ecc_montgomery_normalise takes a point with X and Z coordinates, and
normalises it to Z=1 by means of multiplying X by the inverse of Z and
then setting Z=1.
If you pass in a point with Z=0, representing the curve identity, then
it would be nice to still get the identity back out again afterwards.
We haven't really needed that property until now, but I'm about to
want it.
Currently, what happens is that we try to invert Z mod p; fail, but
don't notice we've failed, and come out with some nonsense value as
the inverse; multiply X by that; and then _set Z to 1_. So the output
value no longer has Z=0.
This commit changes things so that we multiply Z by the inverse we
computed. That way, if Z started off 0, it stays 0.
Also made the same change in the other two curve types, on general
principles, though I don't yet have a use for that.
The number of people has been steadily increasing who read our source
code with an editor that thinks tab stops are 4 spaces apart, as
opposed to the traditional tty-derived 8 that the PuTTY code expects.
So I've been wondering for ages about just fixing it, and switching to
a spaces-only policy throughout the code. And I recently found out
about 'git blame -w', which should make this change not too disruptive
for the purposes of source-control archaeology; so perhaps now is the
time.
While I'm at it, I've also taken the opportunity to remove all the
trailing spaces from source lines (on the basis that git dislikes
them, and is the only thing that seems to have a strong opinion one
way or the other).
Apologies to anyone downstream of this code who has complicated patch
sets to rebase past this change. I don't intend it to be needed again.
This will let my upcoming new test of memory access patterns run a
sequence of tests on different elliptic-curve data which is stored at
the same address each time.
It was computing the RHS of the curve equation affinely, without
taking account of the point's Z coordinate. In other words, it would
work OK for a point you'd _only just_ imported into ecc.c which was
still represented with a denominator of 1, but it would give the wrong
answer for points coming out of computation after that.
I've moved the simple version into ecc_weierstrass_point_new_from_x,
since the only reason it was in a separate function at all was so it
could be reused by point_valid, which I now realise it can't.
The old 'Bignum' data type is gone completely, and so is sshbn.c. In
its place is a new thing called 'mp_int', handled by an entirely new
library module mpint.c, with API differences both large and small.
The main aim of this change is that the new library should be free of
timing- and cache-related side channels. I've written the code so that
it _should_ - assuming I haven't made any mistakes - do all of its
work without either control flow or memory addressing depending on the
data words of the input numbers. (Though, being an _arbitrary_
precision library, it does have to at least depend on the sizes of the
numbers - but there's a 'formal' size that can vary separately from
the actual magnitude of the represented integer, so if you want to
keep it secret that your number is actually small, it should work fine
to have a very long mp_int and just happen to store 23 in it.) So I've
done all my conditionalisation by means of computing both answers and
doing bit-masking to swap the right one into place, and all loops over
the words of an mp_int go up to the formal size rather than the actual
size.
I haven't actually tested the constant-time property in any rigorous
way yet (I'm still considering the best way to do it). But this code
is surely at the very least a big improvement on the old version, even
if I later find a few more things to fix.
I've also completely rewritten the low-level elliptic curve arithmetic
from sshecc.c; the new ecc.c is closer to being an adjunct of mpint.c
than it is to the SSH end of the code. The new elliptic curve code
keeps all coordinates in Montgomery-multiplication transformed form to
speed up all the multiplications mod the same prime, and only converts
them back when you ask for the affine coordinates. Also, I adopted
extended coordinates for the Edwards curve implementation.
sshecc.c has also had a near-total rewrite in the course of switching
it over to the new system. While I was there, I've separated ECDSA and
EdDSA more completely - they now have separate vtables, instead of a
single vtable in which nearly every function had a big if statement in
it - and also made the externally exposed types for an ECDSA key and
an ECDH context different.
A minor new feature: since the new arithmetic code includes a modular
square root function, we can now support the compressed point
representation for the NIST curves. We seem to have been getting along
fine without that so far, but it seemed a shame not to put it in,
since it was suddenly easy.
In sshrsa.c, one major change is that I've removed the RSA blinding
step in rsa_privkey_op, in which we randomise the ciphertext before
doing the decryption. The purpose of that was to avoid timing leaks
giving away the plaintext - but the new arithmetic code should take
that in its stride in the course of also being careful enough to avoid
leaking the _private key_, which RSA blinding had no way to do
anything about in any case.
Apart from those specific points, most of the rest of the changes are
more or less mechanical, just changing type names and translating code
into the new API.
