{
  "abstract": "We study distributed storage over public communication channels where privacy is realized using shared secret keys. Specifically, a user wishes to store a file across $L$ servers such that any subset of at least $t$ servers can reconstruct the file, while any subset of at most $z$ colluding servers learns no more than a fraction $α$ of the file. Unlike classical secret-sharing models that assume secure communication channels between the user and each server, we consider a setting where all transmissions occur over a public channel and the user shares an individual secret key of length $n$ bits with each server. For a fixed key length $n$, we characterize the trade-off between the privacy leakage parameter $α$ and the maximum file size that can be securely stored. Additionally, we determine the minimum local randomness, public communication, and storage required to achieve this optimal trade-off.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39112",
  "author_total": 2,
  "authors": [
    {
      "name": "Maryam Keshvari"
    },
    {
      "name": "Remi A. Chou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpnam77gakg9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39112",
  "fulltext_url": null,
  "id": "bpnam77gakg9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39112",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpnam77gakg9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39112"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Communication and Privacy Trade-Offs in Distributed Storage With Shared Secret Keys",
  "title_text": "Communication and Privacy Trade-Offs in Distributed Storage With Shared Secret Keys",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bpnam77gakg9j",
  "venue": "arXiv",
  "versions": []
}