Title: Introduction of Improved Repairing Locality into Secret Sharing Schemes with Perfect Security,
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.