Kriptolojide eliptik eğri algoritmasının uygulanması

In this study, it's aimed to explore the elliptic curve encryption algorithms, to build the algorithms, to provide information on mathematical basis and to implement a sample java program on elliptic curve algorithm. Contemporarily, the use of elliptic curves on cryptography gradually ascends and it plays an essential role in public key cryptography. One of the very important basics of elliptic curve cryptography is to transform the characters in the text that is to be transmitted to the points on xy coordinate system. This transformation not only converts the text to points on the ellyptic curve but also helps to get the original text from the points placed on the elliptic curve. Since the elliptic curve cryptography is based on public key encryption, the process starts with the transmission of the setting parameters over an insecure media. These setting parameters are called the field parameters. The strength of the ellyptic curve cryptography stems from the difficulty of solution of eliptic curve discrete logarithm(Yavuz, 2008). In encryption, sender first sets his own public key K by K=dL where L is generator point, and d is private key. Let M be the text to transmit, she then prepares the encrypted message U, using the receiver's public key Q by: ( , ) 2 1 U dL M dQ U M dQ U dL The receiver, then decrypts the text message M from received message U, using her private key k, that she used to create her own public key, by: M U kU M dQ dQ kU k dL d kL dQ U dL M dQ U dL and U M dQ ( ) ( ) ( ) ( , ) 2 1 1 1 2 Sample encryption program that is introduced in this article is programmed in java pogramming language in NetBeans IDE 6.9 without using standard cryptology libraries such that basic java language is employed. When the program first starts, a screen as in fig.1 is displayed.