The more features and options I add to PrimeCandidateSource, the more
cumbersome it will be to replicate each one in a command-line option
to the ultimate primegen() function. So I'm moving to an API in which
the client of primegen() constructs a PrimeCandidateSource themself,
and passes it in to primegen().
Also, changed the API for pcs_new() so that you don't have to pass
'firstbits' unless you really want to. The net effect is that even
though we've added flexibility, we've also simplified the call sites
of primegen() in the simple case: if you want a 1234-bit prime, you
just need to pass pcs_new(1234) as the argument to primegen, and
you're done.
The new declaration of primegen() lives in ssh_keygen.h, along with
all the types it depends on. So I've had to #include that header in a
few new files.
I've replaced the random number generation and small delta-finding
loop in primegen() with a much more elaborate system in its own source
file, with unit tests and everything.
Immediate benefits:
- fixes a theoretical possibility of overflowing the target number of
bits, if the random number was so close to the top of the range
that the addition of delta * factor pushed it over. However, this
only happened with negligible probability.
- fixes a directional bias in delta-finding. The previous code
incremented the number repeatedly until it found a value coprime to
all the right things, which meant that a prime preceded by a
particularly long sequence of numbers with tiny factors was more
likely to be chosen. Now we select candidate delta values at
random, that bias should be eliminated.
- changes the semantics of the outermost primegen() function to make
them easier to use, because now the caller specifies the 'bits' and
'firstbits' values for the actual returned prime, rather than
having to account for the factor you're multiplying it by in DSA.
DSA client code is correspondingly adjusted.
Future benefits:
- having the candidate generation in a separate function makes it
easy to reuse in alternative prime generation strategies
- the available constraints support applications such as Maurer's
algorithm for generating provable primes, or strong primes for RSA
in which both p-1 and p+1 have a large factor. So those become
things we could experiment with in future.
