Hierarchy-based cheating detection and cheater identification in secret sharing schemes

Abstract

Secret sharing scheme holds an important position in the domain of cryptography. Shamir's discovery of secret sharing scheme in 1979 followed a concept where a secret is distributed among a set of entrants, where each of the entrants gets a partial information about the secret, called the share, and pooling a minimum number of shares, called threshold, secret reconstruction is accomplished. Though, the original proposal is elegant enough, Tompa and Wall in 1988 suggested that attack by the participants is viable in Shamirs scheme. Since this finding, many works have been carried out to detect cheating and cheaters using various theories. In our work, we modify Shamir's design with the exclusive objective of detecting cheating/ identifying cheaters. We extend Shamir's threshold secret sharing scheme by adding the concept of hierarchy to achieve the objective of finding conspiracy and conspirator(s). We restrict the dealer to generate more number of shares than participants and distribute these shares based on a hierarchical model. The analysis of our design shows how the objective of cheating detection/identification is achieved with high accuracy and professionalism.