Secret Sharing Schemes Based on Min-Entropies
- M. Iwamoto and J. Shikata
- IEEE ISIT 2014
Fundamental results are clarified with respect to secret sharing schemes (SSSs) in which security and each share size are measured by (conditional) min-entropies. We first formalize a unified framework of SSS based on conditional Rényi entropies, which includes SSSs based on Shannon and min entropies etc., as special cases. By deriving the lower bound of share sizes in terms of Rényi entropies, we can derive the lower bounds of share sizes measured by Shannon and min entropies in a unified manner. Then, we focus on the existence of SSSs based on min-entropies for several important settings. In the traditional SSSs based on (conditional) Shannon entropies, it is known that; (1) there exists a SSS for arbitrary secret information and arbitrary access structure, and; (2) for every integers k and n (k ≤ n), the ideal (k,n)-threshold scheme exists when secret information is uniform or deterministic. Corresponding to these results, we clarify the following: (1') there exists a SSS for arbitrary binary secret information and arbitrary access structure, and; (2') for every integers k and n (k ≤ n), the ideal (k,n)-threshold scheme exists even if the secret is neither uniform nor deterministic.