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For conventional secret sharing, if cheaters can submit possibly forgedshares after observing shares of the honest users in the reconstruction phasethen they cannot only disturb the protocol but also only they may reconstructthe true secret. To overcome the problem, secret sharing scheme with propertiesof cheater-identification have been proposed. Existing protocols forcheater-identifiable secret sharing assumed non-rushing cheaters or honestmajority. In this paper, we remove both conditions simultaneously, and give itsuniversal construction from any secret sharing scheme. To resolve this end, wepropose the concepts of "individual identification" and "agreedidentification".

Universal Construction of Cheater-Identifiable Secret Sharing Against Rushing Cheaters Based on Message Authentication