Key generation
==============
Key generation shows progress by printing different characters to
stderr:
"." Last 10 Miller-Rabin tests failed
"+" Miller-Rabin test succeeded
"!" Reloading the pool with fresh prime numbers
"^" Checking a new value for the generator
"<" Size of one factor decreased
">" Size of one factor increased
The prime number for Elgamal is generated this way:
1) Make a prime number q of 160, 200, 240 bits (depending on the keysize)
2) Select the length of the other prime factors to be at least the size
of q and calculate the number of prime factors needed
3) Make a pool of prime numbers, each of the length determined in step 2
4) Get a new permutation out of the pool or continue with step 3
if we have tested all permutations.
5) Calculate a candidate prime p = 2 * q * p[1] * ... * p[n] + 1
6) Check that this prime has the correct length (this may change q if
it seems not to be possible to make a prime of the desired length)
7) Check whether this is a prime using trial divisions and the
Miller-Rabin test.
8) Continue with step 4 if we did not find a prime in step 7.
9) Find a generator for that prime.
This algorithm is based on Lim and Lee's suggestion from the
Crypto '97 proceedings p. 260.