This uses the new quartic-solver mod p to generate all the values in
Curve25519 that can end up at the curve identity by repeated
application of the doubling formula.
I'm about to want to solve quartics mod a prime, which means I'll need
to be able to take cube roots mod p as well as square roots.
This commit introduces a more general class which can take rth roots
for any prime r, and moreover, it can do it in a general cyclic group.
(You have to tell it the group's order and give it some primitives for
doing arithmetic, plus a way of iterating over the group elements that
it can use to look for a non-rth-power and roots of unity.)
That system makes it nicely easy to test, because you can give it a
cyclic group represented as the integers under _addition_, and then
you obviously know what all the right answers are. So I've also added
a unit test system checking that.
I'm about to want to expand the underlying number-theory code, so I'll
start by moving it into a file where it has room to grow without
swamping the main purpose of eccref.py.
The __truediv__ pair makes the whole program work in Python 3 as well
as 2 (it was _so_ nearly there already!), and __int__ lets you easily
turn a ModP back into an ordinary Python integer representing its
least positive residue.
