Introduction of Improved Repairing Locality into Secret Sharing Schemes with Perfect Security

TL;DR

This paper proposes a novel secret sharing scheme that improves repairing locality while maintaining perfect security by decoupling repair and secret recovery processes and introducing dedicated redundancies.

Contribution

It introduces a method to enable secure local repairing in secret sharing schemes by generating dedicated redundancies and a random placement mechanism.

Findings

Achieves improved repairing locality with perfect security.

Decouples repair process from secret recovery for enhanced security.

Maximizes security of redundancies through a novel placement mechanism.

Abstract

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.