{"paper":{"title":"On the Capacity of Secure Distributed Batch Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Syed A. Jafar, Zhuqing Jia","submitted_at":"2019-08-19T17:52:22Z","abstract_excerpt":"The problem of secure distributed batch matrix multiplication (SDBMM) studies the communication efficiency of retrieving a sequence of desired matrix products ${\\bf AB}$ $=$ $({\\bf A}_1{\\bf B}_1,$ ${\\bf A}_2{\\bf B}_2,$ $\\cdots,$ ${\\bf A}_S{\\bf B}_S)$ from $N$ distributed servers where the constituent matrices ${\\bf A}=({\\bf A}_1, {\\bf A}_2, \\cdots, {\\bf A}_S)$ and ${\\bf B}=({\\bf B}_1, {\\bf B}_2,\\cdots,{\\bf B}_S)$ are stored in $X$-secure coded form, i.e., any group of up to $X$ colluding servers learn nothing about ${\\bf A, B}$. It is assumed that ${\\bf A}_s\\in\\mathbb{F}_q^{L\\times K}, {\\bf B}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06957","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06957/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}