Practical Secret Sharing Scheme Realizing Generalized Adversary Structure

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