Mark Wooding pointed out that my comment in make1305.py was completely
wrong, and that the stated strategy for reducing a value mod 2^130-5
would not in fact completely reduce all inputs in the range - for the
most obvious reason, namely that the numbers between 2^130-5 and 2^130
would never have anything subtracted at all.
Implemented a replacement strategy which my tests suggest will do the
right thing for all numbers in the expected range that are anywhere
near an integer multiple of the modulus.
As I mentioned in the previous commit, I'm going to want PuTTY to be
able to run sensibly when compiled with 64-bit Visual Studio,
including handling bignums in 64-bit chunks for speed. Unfortunately,
64-bit VS does not provide any type we can use as BignumDblInt in that
situation (unlike 64-bit gcc and clang, which give us __uint128_t).
The only facilities it provides are compiler intrinsics to access an
add-with-carry operation and a 64x64->128 multiplication (the latter
delivering its product in two separate 64-bit output chunks).
Hence, here's a substantial rework of the bignum code to make it
implement everything in terms of _those_ primitives, rather than
depending throughout on having BignumDblInt available to use ad-hoc.
BignumDblInt does still exist, for the moment, but now it's an
internal implementation detail of sshbn.h, only declared inside a new
set of macros implementing arithmetic primitives, and not accessible
to any code outside sshbn.h (which confirms that I really did catch
all uses of it and remove them).
The resulting code is surprisingly nice-looking, actually. You'd
expect more hassle and roundabout circumlocutions when you drop down
to using a more basic set of primitive operations, but actually, in
many cases it's turned out shorter to write things in terms of the new
BignumADC and BignumMUL macros - because almost all my uses of
BignumDblInt were implementing those operations anyway, taking several
lines at a time, and now they can do each thing in just one line.
The biggest headache was Poly1305: I wasn't able to find any sensible
way to adapt the existing Python script that generates the various
per-int-size implementations of arithmetic mod 2^130-5, and so I had
to rewrite it from scratch instead, with nothing in common with the
old version beyond a handful of comments. But even that seems to have
worked out nicely: the new version has much more legible descriptions
of the high-level algorithms, by virtue of having a 'Multiprecision'
type which wraps up the division into words, and yet Multiprecision's
range analysis allows it to automatically drop out special cases such
as multiplication by 5 being much easier than multiplication by
another multi-word integer.
Rather than doing arithmetic mod 2^130-5 using the general-purpose
Bignum library, which requires lots of mallocs and frees per operation
and also uses a general-purpose divide routine for each modular
reduction, we now have some dedicated routines in sshccp.c to do
arithmetic mod 2^130-5 in a more efficient way, and hopefully also
with data-independent performance.
Because PuTTY's target platforms don't all use the same size of bignum
component, I've arranged to auto-generate the arithmetic functions
using a Python script living in the 'contrib' directory. As and when
we need to support an extra BignumInt size, that script should still
be around to re-run with different arguments.
