CTRU, a new public-key cryptosystem is introduced. In this analogue of NTRU, the ring of integers is replaced by the ring of polynomials in one variable over a finite field. Attacks based on either the LLL algorithm or the Chinese Remainder Theorem are avoided. An important tool of cryptanalys- is is the Popov normal form of matrices with polynomial entries. The speed of encryption/decryption of CTRU is the same as NTRU for the same value of N. An implementation in Aldor is described.