An Anti-cheating Block Secret Sharing Scheme Based on Cyclic Codes

In secret sharing, cheaters may reconstruct and recover the secret by providing faked shares, but the honest participants get no information about it. The anti-cheating secret sharing scheme can detect cheating and identify cheaters, so that it can effectively resist cheating attacks. In this paper, we construct a Cyclic Codes-based (k, n)-block secret sharing scheme against cheating. If there are more than k participants reconstructing the secret, we can detect cheating and identify cheaters. We discuss the relationship between the length of the secret block and the computational complexity, the length of the secret block and the storage space. Also, we give the upper bound of the number of identifiable cheaters. When there are no fewer than k honest participants, we can identify all cheaters.