A Secret Sharing Scheme Based on Group Presentations and the Word Problem
Maggie Habeeb, Delaram Kahrobaei, Vladimir Shpilrain · Contemporary mathematics - American Mathematical Society · 2012
A ( t , n ) (t,n) -threshold secret sharing scheme is a method to distribute a secret among n n participants in such a way that any t t participants can recover the secret, but no t − 1 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 ) (t,n) -threshold scheme that is a combination of Shamir’s scheme and the group-theoretic scheme proposed in this paper.