  For conventional secret sharing, if cheaters can submit possibly forged
shares after observing shares of the honest users in the reconstruction phase
then they cannot only disturb the protocol but also only they may reconstruct
the true secret. To overcome the problem, secret sharing scheme with properties
of cheater-identification have been proposed. Existing protocols for
cheater-identifiable secret sharing assumed non-rushing cheaters or honest
majority. In this paper, we remove both conditions simultaneously, and give its
universal construction from any secret sharing scheme. To resolve this end, we
propose the concepts of "individual identification" and "agreed
identification".
