Elliptic curve cryptography on constraint environments

The main target of this work is to expose the capacities that make elliptic curve cryptography the most suitable one to be implemented in environments with several constraints related to processor speed, bandwidth, security and memory. We have analyzed several elliptic curve cryptosystems with other public key ones. We have made a comparison among different public key cryptosystems (such as ElGamal for encryption and Diffie-Hellman for key exchanging) and the corresponding ones based on elliptic curve theory; highlighting algorithm speed characteristics.