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     moduli — Diffie-Hellman moduli


     The /etc/ssh/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/ssh/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.