Based On The The Oef Ecc Domain Parameters Selected To Study

The information safety has special meaning to the politics, economy and military of a nation. As one of the essential tools of information safety, cryptology has an increasing trend that it gains more attention than before. The traditional symmetric cryptosystem has grown up; however, there are some problems with the distribution of key and how to save them. Also, it is hard to make the digital signature come true. Because the public-key cryptosystem provides confidentiality, authentication, data integrity and non repudiation, it satisfied with all requirements of information safety.In the known public-key cryptosystems, the elliptic curve cryptosystem ECC has the highest strength safety in each bit that can achieve comparative higher safety with less costs and time. Until now, pure exponential-time algorithm is still the best way to solve elliptic curve discrete logarithm problem. In addition, there are abundant source of elliptic curve that has amount of different elliptic curve in the same finite field; thus, it provides additional assurance for the safety. Because of the stable safety, it can believe that ECC will be the most general technology in public-key cryptosystems eventually.This thesis is composed by the following parts:First, the thesis discusses and analysis the mathematics foundation and research direction of ECC; also, it points out the main contents of research, which is the select method of safe parameter of ECC based on OEF that includes the selection of finite field, elliptic curve and base point.