Multisecret sharing immune against cheating

Cheating in multisecret sharing is considered. Multisecret sharing is defined by a mapping F: GF(p^t)ⁿ → GF(p^t)^m that provides a generic model. In this model, we propose nonlinear multisecret sharing that is immune against cheaters. Two cheating strategies are considered. In the first one, all cheaters always submit their invalid shares and they collectively know their own valid shares. In the second one, some cheaters may submit their valid shares while again sharing their knowledge about their valid shares. The combiner (or recovery algorithm) interacts with shareholders by collecting shares from them and distributing the recovered secrets back to active participants. Two different scenarios are considered when the combiner recreates all secrets (this is simultaneous recovery) or gradually (so called sequential recovery). Probabilities of successful cheating are derived and constructions for cheating immune multisecret sharing are given.