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.\" Copyright (c) 2008 Damien Miller <djm@mindrot.org>
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.Dd $Mdocdate: April 16 2022 $
.Dt MODULI 5
.Os
.Sh NAME
.Nm moduli
.Nd Diffie-Hellman moduli
.Sh DESCRIPTION
The
.Pa /etc/moduli
file contains prime numbers and generators for use by
.Xr sshd 8
in the Diffie-Hellman Group Exchange key exchange method.
.Pp
New moduli may be generated with
.Xr ssh-keygen 1
using a two-step process.
An initial
.Em candidate generation
pass, using
.Ic ssh-keygen -M generate ,
calculates numbers that are likely to be useful.
A second
.Em primality testing
pass, using
.Ic 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
.Xr sshd 8 .
This
.Nm
format is used as the output from each pass.
.Pp
The file consists of newline-separated records, one per modulus,
containing seven space-separated fields.
These fields are as follows:
.Bl -tag -width Description -offset indent
.It timestamp
The time that the modulus was last processed as YYYYMMDDHHMMSS.
.It type
Decimal number specifying the internal structure of the prime modulus.
Supported types are:
.Pp
.Bl -tag -width 0x00 -compact
.It 0
Unknown, not tested.
.It 2
"Safe" prime; (p-1)/2 is also prime.
.It 4
Sophie Germain; 2p+1 is also prime.
.El
.Pp
Moduli candidates initially produced by
.Xr ssh-keygen 1
are Sophie Germain primes (type 4).
Further primality testing with
.Xr ssh-keygen 1
produces safe prime moduli (type 2) that are ready for use in
.Xr sshd 8 .
Other types are not used by OpenSSH.
.It tests
Decimal number indicating the type of primality tests that the number
has been subjected to represented as a bitmask of the following values:
.Pp
.Bl -tag -width 0x00 -compact
.It 0x00
Not tested.
.It 0x01
Composite number \(en not prime.
.It 0x02
Sieve of Eratosthenes.
.It 0x04
Probabilistic Miller-Rabin primality tests.
.El
.Pp
The
.Xr ssh-keygen 1
moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02).
Subsequent
.Xr ssh-keygen 1
primality tests are Miller-Rabin tests (flag 0x04).
.It trials
Decimal number indicating the number of primality trials
that have been performed on the modulus.
.It size
Decimal number indicating the size of the prime in bits.
.It generator
The recommended generator for use with this modulus (hexadecimal).
.It modulus
The modulus itself in hexadecimal.
.El
.Pp
When performing Diffie-Hellman Group Exchange,
.Xr sshd 8
first estimates the size of the modulus required to produce enough
Diffie-Hellman output to sufficiently key the selected symmetric cipher.
.Xr sshd 8
then randomly selects a modulus from
.Fa /etc/moduli
that best meets the size requirement.
.Sh SEE ALSO
.Xr ssh-keygen 1 ,
.Xr sshd 8
.Sh STANDARDS
.Rs
.%A M. Friedl
.%A N. Provos
.%A W. Simpson
.%D March 2006
.%R RFC 4419
.%T Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol
.Re