The trapdoor one-way function in NTRU is different from previous ones.Its one-wayness depends on the randomness of session keys

and decryption needs not any information about the session key.Someone called this kind of functions as "probabilistic" trapdoor one-way function.We believe this cannot show all the particularities.So we proposed a new notion

i.e.trapdoor one-way function with an auxiliary random variable

by which we can also unify the trapdoor one-way function model of probabilistic public key encryptions.The concept has been extended to the situation of higher dimension

and possible use has been discussed finally.