awk Division and modulus Post: 302380735

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moduli

MODULI(5)						      BSD File Formats Manual							 MODULI(5)

NAME

     moduli -- Diffie-Hellman moduli

DESCRIPTION

     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, calcu-
     lates 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) pri-
			mality 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 out-
     put to sufficiently key the selected symmetric cipher.  sshd(8) then randomly selects a modulus from /etc/ssh/moduli that best meets the size
     requirement.

SEE ALSO

     ssh-keygen(1), sshd(8)

STANDARDS

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

BSD
								September 26, 2012							       BSD