Public-key Cryptography: Theory and Practice

**2.12. Hyperelliptic Curves

Hyperelliptic curves are generalizations of elliptic curves. We cannot define a group structure on a general hyperelliptic curve in the way as we did for elliptic curves. We instead work in the Jacobian of a hyperelliptic curve. For an elliptic curve E over an algebraically closed field K, the Jacobian is canonically isomorphic to the group E(K). Thus one can as well use the techniques for hyperelliptic curves for describing and working in elliptic curve groups. However, the exposition of the previous section turns out to be more intuitive and computationally oriented.

2.12.1. The Defining Equations

A hyperelliptic ...