This is another application of the existing mp_bezout_into, which
needed a tweak or two to cope with the numbers not necessarily being
coprime, plus a wrapper function to deal with shared factors of 2.
It reindents the entire second half of mp_bezout_into, so the patch is
best viewed with whitespace differences ignored.
This is a third random-number generation function, with an API in
between the too-specific mp_random_bits and the too-general
mp_random_in_range. Now you can generate a value between 0 and n
without having to either make n a power of 2, or tediously allocate a
zero mp_int to be the lower limit for mp_random_in_range.
Implementation is done by sawing the existing mp_random_in_range into
two pieces and exposing the API between them.
This is a version of mp_lshift_fixed_into() which allocates the output
number, which it can do because you know the size of the original
number and are allowed to treat the shift count as non-secret.
(By contrast, mp_lshift_safe() would be a nonsensical function - if
you're trying to keep the shift count secret, you _can't_ use it as a
parameter of memory allocation! In that situation you have no choice
but to allocate memory based on a fixed upper bound.)
There was previously no safe left shift at all, which is an omission.
And rshift_safe_into was an odd thing to be missing, so while I'm
here, I've added it on the basis that it will probably be useful
sooner or later.
This is in preparation for a PRNG revamp which will want to have a
well defined boundary for any given request-for-randomness, so that it
can destroy the evidence afterwards. So no more looping round calling
random_byte() and then stopping when we feel like it: now you say up
front how many random bytes you want, and call random_read() which
gives you that many in one go.
Most of the call sites that had to be fixed are fairly mechanical, and
quite a few ended up more concise afterwards. A few became more
cumbersome, such as mp_random_bits, in which the new API doesn't let
me load the random bytes directly into the target integer without
triggering undefined behaviour, so instead I have to allocate a
separate temporary buffer.
The _most_ interesting call site was in the PKCS#1 v1.5 padding code
in sshrsa.c (used in SSH-1), in which you need a stream of _nonzero_
random bytes. The previous code just looped on random_byte, retrying
if it got a zero. Now I'm doing a much more interesting thing with an
mpint, essentially scaling a binary fraction repeatedly to extract a
number in the range [0,255) and then adding 1 to it.
I wrote it for the sake of a test-system design I had in mind at the
time, but that design changed after I committed, and now I think
_even_ my upcoming test application won't need to copy MontyContexts.
So I'll remove the function now, so as not to have to pointlessly
write tests for it :-)
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.
