t-cheater identifiable (k, n) threshold secret sharing schemes

Abstract

In this paper, we show that there exists a t-cheater identifiable (k, n) threshold secret sharing scheme such as follows for cheating probability ε > 0. If k ≥ 3t + 1, then 1.1. Just k participants are enough to identify who are cheaters. 2.2. |V i| is independent of n. That is, |V i| = |S|(1/ε)(t+2), whereS denotes the set of secrets and V i denotes the set of shares of a participant P i, respectively. (Previously, no schemes were known which satisfy both requirements.) Further, we present a lower bound on |V i| 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.