A Secret Sharing Scheme Based on Group Presentations and the Word Problem

Maggie Habeeb; Delaram Kahrobaei; Vladimir Shpilrain

Paper 2012/246

A Secret Sharing Scheme Based on Group Presentations and the Word Problem

Maggie Habeeb, Delaram Kahrobaei, and Vladimir Shpilrain

Abstract

A $(t,n)$-threshold secret sharing scheme is a method to distribute a secret among $n$ participants in such a way that any $t$ participants can recover the secret, but no $t-1$ participants can. In this paper, we propose two secret sharing schemes using non-abelian groups. One scheme is the special case where all the participants must get together to recover the secret. The other one is a $(t,n)$-threshold scheme that is a combination of Shamir's scheme and the group-theoretic scheme proposed in this paper.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Unknown where it was published
Keywords: secret sharing
Contact author(s): shpil @ groups sci ccny cuny edu
History: 2012-05-03: received
Short URL: https://ia.cr/2012/246
License: CC BY

BibTeX

@misc{cryptoeprint:2012/246,
      author = {Maggie Habeeb and Delaram Kahrobaei and Vladimir Shpilrain},
      title = {A Secret Sharing Scheme Based on Group Presentations and the Word Problem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/246},
      year = {2012},
      url = {https://eprint.iacr.org/2012/246}
}