I recently encountered a paper [1] which catalogues all kinds of
things that can go wrong when one party in a discrete-log system
invents a prime and the other party chooses an exponent. In
particular, some choices of prime make it reasonable to use a short
exponent to save time, but others make that strategy very bad.
That paper is about the ElGamal encryption scheme used in OpenPGP,
which is basically integer Diffie-Hellman with one side's key being
persistent: a shared-secret integer is derived exactly as in DH, and
then it's used to communicate a message integer by simply multiplying
the shared secret by the message, mod p.
I don't _know_ that any problem of this kind arises in the SSH usage
of Diffie-Hellman: the standard integer DH groups in SSH are safe
primes, and as far as I know, the usual generation of prime moduli for
DH group exchange also picks safe primes. So the short exponents PuTTY
has been using _should_ be OK.
However, the range of imaginative other possibilities shown in that
paper make me nervous, even so! So I think I'm going to retire the
short exponent strategy, on general principles of overcaution.
This slows down 4096-bit integer DH by about a factor of 3-4 (which
would be worse if it weren't for the modpow speedup in the previous
commit). I think that's OK, because, firstly, computers are a lot
faster these days than when I originally chose to use short exponents,
and secondly, more and more implementations are now switching to
elliptic-curve DH, which is unaffected by this change (and with which
we've always been using maximum-length exponents).
[1] On the (in)security of ElGamal in OpenPGP. Luca De Feo, Bertram
Poettering, Alessandro Sorniotti. https://eprint.iacr.org/2021/923
This clears up another large pile of clutter at the top level, and in
the process, allows me to rename source files to things that don't all
have that annoying 'ssh' prefix at the top.
