分野別セミナー

In the basic form of secret sharing schemes, it was assumed that everyone involved with the protocol is semi-honest. But for the real life scenario, this assumption may not hold good due to the presence of adversary. This idea leads to the development of secret sharing under various adversarial models. It may happen that some participants behave maliciously during the execution of the protocol. Malicious participants may submit incorrect shares resulting in incorrect secret reconstruction. Secret sharing schemes that either detect or identify participants who submit incorrect shares during the recovery of secret have been extensively studied. Tompa and Woll first presented a cheater-detecting secret sharing scheme and this work is followed by several other works. McEliece and Sarwate were the rst to point out cheater identication in secret sharing schemes and this work is followed by several other works. Veriable secret sharing schemes have been proposed for environments where the shares given to participants by the dealer may not be correct i.e., the dealer of these shares may be corrupted. These typically involve protocols that can be performed by various subsets of participants in order to check that the shares they possess are consistent in some sense. While such schemes make it apparent that cheating has occurred, they do not necessarily permit honest participants to recover the correct secret. This observation led to robust secret sharing schemes. Here, we consider, mainly, cheating identiable and robust secret sharing schemes with honest majority. We will discuss about recent constructions of cheating identiable and robust secret sharing schemes.