Implementation of shamir secret sharing technique (Mobile app)

Four nodes (mobile) in a network where one node will be considered as a central node responsible for generating and distributing the secret key shares to the other nodes using Shamir secret sharing technique. (A Pre-shared key will be used by the central node to distribute the key shares to the other nodes) This technique will include the following steps 1. Selecting a random polynomial to generate the key shares for each mobile node 2. Distribution of the secret key shares by the central node to the other nodes using a pre-shared key 3. Combining the key shares to generate the secret key