DESCRIPTION
The
/etc/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
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
moduli 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:
-
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:
-
0
-
Unknown, not tested.
-
2
-
"Safe" prime; (p-1)/2 is also prime.
-
4
-
Sophie Germain; 2p+1 is also prime.
Moduli candidates initially produced by ssh-keygen(1) are Sophie Germain primes (type 4). Further 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:
-
0x00
-
Not tested.
-
0x01
-
Composite number – not prime.
-
0x02
-
Sieve of Eratosthenes.
-
0x04
-
Probabilistic 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 the number of primality 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
/etc/moduli that best meets the size requirement.