The use of Java in developing commercial Internet applications is growing very rapidly. A major requirement for e-commerce applications is the provision of security. In this work we consider Elliptic Curve Cryptography (ECC) because of the high level of security it provides with small key sizes. ECC is ideal for use on constrained environments such as pagers, personal digital assistants, cellular phones and smart cards. We implement the ECC algorithms approved by the National Institute of Standards and Technology (NIST) in Java on the Dell Inspiron 7500. The speeds of the various ECC algorithms are provided.