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Title:
On Cheating Immune Secret Sharing
Authors: An Braeken, Svetla Nikova, Ventzislav Nikov
Abstract: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 {\textit et.~al} on the number of cheaters tolerated in such scheme. Our proof is much simpler than the proof of D’Arco {\textit 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 \ell over any finite field.
ePrint: https://eprint.iacr.org/2004/200
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