{
  "abstract": "We study the secure multiple key-cast problem over noiseless networks under node-based eavesdroppers, where one or more source nodes participate in the generation of distinct secret keys to be shared among designated terminal subsets, while an eavesdropper observing up to $\\ell$ nodes, including possibly source nodes, obtains no information about the keys. For the single-source setting, we first consider networks in which every node is $d$-vertex connected from the source. We show that a secure key rate of $d-\\ell$ is achievable for all such networks. We further show that this rate is optimal by exhibiting $d$-vertex-connected networks whose secure key-cast capacity is at most $d-\\ell$. We next study networks in which only the terminal nodes are $d$-vertex connected from the source, while other network nodes may not satisfy this connectivity condition and may be partially-connected. We show that secure multiple key-cast remains achievable in the presence of such partially-connected nodes, and derive coding schemes whose rate depends on the minimum network vertex-connectivity from the source and certain additional network properties. Finally, we generalize these results, for both $d$-vertex-connected networks and networks containing partially-connected nodes, to the multi-source setting; showing that secure multiple key-cast remains achievable even when the eavesdropper may observe all but one of the source nodes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12209",
  "author_total": 2,
  "authors": [
    {
      "name": "Reza Sayyari"
    },
    {
      "name": "Michael Langberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8749tfar2esxd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12209",
  "fulltext_url": null,
  "id": "8749tfar2esxd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12209",
  "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",
      "2208|Wireless Communication Security Techniques"
    ]
  ],
  "openalex": "W7160981225",
  "pdf_url": "https://arxiv.org/pdf/2605.12209",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8749tfar2esxd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2605.12209",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12209"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes",
  "title_text": "Secure (Multiple) Key-Cast over Networks: Multiple Eavesdropping Nodes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/8749tfar2esxd",
  "venue": "arXiv",
  "versions": []
}