## NAME

`moduli`

—
Diffie-Hellman moduli

## 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 -M
generate
```

, calculates numbers that are likely to be useful. A second
*primality
testing* pass, using `ssh-keygen -M screen`

,
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.

## SEE ALSO

## STANDARDS

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