Ideal Hierarchical (t, n) Secret Sharing Schemes

A secret sharing scheme divides a secret into multiple shares by a dealer and shared among shareholders in such a way that any authorized subset of shareholders can reconstruct the secret; whereas any un-authorized subset of shareholders cannot recover the secret. If the maximal length of shares is equal to the length of the secret in a secret sharing scheme, the scheme is called ideal. If the shares corresponding to each un-authorized subset provide absolutely no information, in the information-theoretic sense, the scheme is called perfect. Shamir proposed the first (t, n) threshold secret sharing scheme and it is ideal and perfect. In this paper, we propose two modifications of Shamir’s secret sharing scheme. In our first modification, each shareholder keeps both x-coordinate and y-coordinate of a polynomial as private share. In our second modification, dealer uses polynomial with degree larger than the threshold value t to generate shares for a (t, n) threshold scheme. We show that these ∗Corresponding author. Tel: +86-134-6672-0505, Fax: +86-10-88258713. Email addresses: [email protected] (Changlu Lin ), [email protected] (Lein Harn), [email protected] (Dingfeng Ye) Preprint submitted to Information Sciences May 4, 2009 two modified schemes are ideal and perfect. Using these two modifications, we design two hierarchical secret sharing schemes: multilevel threshold secret sharing (MTSS), and compartmented threshold secret sharing (CTSS). We prove that these two schemes are secure.