A Scheme of Detecting Cheaters Wholly in Threshold Secret Sharing for Mobile Ad Hoc Networks

Because of the distributed character of Mobile Ad hoc Networks, secret sharing is a ideal scheme for keeping system secret information. However, methods of detecting cheaters wholly in threshold secret sharing are few, so far. If another participant can join the t participants, t+1 participants in total, according to the scheme proposed in this paper, the existence of cheaters can be checked out only calculating equations once, requiring no other information. This scheme is a perfect sharing scheme. Its information rate is 1. The probability of one cheater's success is 0 and it is less than 1/p (where p is a large prime) for two or three cheaters in probability of success.