A Survey and Refinement of Repairable Threshold Schemes

We consider repairable threshold schemes (RTSs), which are threshold schemes that enable a player to securely reconstruct a lost share with help from their peers. We summarise and, where possible, refine existing RTSs and introduce a new parameter for analysis, called the repair metric. We then explore using secure regenerating codes as RTSs and find them to be immediately applicable. We compare all RTS constructions considered and conclude by presenting the best candidate solutions for when either communication complexity or information rate is prioritised

Designing Efficient Algorithms for Combinatorial Repairable Threshold Schemes

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