How to share a secret with cheaters
Journal of Cryptology
Some improved bounds on the information rate of perfect secret sharing schemes
Journal of Cryptology
Communications of the ACM
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The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.