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A network reliability approach to the analysis of combinatorial repairable threshold schemes. (English) Zbl 1419.94057

Summary: A repairable threshold scheme (which we abbreviate to RTS) is a \( (\tau,n) \)-threshold scheme in which a subset of players 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. Combinatorial repairable threshold schemes (or combinatorial RTS) were recently introduced by D. R. Stinson and R. Wei [Des. Codes Cryptography 86, No. 1, 195–210 (2018; Zbl 1400.94186)]. In these schemes, “multiple shares” are distributed to each player, as defined by a suitable combinatorial design called the distribution design. In this paper, we study the reliability of these combinatorial repairable threshold schemes in a setting where players may not be available to take part in a repair of a given player’s share. Using techniques from network reliability theory, we consider the probability of existence of an available repair set, as well as the expected number of available repair sets, for various types of distribution designs.

MSC:

94A62 Authentication, digital signatures and secret sharing
05B05 Combinatorial aspects of block designs
90B25 Reliability, availability, maintenance, inspection in operations research

Citations:

Zbl 1400.94186
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