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ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
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Almost optimum t-cheater identifiable secret sharing schemes
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Brief announcement: optimal amortized secret sharing with cheater identification
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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In this paper, we show that there exists a t-cheater identifiable (k, n) threshold secret sharing scheme such as follows for cheating probability 驴 O. If k ≥ 3t + 1, then 1. Just k participants are enough to identify who are cheaters. 2. |Vi| is independent of n. That is, |Vi| = |S|(l/驴)(t+2), where S denotes the set of secrets and Vi denotes the set of shares of a participant Pi, respectively. (Previously, no schemes were known which satisfy both requirements.) Further, we present a lower bound on |Vi| for our model and for the model of Tompa and Woll. Our bound for the TW model is much more tight than the previous bound.