The Jacobian on a hyperelliptic curve is an Abelian group and as such it can serve as group for the order, thus making the system more efficient.
42.
The allowable power " k " has to be determined by analysis of the possible pole at the point at infinity on the corresponding hyperelliptic curve.
43.
In this page, we describe more about real hyperelliptic curves, these are curves having two points at infinity while imaginary hyperelliptic curves have one point at infinity.
44.
In this page, we describe more about real hyperelliptic curves, these are curves having two points at infinity while imaginary hyperelliptic curves have one point at infinity.
45.
While this model is the simplest way to describe hyperelliptic curves, such an equation will have a singular point " at infinity " in the projective plane.
46.
From this picture it is immediately clear that we cannot use the chords and tangents method to define a group law on the set of points of a hyperelliptic curve.
47.
There are two types of hyperelliptic curves : "'real hyperelliptic curves "'and imaginary hyperelliptic curves which differ by the number of points at infinity.
48.
There are two types of hyperelliptic curves : "'real hyperelliptic curves "'and imaginary hyperelliptic curves which differ by the number of points at infinity.
49.
There are two types of hyperelliptic curves : "'real hyperelliptic curves "'and imaginary hyperelliptic curves which differ by the number of points at infinity.
50.
For more information about the operations based on the use of these coordinates see http : / / hyperelliptic . org / EFD / g1p / auto-jintersect-extended . html
