Secret Sharing Schemes on Compartmental Access Structure in Presence of Cheaters

TLDR: This paper presents definitions of cheating detectable, cheater identifiable and robust secret sharing schemes in compartmental access structure and their realization through five different constructions in the information-theoretic setting and proposes protocols secure against rushing adversary.

Abstract: Various adversarial scenarios have been considered in secret sharing for threshold access structure. However, threshold access structure can not provide efficient solution when participants are classified in different compartments. Of many access structures for which ideal secret sharing schemes can be realized, compartmental access structure is an important one. This paper is targeted to initiate the study of secret sharing schemes for compartmental access structure secure against malicious adversary. This paper presents definitions of cheating detectable, cheater identifiable and robust secret sharing schemes in compartmental access structure and their realization through five different constructions in the information-theoretic setting. Moreover in case of cheater identification and robustness, proposed protocols are secure against rushing adversary who are allowed to submit (possibly forged) shares after observing shares of the honest participants in the reconstruction phase.