The Optimization And Design Of The Hyperelliptic Curve Cryptography

The Hyperelliptic Curve Cryptography is an expansion of the Elliptic Curve Cryptography, its security is based on the difficulty of solving the Hyperelliptic Curve Discrete Problem. Compared with other public key cryptography, HECC has advantages of shorter key size, higher security, and more curve along with larger genus. It can almost simulate all protocols such as DSA. Therefore, more and more people are attracted by this task, and it has become the new hotspot of the public key cryptography.The major work of this paper is the research of HECC over F2 and genus two. Firstly, the scalar multiplication and the complex operation kD1 + lD2are optimized. Then we do some research on the basic protocols. For managing to be consistent about exchange and protection of the information before safely exchanging data, we design the diffie-hellman protocol; for keeping safe in the process of transmitting data, we design the encryption protocol; for proving the integrality of the news and the reliability of sending source,we design the digital signature protocol. Upon the above work, we design a cryptography scheme according to practical requirements. Based on the hyperelliptic curve digital signature protocol, we design a blind signature scheme which is efficient and has higher safety. At last, according to the above optimizations and improvements, a hyperelliptic curve cryptography is implemented and is applied into File Transfer design.Experiment shows, as optimization and design of this paper, the efficiency and security of the hyperelliptic curve cryptography are improved in a certain extent.Therefore, it is significative for HECC turning to practicality by the research of the paper.