Research And Realization Of NTRU

As a part of public-key cryptography, NTTU cryptosystem has large potentials on development. Compared with RSA and ECC cryptosystem which is used in a wide range of applications,NTRU cryptosystem can produce the key pair more quickly under the same security requirements. Besides, the speed of encryption and decryption is higher than some others.As a result of easier operation as well as less running time. And it is fit for the development of the small-embedded equipment,such as IC card.NTRU, is based on the hard problem of lattice,in the whole flow of which it just involves with addition ,multiplication and inverse in the truncated polynomial ring.For NTRU,except the security and speed,another problem which should be considered is the decryption failure.And this problem can be solved by choosing reasonable parameters to control the decryption failure probability in a small range.In this paper we introduce the history of NTRU, the application in the market and standardization development;Then we introduce the basic theory and flow in details, talk about the parameters choosing considering decryption failure, provide the parameters from the standardization draft;Then something about three lattice-reduced algorithms Gauss,LLL,BKZ-LLL algorithm;Then NTRUSign-the signature schemes;In the last we realize the algorithm and give the experiment data for reference.