Computationally perfect compartmented secret sharing schemes based on MDS codes

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 ( mn 3 ), where n is the number of participants and m is the number of compartments.

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