Increasing the efficiency of the key generation algorithm for NTRU with the help of the norm field

Conceptually, a signature scheme consists of three steps: private key generation, signature, and authentication. Private key generation in NTRU-based signature schemes on a typical laptop (Intel Core i7-6567U 3.30 GHz) takes a long time (more than one second), while signature and verification take much less time (for example, a thousandths of a second). The current paper deals with providing solutions to reduce the time of private key generation. In this paper, the previous methods are studied and then a new method based on the norm field is introduced and it is shown that the execution time is significantly reduced by using it.