Year: 2026
Type: preprint
Abstract: We study the randomness required to share possibly correlated secret bits among parties connected by a graph. A dealer places shares on the edges so that each party can recover its own secret from its incident shares and learn nothing about the others beyond what its own secret reveals. Anilkumar et al. completely determined the minimum randomness required for three binary secrets. We extend this study to four secrets and obtain results for arbitrary numbers of secrets on general graphs. For four parties on a complete graph, we determine the minimum number of random states for every set of permitted secret combinations: the possible values are one, two, three and four. We also characterize when one random bit suffices on an arbitrary graph.
Source: arXiv (Cornell University)
Author: Marszalik, Piotr
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220980440