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1 .\" $OpenBSD: moduli.5,v 1.12 2008/06/26 05:57:54 djm Exp $
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3 .\" Copyright (c) 2008 Damien Miller <djm@mindrot.org>
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5 .\" Permission to use, copy, modify, and distribute this software for any
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16 .Dd $Mdocdate: June 26 2008 $
17 .Dt MODULI 5
18 .Os
19 .Sh NAME
20 .Nm moduli
21 .Nd Diffie Hellman moduli
22 .Sh DESCRIPTION
23 The
24 .Pa /etc/moduli
25 file contains prime numbers and generators for use by
26 .Xr sshd 8
27 in the Diffie-Hellman Group Exchange key exchange method.
28 .Pp
29 New moduli may be generated with
30 .Xr ssh-keygen 1
31 using a two-step process.
32 An initial
33 .Em candidate generation
34 pass, using
35 .Ic ssh-keygen -G ,
36 calculates numbers that are likely to be useful.
37 A second
38 .Em primality testing
39 pass, using
40 .Ic ssh-keygen -T
41 provides a high degree of assurance that the numbers are prime and are
42 safe for use in Diffie Hellman operations by
43 .Xr sshd 8 .
44 This
45 .Nm
46 format is used as the output from each pass.
47 .Pp
48 The file consists of newline-separated records, one per modulus,
49 containing seven space separated fields.
50 These fields are as follows:
51 .Pp
52 .Bl -tag -width Description -offset indent
53 .It timestamp
54 The time that the modulus was last processed as YYYYMMDDHHMMSS.
55 .It type
56 Decimal number specifying the internal structure of the prime modulus.
57 Supported types are:
58 .Pp
59 .Bl -tag -width 0x00 -compact
60 .It 0
61 Unknown, not tested
62 .It 2
63 "Safe" prime; (p-1)/2 is also prime.
64 .It 4
65 Sophie Germain; (p+1)*2 is also prime.
66 .El
67 .Pp
68 Moduli candidates initially produced by
69 .Xr ssh-keygen 1
70 are Sophie Germain primes (type 4).
71 Futher primality testing with
72 .Xr ssh-keygen 1
73 produces safe prime moduli (type 2) that are ready for use in
74 .Xr sshd 8 .
75 Other types are not used by OpenSSH.
76 .It tests
77 Decimal number indicating the type of primality tests that the number
78 has been subjected to represented as a bitmask of the following values:
79 .Pp
80 .Bl -tag -width 0x00 -compact
81 .It 0x00
82 Not tested
83 .It 0x01
84 Composite number - not prime.
85 .It 0x02
86 Sieve of Eratosthenes
87 .It 0x04
88 Probabalistic Miller-Rabin primality tests.
89 .El
90 .Pp
91 The
92 .Xr ssh-keygen 1
93 moduli candidate generation uses the Sieve of Eratosthenes (flag 0x02).
94 Subsequent
95 .Xr ssh-keygen 1
96 primality tests are Miller-Rabin tests (flag 0x04).
97 .It trials
98 Decimal number indicating of primaility trials that have been performed
99 on the modulus.
100 .It size
101 Decimal number indicating the size of the prime in bits.
102 .It generator
103 The recommended generator for use with this modulus (hexadecimal).
104 .It modulus
105 The modulus itself in hexadecimal.
106 .El
107 .Pp
108 When performing Diffie Hellman Group Exchange,
109 .Xr sshd 8
110 first estimates the size of the modulus required to produce enough
111 Diffie Hellman output to sufficiently key the selected symmetric cipher.
112 .Xr sshd 8
113 then randomly selects a modulus from
114 .Fa /etc/moduli
115 that best meets the size requirement.
116 .Pp
117 .Sh SEE ALSO
118 .Xr ssh-keygen 1 ,
119 .Xr sshd 8 ,
120 .Rs
121 .%R RFC 4419
122 .%T "Diffie-Hellman Group Exchange for the Secure Shell (SSH) Transport Layer Protocol"
123 .%D 2006
124 .Re