MODULI(5) File Formats and Configurations MODULI(5)


moduli - Diffie-Hellman moduli


The /usr/share/lib/ssh/moduli file contains prime numbers and generators
for use by sshd(8) in the Diffie-Hellman Group Exchange key exchange

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

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

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

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 /usr/share/lib/ssh/moduli that best meets the size


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.

illumos April 16, 2022 illumos