Two types of new subliminal channels are constructed respectively based on provable secure public key cryptosystems and identity recognition in some network applications. Research shows that there are some new characteristics which are in favor of covert communication in our constructions. It is hard to make the subliminal channels free, and the channels have large capacity and high transmission efficiency. We also point out that the hardness to make the channels free is disadvantageous to the warden who tries to thwart the covert communication. Two types of new subliminal channels are constructed respectively based on provable secure public key cryptosystems and identity recognition in some network applications. Research shows that there are some new characteristics which are in favor of covert communication in our constructions. It is hard to make the subliminal channels free, and the channels have large capacity and high transmission efficiency. We also point out that the hardness to make the channels free is disadvantageous to the warden who tries to thwart the covert communication.