1.\" $OpenBSD: moduli.5,v 1.19 2022/04/16 04:30:10 dtucker Exp $ 2.\" 3.\" Copyright (c) 2008 Damien Miller <djm@mindrot.org> 4.\" 5.\" Permission to use, copy, modify, and distribute this software for any 6.\" purpose with or without fee is hereby granted, provided that the above 7.\" copyright notice and this permission notice appear in all copies. 8.\" 9.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16.Dd $Mdocdate: April 16 2022 $ 17.Dt MODULI 5 18.Os 19.Sh NAME 20.Nm moduli 21.Nd Diffie-Hellman moduli 22.Sh DESCRIPTION 23The 24.Pa /etc/moduli 25file contains prime numbers and generators for use by 26.Xr sshd 8 27in the Diffie-Hellman Group Exchange key exchange method. 28.Pp 29New moduli may be generated with 30.Xr ssh-keygen 1 31using a two-step process. 32An initial 33.Em candidate generation 34pass, using 35.Ic ssh-keygen -M generate , 36calculates numbers that are likely to be useful. 37A second 38.Em primality testing 39pass, using 40.Ic ssh-keygen -M screen , 41provides a high degree of assurance that the numbers are prime and are 42safe for use in Diffie-Hellman operations by 43.Xr sshd 8 . 44This 45.Nm 46format is used as the output from each pass. 47.Pp 48The file consists of newline-separated records, one per modulus, 49containing seven space-separated fields. 50These fields are as follows: 51.Bl -tag -width Description -offset indent 52.It timestamp 53The time that the modulus was last processed as YYYYMMDDHHMMSS. 54.It type 55Decimal number specifying the internal structure of the prime modulus. 56Supported types are: 57.Pp 58.Bl -tag -width 0x00 -compact 59.It 0 60Unknown, not tested. 61.It 2 62"Safe" prime; (p-1)/2 is also prime. 63.It 4 64Sophie Germain; 2p+1 is also prime. 65.El 66.Pp 67Moduli candidates initially produced by 68.Xr ssh-keygen 1 69are Sophie Germain primes (type 4). 70Further primality testing with 71.Xr ssh-keygen 1 72produces safe prime moduli (type 2) that are ready for use in 73.Xr sshd 8 . 74Other types are not used by OpenSSH. 75.It tests 76Decimal number indicating the type of primality tests that the number 77has been subjected to represented as a bitmask of the following values: 78.Pp 79.Bl -tag -width 0x00 -compact 80.It 0x00 81Not tested. 82.It 0x01 83Composite number \(en not prime. 84.It 0x02 85Sieve of Eratosthenes. 86.It 0x04 87Probabilistic Miller-Rabin primality tests. 88.El 89.Pp 90The 91.Xr ssh-keygen 1 92moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02). 93Subsequent 94.Xr ssh-keygen 1 95primality tests are Miller-Rabin tests (flag 0x04). 96.It trials 97Decimal number indicating the number of primality trials 98that have been performed on the modulus. 99.It size 100Decimal number indicating the size of the prime in bits. 101.It generator 102The recommended generator for use with this modulus (hexadecimal). 103.It modulus 104The modulus itself in hexadecimal. 105.El 106.Pp 107When performing Diffie-Hellman Group Exchange, 108.Xr sshd 8 109first estimates the size of the modulus required to produce enough 110Diffie-Hellman output to sufficiently key the selected symmetric cipher. 111.Xr sshd 8 112then randomly selects a modulus from 113.Fa /etc/moduli 114that best meets the size requirement. 115.Sh SEE ALSO 116.Xr ssh-keygen 1 , 117.Xr sshd 8 118.Sh STANDARDS 119.Rs 120.%A M. Friedl 121.%A N. Provos 122.%A W. Simpson 123.%D March 2006 124.%R RFC 4419 125.%T Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol 126.Re 127