Title: Computationally perfect compartmented secret sharing schemes based on MDS codes

Authors: Appala Naidu Tentu; Prabal Paul; V.Ch. Venkaiah

Addresses: CR Rao Advanced Institute of Mathematics, Statistics, and Computer Science, University of Hyderabad Campus, Hyderabad-500046, India ' Department of Mathematics, Birla Institute of Technology and Science, Pilani, Goa Campus, GOA-403726, India ' School of Computer and Information Sciences, University of Hyderabad, Hyderabad-500046, India

Abstract: Two compartmented secret sharing schemes are proposed in this paper. Constructions of the proposed schemes are based on the maximum distance separable (MDS) codes. One of the proposed schemes is perfect in classical sense and the other scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorised set can always reconstruct the secret in polynomial time whereas for an unauthorised set this is computationally hard. This is in contrast to some of the existing schemes in the literature, in which an authorised set can recover the secret only with certain probability. Also, in our schemes unlike in some of the existing schemes, the size of the ground field need not be extremely large. One of the proposed schemes is shown to be ideal and the information rate for the other scheme is 1/2. Both the schemes are efficient and require O(mn³), where n is the number of participants and m is the number of compartments.

Keywords: compartmented access structure; computationally perfect; ideal; MDS code; secret sharing schemes; maximum distance separable.

DOI: 10.1504/IJTMCC.2014.067378

International Journal of Trust Management in Computing and Communications, 2014 Vol.2 No.4, pp.353 - 378

Received: 24 Apr 2014
Accepted: 20 Sep 2014

Published online: 07 Feb 2015 *

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