t-Cheater Identifiable (k, n) Threshold Secret Sharing Schemes

In this paper, we show that there exists a t-cheater identifiable (k, n) threshold secret sharing scheme such as follows for cheating probability ? > 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/?)(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.