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Journal of Mathematical Cryptology

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Volume 12, Issue 1


A survey and refinement of repairable threshold schemes

Thalia M. Laing
  • Corresponding author
  • Security Lab, HP Inc., Long Down Avenue, Stoke Gifford, Bristol, BS34 8QZ; and Information Security Group, Royal Holloway University of London, Egham, Surrey, TW20 0EX, United Kingdom
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/ Douglas R. Stinson
Published Online: 2018-02-09 | DOI: https://doi.org/10.1515/jmc-2017-0058


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.

Keywords: Threshold schemes; repairability; combinatorial designs; regenerating codes

MSC 2010: 94A62


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About the article

Received: 2017-11-28

Revised: 2018-01-22

Accepted: 2018-02-02

Published Online: 2018-02-09

Published in Print: 2018-03-01

Funding Source: Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Award identifier / Grant number: RGPIN-03882

Research supported by NSERC discovery grant RGPIN-03882.

Citation Information: Journal of Mathematical Cryptology, Volume 12, Issue 1, Pages 57–81, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2017-0058.

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