication: Trade-Offs in Download Rate, Randomness, and Privacy","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 $α\\in [0, 1]$, 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.","short_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 priva...","url_abs":"https://arxiv.org/abs/2509.15047","url_pdf":"https://arxiv.org/pdf/2509.15047v1","authors":"[\"Amirhosein Morteza\",\"Remi A. Chou\"]","published":"2025-09-18T15:10:43Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"cs.CR\"]","methods":"[]","has_code":false}