Research And Application Of NTRU In Mobile Computing Security

With the development of Internet technology and the popularity of smart devices, mobile computing in people's daily lives is more and more common, which indicating a huge market potential. However, because of mobile terminal equipment's own limitations and other factors, the security becomes a key factor for further development of mobile computing. Therefore, research on the security of mobile computing has important significance.From the perspective of cryptography, NTRU public key cryptosystem and its applications in the security of mobile computing is studied in this paper. Among kinds of encryption algorithms, the symmetric key cryptography has high speed, but the two communicating parties use the same key, which brings a lot of difficulties to key negotiation and management. The public key cryptography can just solve these problems, but it is much slower than the symmetric key cryptography. Therefore, usually the two are combined to use. NTRU algorithm, a relatively new public key algorithm, which has advantages of high speed, low memory use and high security, is more suitable for resource-limited devices than other public key algorithms. In this paper we first briefly introduce NTRU algorithm's underlying difficult problems in lattice, then the basic principle of NTRU and its inherent flaws, decryption failure, are analyzed, and another important issue in algorithm, the inverse of a polynomial, is studied. On this basis, we consider the optimization of NTRU. In the key generation process, one complex operation is computing the inverse of the private key; in the total process of the algorithm, the mainly time-consuming operation is polynomial convolution. From these two considerations, this paper changes the forms of the private key f and the modulus p, and uses low Hamming weight polynomial product, to improve the efficiency of NTRU algorithm. Changing the form of private key can save time in the key generation and the decryption; By using low Hamming weight polynomial product, some polynomial convolution's speed can be raised by 2 times. Then, an experiment is made to compare the time required by NTRU-251 and RSA-1024, which are in the same security level, in the key generation, encryption and decryption, showing the advantages of NTRU. In the digital signature, the paper focuses on the NTRUSign algorithm. At the end of the paper, by using NTRU algorithm in a mobile ticket reservation system, its application in a real system is studied.