Elliptic and Hyperelliptic Curve Cryptography is the first exhaustive study of virtually all of the mathematical aspects of public key cryptography based on the discrete log system. This carefully constructed volume is a state-of-the-art study that explores both theory and applications. The book covers most aspects of elliptic curves and hyperelliptic curve cryptography and provides a detailed study on the smart card, including information on its main components, electronic properties, and attacks on the embedded memory. Standards on elliptic curve cryptography are provided along with information on some of the legal aspects of cryptography in the European Union and the United States.