Practical Secret Sharing Scheme Realizing Generalized Adversary Structure

Most existing secret sharing schemes are constructed to realize generalaccess structure, which is defined in terms of authorized groups of participants, and is unable tobe applied directly to the design of intrusion tolerant system, which often concerns corruptiblegroups of participants instead of authorized ones. Instead, the generalized adversary structure,which specifies the corruptible subsets of participants, can be determined directly by exploit ofthe system setting and the attributes of all participants. In this paper an efficient secret sharingscheme realizing generalized adversary structure is proposed, and it is proved that the schemesatisfies both properties of the secret sharing scheme, i.e., the reconstruction property and theperfect property. The main features of this scheme are that it performs modular additions andsubtractions only, and each share appears in multiple share sets and is thus replicated. The formeris an advantage in terms of computational complexity, and the latter is an advantage when recoveryof some corrupted participants is necessary. So our scheme can achieve lower computation cost andhigher availability. Some reduction on the scheme is also done finally, based on an equivalencerelation defined over adversary structure. Analysis shows that reduced scheme still preserves theproperties of the original one.

THE OPTIMAL LINEAR SECRET SHARING SCHEME FOR ANY GIVEN ACCESS STRUCTURE

Any linear code can be used to construct a linear secret sharing scheme.In this paper,it is shown how to decide optimal linear codes(i.e.,with the biggest information rate)realizing a given access structure over finite fields.It amounts to solving a system of quadratic equations constructed from the given access structure and the corresponding adversary structure.The system becomes a linear system for binary codes.An algorithm is also given for finding the adversary structure for any given access structure.