On Cheating Immune Secret Sharing

An Braeken; Svetla Nikova; Ventzislav Nikov

Paper 2004/200

On Cheating Immune Secret Sharing

An Braeken, Svetla Nikova, and 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.

Metadata

Available format(s): PDF PS
Publication info: Published elsewhere. Published in the Proc. of the 25th Symposium on Information Theory in the Benelux
Keywords: secret sharing schemes
Contact author(s): svetla nikova @ esat kuleuven ac be
History: 2004-08-16: received
Short URL: https://ia.cr/2004/200
License: CC BY

BibTeX

@misc{cryptoeprint:2004/200,
      author = {An Braeken and Svetla Nikova and Ventzislav Nikov},
      title = {On Cheating Immune Secret Sharing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/200},
      year = {2004},
      url = {https://eprint.iacr.org/2004/200}
}