Simuleringar av elliptiska kurvor för elliptisk kryptografi

Sammanfattning: This thesis describes the theory behind elliptic-curve Diffie-Hellman key exchanges. All the way from the definition of a group until how the operator over an elliptic curve forms an abelian group. This is illustrated with clear examples. After that a smaller study is made to determine if there is a connection betweenthe size of the underlying field, the amount of points on the curve and the order of the points to determine how hard it is to find out the secret key in elliptic-curve Diffie-Hellman key exchanges. No clear connection is found. Since elliptic curves over extension fields have more computational heavy operations, it is concluded that these curves serve no practical use in elliptic-curve Diffie-Hellman key exchange.