9 Hyperelliptic Cryptosystems

We will now work with a specific collection of examples of algebraic schemes that can be used for cryptosystems--hyperelliptic curves. In this case we can explicitly give a system of representatives for the elements of the K-group, a mechanism for ``reducing'' any element to one of these representing elements and also a bound for the size of the group. We will see in the next section how such information about a group can be used to make computations with the group efficient.