Paper 2012/246

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

Maggie Habeeb and 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.