Repairable Threshold Secret Sharing Schemes

In this paper, we propose a class of new threshold secret sharing schemes with repairing function between shares. Specifically, each share, when it is broken or lost, can be repaired by some others without the help of the dealer. Further, a construction of such repairable threshold secret sharing schemes is designed by applying linearized polynomials and regenerating codes in distributed storage systems. In addition, a new repairing rate is introduced to characterize the performance and efficiency of the repairing function, and a tight upper bound is derived, which implies the optimality of repair. Under this optimality, we further discuss the optimality of traditional information rate which describes the efficiency of secret sharing schemes in the aspect of storage. Finally, we find that, by applying the minimum bandwidth regenerating codes in distributed storage systems to our construction, our proposed schemes can achieve such optimality of repairing and information rates. Index Terms threshold secret sharing schemes, repairable threshold schemes, the repairing rate, the information rate, optimality.