Research On Application Of Elliptic Curve Cryptosystem

With the development and application of information technology, the problem of information security becomes more and more important. In order to improve the security, secrecy and reliability of the communication, we need cryptosystem of high reliability and good security. The elliptic curve cryptosystem used in public cryptosystem is one has the best security coefficient. The elliptic curve cryptosystem provides the highest strength of any cryptosystem known. Because it has shorter key size, less computation, less memory space and lower bandwidth, so it has wide application prospect in information security field.This article first carries on the brief introduction to the elliptic curve cryptosystem. After that, has analyzed the elliptic curve cryptosystem related theory, including elliptic curve basic concept, elliptic curve cryptosystem mathematics theory, elliptic curve cryptosystem attack present situation and so on. Proposed the detecting prime number algorithm, the multiplication opposite element algorithm, and the elliptic curve cryptosystem stochastic production algorithm based on above theory. The article also proposed the encryption and digital signature application algorithms. Then, some algorithms are implemented with the Java technology, including the elliptic curve cryptosystem stochastic production algorithm and the key exchange, encryption and digital signature application algorithms. Finally has confirmed these algorithms feasibility.