A study of the elliptic curve cryptology applies to the next generation protocol

In recent years, Internet and the electronic commerce are very hot. Not only people start to care about the network security level where they use credit cards to order they want but also they have the idea about the network security. At the moment, the algorithm of RSA (Rivest-Shamir-Adleman) is used by the public key cryptology and digital signature. When end users need to send data to another one through Internet and input important data about one´s secrets to a database. In order to avoid someone get their data, their data will be protective by security administrator. But those technologies which can break the RSA (Rivest-Shamir-Adleman) are more and more perfect to make the algorithm of RSA (Rivest-Shamir-Adleman) needing more and more bytes to save our data. This action has long computing time and network transmission over loading. In elliptic curve cryptology, its bytes are less than RSA (Rivest-Shamir-Adleman). It can to let computer performance and network transmission be good and fast. Although the next generation protocol modifies from IPv4 and applies to IPSEC, it is not still perfect for network security. The unit of IP Security Protocol can´t coexist with the unit of IPv6 protocol service when IPv6 packets pass IPv4 protocol and network address transfer´s field. For those weaknesses, one will discuss elliptic curve cryptology how to translate in IPv6 protocol, and compare the performance of elliptic curve cryptology and RSA in IPv6 protocol.