An efficient construction of secret sharing for generalized adversary structure and its reduction

A secret sharing scheme for generalized adversary structure is a method of sharing a secret among a finite set of participants in such a way that only certain pre-specified subsets of participants cannot recover the secret. This paper proposes an efficient secret sharing scheme realizing the generalized adversary structure, and proves that the scheme satisfies both reconstruction and perfect properties of the secret sharing. The main feature of this scheme is that it performs modular additions and subtractions only, and so can achieve lower computation cost. Then, the reduction on the scheme is done based on an equivalence relation defined over the adversary structure. Analysis shows that the reduced scheme still preserves the desired properties of the original one.