Abstract: Secret sharing plays an important role in information security and data privacy. Based on LUC cryptosystem, a (t, n) threshold secret sharing scheme is proposed in this paper, which has the capability to identify cheater. In the secret recovery phase, each participant is allowed to check whether another participant provides the true share or not, which can prevent adversaries from getting the secret and the participants cheating each other efficiently. Each participant's share is as short as the shared secret. Therefore, this scheme is an ideal one with the information rate 1. The security of this scheme is based on that of the LUC cryptosystem and Shamir's (t, n) threshold secret sharing scheme.