Abstract:
Cheating-immune secret sharing schemes are secret sharing schemes where dishonest participants, during the reconstruction phase, have no advantage in submitting incorrect shares (i.e., cheating), compared to honest participants. In particular, they get no information at all on the true secret that would be reconstructed if they submit correct shares. In this paper we study properties and constraints holding for cheating-immune secret sharing schemes. We show that a perfect secret sharing scheme cannot be cheating-immune. Then, we prove an upper bound on the number of tolerated cheaters in such schemes, and we propose a modified version of an existing construction to realize cheating-immune secret sharing schemes. Finally, we discuss some open problems.