Engineering and Technology Journal

In this paper, we propose a new version of the NTRU public key cryptosystem called CQTRU. It is a four-dimensional cryptosystem based on the commutative quaternion ring. This public key system has an ability to encrypt four sets of data in each session. Therefore, it gains the positive points and the strength of NTRU cryptosystems. The definition of the ring of CQTRU is introduced with the definition of its operations. The three phases of the new proposed system (key generation, encryption and decryption) are discussed in details, in addition to the decryption failure probability, key security and message security. Finally, the resistance of CQTRU's against lattice attack is investigated.

This paper proposed a new method to attack the NTRU cryptosystem [Hof00a,
Hof98b]. It tried to exploit the public information about the parameters of NTRU
cryptosystem and using the public key, to recover the private keys without delving
in the detail of encryption and decryption. It depended on extant knowledge about
the number of 1’s and -1’s in the private keys coefficients, f and g, which are
used in public key generation. It tried to make use of the polynomial that has
private key coefficients properties. The proposed attack was able to recover a
unique polynomial that represented the private key f and corresponding to private
key g, or their rotations. But, this attack remains expensive in time and depends on
the way of how to start in choice the permutation