Modified Shamir’s Key-Sharing Scheme with Compulsory Participants

Encryption is a widely employed means of communication between many entities. The presence of a secret key is necessary for the decryption of encrypted data. A frequently employed approach by a collective of shareholders involves the implementation of a secret-sharing system. In this system, if any of the shareholders disclose their secret shares, it becomes possible to reconstruct the key. One example of a technique is Shamir’s covert sharing scheme (Shamir in Commun ACM 22(11), 1979). Shamir’s secret-sharing method involves the partitioning of a secret S by the dealer into n distinct shadows, which are subsequently distributed among shareholders. This distribution is designed so that the retrieval of the secret is possible by any K or more shadows, yet the acquisition of any meaningful information regarding the secret S is prevented by less than K out of the n shadows. The secret S serves as the crucial element for decrypting the data. This study investigates the application of Shamir’s secret-sharing approach in the context of key renewal, specifically focusing on cases when the minimum number of participants required is equal to or less than K. There exists a predetermined quantity of obligatory shadows inside the set of K shadows. One example of a compulsory shadow can be observed in the role of a bank manager who is consistently obligated to furnish a key for the purpose of unlocking a bank locker. The obligatory shadows, along with the discretionary shadows that remain, converge to form the clandestine S. The utilization of Shamir’s secret-sharing technique facilitates the computation of the optimal shadows.