{"paper":{"title":"Gruppen secret sharing, or, how to share several secrets if you must?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Laszlo Csirmaz","submitted_at":"2013-10-17T10:46:32Z","abstract_excerpt":"Each member of an $n$-person team has a secret, say a password. The $k$ out of $n$ gruppen secret sharing requires that any group of $k$ members should be able to recover the secrets of the other $n-k$ members, while any group of $k-1$ or less members should have no information on the secret of other team member even if other secrets leak out. We prove that when all secrets are chosen independently and have size $s$, then each team member must have a share of size at least $(n-k)s$, and we present a scheme which achieves this bound when $s$ is large enough. This result shows a significant savi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4652","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}