A 'strong' prime, as defined by the Handbook of Applied Cryptography,
is a prime p such that each of p-1 and p+1 has a large prime factor,
and that the large factor q of p-1 is such that q-1 in turn _also_ has
a large prime factor.
HoAC says that making your RSA key using primes of this form defeats
some factoring algorithms - but there are other faster algorithms to
which it makes no difference. So this is probably not a useful
precaution in practice. However, it has been recommended in the past
by some official standards, and it's easy to implement given the new
general facility in PrimeCandidateSource that lets you ask for your
prime to satisfy an arbitrary modular congruence. (And HoAC also says
there's no particular reason _not_ to use strong primes.) So I provide
it as an option, just in case anyone wants to select it.
The change to the key generation algorithm is entirely in sshrsag.c,
and is neatly independent of the prime-generation system in use. If
you're using Maurer provable prime generation, then the known factor q
of p-1 can be used to help certify p, and the one for q-1 to help with
q in turn; if you switch to probabilistic prime generation then you
still get an RSA key with the right structure, except that every time
the definition says 'prime factor' you just append '(probably)'.
(The probabilistic version of this procedure is described as 'Gordon's
algorithm' in HoAC section 4.4.2.)
Most of them are now _mandatory_ P3 scripts, because I'm tired of
maintaining everything to be compatible with both versions.
The current exceptions are gdb.py (which has to live with whatever gdb
gives it), and kh2reg.py (which is actually designed for other people
to use, and some of them might still be stuck on P2 for the moment).
Well, actually, two new test programs. agenttest.py is the actual
test; it depends on agenttestgen.py which generates a collection of
test private keys, using the newly exposed testcrypt interface to our
key generation code.
In this commit I've also factored out some Python SSH marshalling code
from cryptsuite, and moved it into a module ssh.py which the agent
tests can reuse.
