Abstract: NTRU public Key cryptosystem has the problem that multiple private keys correspond to a common pubic key. Firstly the condition of decryption was discussed, and the conception of equivalent keys in NTRU was proposed.Secondly the invertibility of polynomials in truncated polynomial ring and the sem-norm were discussed, and four schemes to construct equivalent keys were presented. Finally the security effect of equivalent keys was analyzed, which indicates that if NTRU parameters are not chosen properly, some special ectuivalent keys will pose a serious security threat to NTRU.

Key words: NTRU public key cryptosystem, `hruncated polynomial ring, Invertible polynomial, Semi-norm, Equivalent keys