Elliptic Curve Cryptography- Status, Challenges and Future trends

In the modern cryptography, the Elliptic Curve takes large and important part. Elliptic Curve usually uses in wireless environments, mobile network and credit card, because it uses a relatively small key with the rest of the public key algorithms. This paper introduces survey of Elliptic Curve by developed classification depends on the concept of the main objective of the studies and reviewed previous survives on this field.