Man page 5 : moduli

moduli - Diffie Hellman moduli

The .Pa /etc/ssh/moduli file contains prime numbers and generators for use by sshd(8) in the Diffie-Hellman Group Exchange key exchange method.

New moduli may be generated with ssh-keygen(1) using a two-step process. An initial .Em candidate generation pass, using ssh-keygen -G , calculates numbers that are likely to be useful. A second .Em 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:

-tag -width Description -offset indent
timestamp The time that the modulus was last processed as YYYYMMDDHHMMSS.
type Decimal number specifying the internal structure of the prime modulus. Supported types are:

-tag -width 0x00 -compact
0 Unknown, not tested
2 "Safe" prime; (p-1)/2 is also prime.
4 Sophie Germain; (p+1)*2 is also prime.

Moduli candidates initially produced by ssh-keygen(1) are Sophie Germain primes (type 4). Futher primality testing with ssh-keygen(1) produces safe prime moduli (type 2) that are ready for use in sshd(8) . Other types are not used by OpenSSH.
tests Decimal number indicating the type of primality tests that the number has been subjected to represented as a bitmask of the following values:

-tag -width 0x00 -compact
0x00 Not tested
0x01 Composite number - not prime.
0x02 Sieve of Eratosthenes
0x04 Probabalistic Miller-Rabin primality tests.

The ssh-keygen(1) moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02). Subsequent ssh-keygen(1) primality tests are Miller-Rabin tests (flag 0x04).
trials Decimal number indicating of primaility trials that have been performed on the modulus.
size Decimal number indicating the size of the prime in bits.
generator The recommended generator for use with this modulus (hexadecimal).
modulus The modulus itself in hexadecimal.

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.

ssh-keygen(1) , sshd(8) , .Rs .%R RFC 4419 .%T "Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol" .%D 2006