On Cheating Immune Secret Sharing

This work addresses the problem of cheating prevention in secret sharing. The scheme is said to be k-cheating immune if any group of k cheaters has no advantage over honest participants. In this paper we study the constraints of cheating immune secret sharing schemes. We give a necessary and sufficient condition for SSSs to be cheating immune. Then, we improve the upper bound of D’Arco et. al on the number of cheaters tolerated in such scheme. Our proof is much simpler than the proof of D’Arco et. al and relies on certain properties of cryptographic Boolean functions. As a result of independent interest we provide a condition given function to be t-resilient and to satisfy the propagation criterion of degree ` over any finite field.