Most of them are now _mandatory_ P3 scripts, because I'm tired of
maintaining everything to be compatible with both versions.
The current exceptions are gdb.py (which has to live with whatever gdb
gives it), and kh2reg.py (which is actually designed for other people
to use, and some of them might still be stuck on P2 for the moment).
This is standardised by RFC 8709 at SHOULD level, and for us it's not
too difficult (because we use general-purpose elliptic-curve code). So
let's be up to date for a change, and add it.
This implementation uses all the formats defined in the RFC. But we
also have to choose a wire format for the public+private key blob sent
to an agent, and since the OpenSSH agent protocol is the de facto
standard but not (yet?) handled by the IETF, OpenSSH themselves get to
say what the format for a key should or shouldn't be. So if they don't
support a particular key method, what do you do?
I checked with them, and they agreed that there's an obviously right
format for Ed448 keys, which is to do them exactly like Ed25519 except
that you have a 57-byte string everywhere Ed25519 had a 32-byte
string. So I've done that.
With all the preparation now in place, this is more or less trivial.
We add a new curve setup function in sshecc.c, and an ssh_kex linking
to it; we add the curve parameters to the reference / test code
eccref.py, and use them to generate the list of low-order input values
that should be rejected by the sanity check on the kex output; we add
the standard test vectors from RFC 7748 in cryptsuite.py, and the
low-order values we just generated.
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.
