Introduction of Improved Repairing Locality into Secret Sharing Schemes with Perfect Security
This addresses a theoretical limitation in distributed storage for secret sharing, enabling more efficient data repair in secure systems, though it is incremental as it builds on known constraints.
The paper tackles the problem of achieving local repairing in secret sharing schemes with perfect security by decoupling secret recovery and share repair processes, introducing dedicated repairing redundancies that are random to the original secret, and achieves improved repairing locality while ensuring security, with the scheme degenerating to existing best schemes if security is compromised.
Repairing locality is an appreciated feature for distributed storage, in which a damaged or lost data share can be repaired by accessing a subset of other shares much smaller than is required for decoding the complete data. However for Secret Sharing (SS) schemes, it has been proven theoretically that local repairing can not be achieved with perfect security for the majority of threshold SS schemes, where all the shares are equally regarded in both secret recovering and share repairing. In this paper we make an attempt on decoupling the two processes to make secure local repairing possible. Dedicated repairing redundancies only for the repairing process are generated, which are random numbers to the original secret. Through this manner a threshold SS scheme with improved repairing locality is achieved on the condition that security of repairing redundancies is ensured, or else our scheme degenerates into a perfect access structure that is equivalent to the best existing schemes can do. To maximize security of the repairing redundancies, a random placement mechanism is also proposed.