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
generation pass, using
calculates numbers that are likely to be useful. A second
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
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:
- The time that the modulus was last processed as YYYYMMDDHHMMSS.
- Decimal number specifying the internal structure of the prime modulus.
Supported types are:
- Unknown, not tested.
- "Safe" prime; (p-1)/2 is also prime.
- 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.
- Decimal number indicating the type of primality tests that the number has
been subjected to represented as a bitmask of the following values:
- Not tested.
- Composite number – not prime.
- Sieve of Eratosthenes.
- 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).
- Decimal number indicating the number of primality trials that have been performed on the modulus.
- Decimal number indicating the size of the prime in bits.
- The recommended generator for use with this modulus (hexadecimal).
- 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.
M. Friedl, N. Provos, and W. Simpson, Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol, RFC 4419, March 2006.