Secret sharing a key in a distributed way, Lagrange vs Newton
Anastassios Voudouris, Ilias Politis, Christos Xenakis · Proceedings of the 17th International Conference on Availability, Reliability and Security · 2022
In secret sharing, a dealer knows the secret it shares. In a distributed key generation (DKG) protocol, a shared secret is collectively generated in a group in a completely distributed way such that any subset of size greater than a threshold can reveal or use the shared secret, while smaller subsets do not have any knowledge about it. The most important aspect is that there is no dealer or trusted party. The core idea of secret sharing schemes is Shamir’s secret sharing method, which uses Lagrange’s interpolation to reconstruct the shared secret key. This paper investigates an alternative method, called Newton’s interpolation and it cites the probability of implementing it on current DKG protocols.