Compartmented Secret Sharing Based on the Chinese Remainder Theorem

A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups. In case of compartmented secret sharing, the set of users is partitioned into compartments and the secret can be recovered only if the number of participants from any compartment is greater than a fixed compartment threshold and the total number of participants is greater than a global threshold. In this paper we present a new compartmented secret sharing scheme by extending the Brickell\u27s construction to the case that the global threshold is strictly greater than the sum of the compartment thresholds and we indicate how to use the threshold secret sharing schemes based on the Chinese remainder theorem in order to decrease the size of shares