Proactive (k, n) threshold secret sharing scheme with variant k and n

A secret sharing scheme protects the secret by distributing it to a group of participants (nodes), and it allows for some groups of participants to collaborate together to reconstruct this secret. With regard to the (k, n) threshold scheme, k out of n or more participants can reconstruct the secret. The proactive secret sharing scheme periodically updates the distributed secret (shadow). Based on such a proactive secret sharing scheme, we propose a completely mobile proactive secret sharing scheme, which not only allows for the changing of participant number n, but arbitrarily changes the threshold k.