Designs, Codes and Cryptography

, Volume 86, Issue 1, pp 195–210 | Cite as

Combinatorial repairability for threshold schemes

  • Douglas R. Stinson
  • Ruizhong Wei


In this paper, we consider methods whereby a subset of players in a (kn)-threshold scheme can “repair” another player’s share in the event that their share has been lost or corrupted. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the (unconditional) security of the threshold scheme, and it should be efficient, where efficiency is measured in terms of the amount of information exchanged during the repairing process. We study two approaches to repairing. The first method is based on the “enrollment protocol” from Nojoumian et al. (IET Inf Secur 4: 202–211, 2010) which was originally developed to add a new player to a threshold scheme (without the participation of the dealer) after the scheme was set up. The second method distributes “multiple shares” to each player, as defined by a suitable combinatorial design. This method results in larger shares, but lower communication complexity, as compared to the first method.


Secret sharing Threshold scheme Repairability Combinatorial design 

Mathematics Subject Classification

94A62 94C30 05B05 



The first author would like to thank Nabiha Asghar and Charlie Colbourn for helpful comments. The authors’ research was supported by NSERC discovery grants.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceLakehead UniversityThunder BayCanada

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