In this paper, we propose to enhance threshold secret sharing schemes based on the Chinese remainder theorem (CRT) by incorporating the well-known RSA Cryptosystem.In the proposed scheme, participants select their secret shadows by themselves. Also, a secure channel among the dealer and participants is no longer needed. In addition,each participant can check whether another participant provides the true secret shadow or not.Furthermore, it allows to reconstruct several secrets parallelly. The scheme is based on the RSA cryptosystem and intractability of the Discrete Logarithm.