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 flrst (t;n) threshold secret sharing scheme and it is ideal and perfect. In this paper, we propose two modiflcations of Shamir’s secret sharing scheme. In our flrst modiflcation, each shareholder keeps both x-coordinate and y-coordinate of a polynomial as private share. In our second modiflcation, dealer uses polynomial with degree larger than the threshold value t to generate shares for a (t;n) threshold scheme. We show that these