International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On Cheating Immune Secret Sharing

An Braeken
Svetla Nikova
Ventzislav Nikov
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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.
  title={On Cheating Immune Secret Sharing},
  booktitle={IACR Eprint archive},
  keywords={secret sharing schemes},
  note={Published in the Proc. of the 25th Symposium on Information Theory in the Benelux 12646 received 16 Aug 2004},
  author={An Braeken and Svetla Nikova and Ventzislav Nikov},