Fast generation of elliptic curves with prime order over extension field of even extension degree

In order to protect the equipment or some important information from evil Internet users, information security technology has played a key role. RSA cryptosystem is the most widely used public-key cryptosystem but its key for ensuring sufficient security reaches about 2000 bits long. Therefore, it is not efficient to implement RSA cryptosystem on terminal with scarce computation resources. On the other hand, elliptic curve cryptosystem (ECC) has the same security level with about 7-fold smaller length key as compared to RSA cryptosystem, it is said that ECC is more practical as compared to RSA.