## Cryptology ePrint Archive: Report 2016/855

Combinatorial Repairability for Threshold Schemes

Douglas R. Stinson and Ruizhong Wei

Abstract: In this paper, we consider methods whereby a subset of players in a $(k,n)$-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-Stinson-Grainger, 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.

Category / Keywords: cryptographic protocols / secret sharing

Date: received 5 Sep 2016, last revised 7 Sep 2016

Contact author: dstinson at uwaterloo ca

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2016/855

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