New moduli may be generated with ssh-keygen1 using a two-step process. An initial candidate generation pass, using ssh-keygen -G calculates numbers that are likely to be useful. A second primality testing pass, using ssh-keygen -T provides a high degree of assurance that the numbers are prime and are safe for use in Diffie Hellman operations by sshd(8). This format is used as the output from each pass.
The file consists of newline-separated records, one per modulus, containing seven space separated fields. These fields are as follows:
Moduli candidates initially produced by ssh-keygen1 are Sophie Germain primes (type 4). Futher primality testing with ssh-keygen1 produces safe prime moduli (type 2) that are ready for use in sshd(8). Other types are not used by OpenSSH.
The ssh-keygen1 moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02). Subsequent ssh-keygen1 primality tests are Miller-Rabin tests (flag 0x04).
When performing Diffie Hellman Group Exchange, sshd(8) first estimates the size of the modulus required to produce enough Diffie Hellman output to sufficiently key the selected symmetric cipher. sshd(8) then randomly selects a modulus from Fa /etc/ssh/moduli that best meets the size requirement.