On Cheating Immune Secret Sharing

An Braeken; Svetla Nikova; Ventzislav Nikov

Paper 2004/200 Original: eprint.iacr.org/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.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2004-08-16: last updated; 2004-08-16: published
Short URL: https://ia.cr/2004/200
License: https://creativecommons.org/licenses/by/4.0/

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}
}