In this paper, a new broadcast encryption scheme is proposed by using the efficient and computationally inexpensive public key cryptosystem NTRU (number theory research unit). In our scheme, we use the idea of RSA and develop this idea from two-party to multi-party, and combine this multi-party public key idea with the multiplication in ring R of NTRU. What we get from this design is extremely efficient encryption and decryption, fast and easy key creation, low memory requirements and revocation property, etc. Moreover, this novel work contains other desirable features, such as traitor tracing. With its complexity only O(log2n), the tracing algorithm of this system is more efficient than that of the previous ones. In this paper, a new broadcast encryption scheme is proposed by using the efficient and computationally inexpensive public key cryptosystem NTRU (number theory research unit). In our scheme, we use the idea of ​​RSA and develop this idea from two-party to multi- party, and combine this multi-party public key idea with the multiplication in ring R of NTRU. What we get from this design is extremely efficient encryption and decryption, fast and easy key creation, low memory requirements and revocation property, etc. Moreover, this novel work contains other desirable features, such as traitor tracing. With its complexity only O (log2n), the tracing algorithm of this system is more efficient than that of the previous ones.