moduli —
Diffie-Hellman moduli
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.
ssh-keygen(1),
sshd(8)
M. Friedl,
N. Provos, and W. Simpson,
Diffie-Hellman Group Exchange for the Secure Shell (SSH)
Transport Layer Protocol, RFC 4419,
March 2006,
2006.