The Application Research Of Hyperbolic Arithmetic In SSL Protocol

SSL(Secure Sockets Layer)protocol is widely used in identity authentication on Internet and secure communication between client and Web server.In this paper,hyperbolic arithmetic over finite fields is used to replace Elliptic Curve Arithmetic in SSL protocol to realize identity authentication and key exchange,its advantages are as follows:①Hyperbolic arithmetic can directly encrypt messages without embedding message codes into hyperbola;②The group structure of hyperbolic arithmetic always constitutes a cyclic group in the finite field and its order can be calculated to facilitate the search for the base point;③the group operation of hyperbolic arithmetic is simple and easy to design and implement;④in the same finite field,the cryptographic space of hyperbolic arithmetic is one order of magnitude larger than that of elliptic curve cryptography;⑤The parameters of hyperbola can be adjusted.By changing the parameter D of hyperbola,different hyperbola can be obtained,which reduces the design cost of hyperbola.The main work of this paper is as follows:(1)Hyperbolic arithmetic is applied to network security protocol for the first time,and the functions of identity authentication and key exchange are realized.(2)In the application of hyperbola,a fast method to get the base point of unit hyperbola and a method to calculate hyperbolic cluster generator are designed.(3)The feasibility and validity ofthe above two methods are proved by programming,and the SSL protocol and design standard of hyperbolic arithmetic are established.(4)In terms of security,hyperbola and elliptic curve have the same discrete logarithmic complexity.Since the SSL protocol is implemented by the OpenSSL cryptographic suite,this paper uses OpenSSL to test the speed of key exchange between elliptic curve and hyperbola.The test results showthat the speed of key exchange between hyperbola and hyperbola is faster than that of elliptic curve.