Based on trapdoor one-way function, this paper presents a RSA -based probabilistic public-key algorithm with security and efficiency and the correctness of algorithm was proved.

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.

One-way trapdoor function has impotents applications in public cryptography.