Computationally Perfect Secret Sharing Scheme Based on Error-Correcting Codes

Abstract

In this paper, we propose a secret sharing scheme for compartmented access structure with lower bounds. Construction of the scheme is based on the Maximum Distance Separable (MDS) codes. The proposed scheme is ideal and computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. This is in contrast to some of the existing schemes in the literature, in which an authorized set can recover the secret only with certain probability. Also, in our scheme unlike in some of the existing schemes, the size of the ground field need not be extremely large. This scheme is efficient and requires O(mn 3), where n is the number of participants and m is the number of compartments. © Springer-Verlag Berlin Heidelberg 2014.