The Price of Privacy: Randomness Complexity of Graph-Based Multi-Secret Sharing
The paper bounds randomness needed to share correlated secrets on graphs, including all four-party cases.
The work studies how much randomness a dealer needs to share possibly correlated secret bits over a graph so each party recovers only its own secret. It extends complete results for three binary secrets to four secrets and to arbitrary numbers on general graphs. On the complete graph with four parties, the minimum number of random states is one, two, three, or four depending on permitted combinations.
- Shares sit on edges so each party recovers only its own secret.
- Four-party complete graphs need one to four random states.
- The paper characterizes when one random bit suffices on any graph.
- It extends complete three-secret results to four and general graphs.
From the original article
1 min read at arxiv.orgWe 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.
By Piotr Marszalik · arxiv.org
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