Research On The Elliptic Curve Cryptography And Its Application In Wireless Network Security

The security of the Elliptic Curve Cryptography (ECC) is built upon the difficulty of solving the elliptic curve discrete logarithm problem. The ECC has advantages of high security, short key size and fewer resources needed over other public key cryptographies. So it is a kind of most promising public key cryptographies and has become a research hotspot of the public cryptography.Since the Elliptic Curve Cryptography needs a lot of complex calculations, optimizing the implementation of the elliptic curve cryptography becomes a very important research direction.The scalar multiplication operation is the most time-consuming operation in the Elliptic Curve Cryptography and determines the performance of the Elliptic Curve Cryptography. In this paper, a lot of research on the existing methods for the optimizing the scalar multiplication were done, and a new improving method for the window non adjacent form was proposed. The improving method shifts the zero elements in the non adjacent form scale representation to the left using a kind of identity transform on the symbol binary sequence and more consecutive zero elements in the non adjacent form can be combined. So, it reduces the numbers of the windows in the window non adjacent form for the scale multiplication, hence, reduces the number of the point adding operations and improves the efficiency of the scalar multiplication operation. In order to verify the validity of the improving method, we design and implement an ECC system which has the ability of encryption and digtital signature based on the Numbery Theory Library. Comparison of the scale multiplication experiment data shows that the improving method has better performance than the window non adjacent form method.Finally, we carry out an in-depth research on the ECC's application in the wireless network security and discuss an ECC based authentication and key agreement protocol for wireless communication. An identifier description of the protocol is defined, the function and safety of the protocol are analysed. Besides, an improving method of the protocol based on a non inversion ECDSA signature scheme is proposed. The improved protocol is more efficiency and more suitable for the wireless network environment.