## Cryptology ePrint Archive: Report 2004/200

On Cheating Immune Secret Sharing

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.

Category / Keywords: secret sharing schemes

Publication Info: Published in the Proc. of the 25th Symposium on Information Theory in the Benelux