Instead of repeatedly looping on the random number generator until it
comes up with two values that have a large enough product, the new
version guarantees only one use of random numbers, by first counting
up all the possible pairs of values that would work, and then
inventing a single random number that's used as an index into that
list.
I've done the selection from the list using constant-time techniques,
not particularly because I think key generation can be made CT in
general, but out of sheer habit after the last few months, and who
knows, it _might_ be useful.
While I'm at it, I've also added an option to make sure the two
firstbits values differ by at least a given value. For RSA, I set that
value to 2, guaranteeing that even if the smaller prime has a very
long string of 1 bits after the firstbits value and the larger has a
long string of 0, they'll still have a relative difference of at least
2^{-12}. Not that there was any serious chance of the primes having
randomly ended up so close together as to make the key in danger of
factoring, but it seems like a silly thing to leave out if I'm
rewriting the function anyway.
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.
In commit 884a7df94 I claimed that all my trait-like vtable systems
now had the generic object type being a struct rather than a bare
vtable pointer (e.g. instead of 'Socket' being a typedef for a pointer
to a const Socket_vtable, it's a typedef for a struct _containing_ a
vtable pointer).
In fact, I missed a few. This commit converts ssh_key, ssh2_cipher and
ssh1_cipher into the same form as the rest.
After Pavel Kryukov pointed out that I have to put _something_ in the
'ssh_key' structure, I thought of an actually useful thing to put
there: why not make it store a pointer to the ssh_keyalg structure?
Then ssh_key becomes a classoid - or perhaps 'traitoid' is a closer
analogy - in the same style as Socket and Plug. And just like Socket
and Plug, I've also arranged a system of wrapper macros that avoid the
need to mention the 'object' whose method you're invoking twice at
each call site.
The new vtable pointer directly replaces an existing field of struct
ec_key (which was usable by several different ssh_keyalgs, so it
already had to store a pointer to the currently active one), and also
replaces the 'alg' field of the ssh2_userkey structure that wraps up a
cryptographic key with its comment field.
I've also taken the opportunity to clean things up a bit in general:
most of the methods now have new and clearer names (e.g. you'd never
know that 'newkey' made a public-only key while 'createkey' made a
public+private key pair unless you went and looked it up, but now
they're called 'new_pub' and 'new_priv' you might be in with a
chance), and I've completely removed the openssh_private_npieces field
after realising that it was duplicating information that is actually
_more_ conveniently obtained by calling the new_priv_openssh method
(formerly openssh_createkey) and throwing away the result.
Simon Tatham