Designing Efficient Algorithms for Combinatorial Repairable Threshold Schemes
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Repairable secret sharing schemes are secret sharing schemes where, without the original dealer who distributed the shares, the participants can combine information from their shares to perform a computation that reconstructs a share for a participant who has lost their share. In this work, we study the repairability of a threshold scheme with respect to the probability that it is possible to perform a repair for a failed share, where each participant in the scheme is available with some probability p. We measure the repairability of a scheme in terms of probability that a repair set is available and in terms of the expected number of available repair sets. Additionally, we design efficient algorithms for determining who to contact when attempting to perform a repair on a failed share for repairable threshold schemes which use 2-designs. We also introduce the use of t-designs, for t > 2, as distribution designs to produce repairable secret sharing schemes with higher repairing degrees and we discuss modifications to the algorithm to account for the different attributes of the designs where t > 2.
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Bailey Kacsmar (2018). Designing Efficient Algorithms for Combinatorial Repairable Threshold Schemes. UWSpace. http://hdl.handle.net/10012/14052