The Reaserch And Implementation Of The NTRU Variant-D-NTRU Algorithm

NTRU is a fast public key cryptosystem (PKC) remaining unbroken. However, the security of the original NTRU cannot be mathematically proven. Several provably secure NTRU modifications were proposed in the literature at the cost of heavily compromising its efficiency and enlarging its ciphertext expansion. In2012, a new NTRU modification called D-NTRU is established by Wang and other person. And they also prove that the D-NTRU is IND-CPA security under the NTRU one-wayness assumption. It is shown that the D-NTRU cryptosystem reduces the ciphertext expansion of the NTRU algorithm, and the encryption and decryption algorithms of D-NTRU perform even asymptotically faster than the NTRU algorithm only at the cost of slightly enlarging the secret and public key sizes. The proof of the IND-CPA security of D-NTRU is completed by introducing another NTRU variant called C-NTRU as a bridge, defining some problems, and then proving the equivalence of these problems by Wang and other person. So the proposed D-NTRU algorithm is more advantageous than the original NTRU algorithm, and much more efficient than all the provably secure variants of NTRU. But just from the theoretical argument is weak, the conclusion still need to prove in practice application. And this paper is from the point of practice application and proves the correctness of the above theory through the implementation of the NTRU and D-NTRU software system. The main reaseach work of this paper can be summarized as follows:1. We implement the NTRU system and D-NTRU system by programming languages in the same computer environment and programming standard. The prototype system includes key generation, encryption, decryption and time statistics.2. Build the test environment and completely test the prototype system. Then we prove that the correctness of NTRU and D-NTRU encryption decryption reach100%within24hours in practical application according to the parameters suggested by Wang and other person. And we also prove that the encryption, decryption speed of D-NTRU prototype system is more efficient than NTRU prototype system.