Cryptology ePrint Archive: Report 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.

Category / Keywords: cryptographic protocols / secret sharing

Date: received 2 May 2012

Contact author: shpil at groups sci ccny cuny edu

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Version: 20120503:095421 (All versions of this report)

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