Improving Key Generation in matrix implementation of NTRU

The lattice based cryptography, firstly presented by Ajtai, is based on the public key cryptosystems and its security is based on the worst-case-problem. One of the strong versionsof lattice based cryptography is NTRU which was proposed according to ring theory and later Nayak et al presented thematrix implementation of NTRU. Their implemented method had a problem in key generation part which was related to the limitations of generating key. Xu-Ren Luo presented a newmethod for finding the inverse of matrix and removed the limitation of key generation but again a problem in keygeneration was found. Since the key generation process is done after the encryption of the message, the same plaintext can notbe deduced during the decryption process. In this paper wediscuss about the current problem and two promising methods for solving and improving this problem are proposed

Keywords:

NTRU , Lattice based cryptography , Matrix implementation , Private and Public key pairs , Encryption , Decryption