A Secret Sharing Scheme Based on Group Presentations and the Word Problem
This work addresses secure secret sharing for cryptography, but it appears incremental as it builds on existing schemes like Shamir's.
The paper tackles the problem of distributing secrets among participants by proposing two secret sharing schemes based on non-abelian groups, including a (t,n)-threshold scheme that combines Shamir's method with a new group-theoretic approach.
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.