example 2.31 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
From owner-cypherpunks@toad.com Mon Sep 25 10:50:51 1995
Received: from minbne.mincom.oz.au by orb.mincom.oz.au with SMTP id AA10562
  (5.65c/IDA-1.4.4 for eay); Wed, 27 Sep 1995 19:41:55 +1000
Received: by minbne.mincom.oz.au id AA19958
  (5.65c/IDA-1.4.4 for eay@orb.mincom.oz.au); Wed, 27 Sep 1995 19:34:59 +1000
Received: from relay3.UU.NET by bunyip.cc.uq.oz.au with SMTP (PP);
          Wed, 27 Sep 1995 19:13:05 +1000
Received: from toad.com by relay3.UU.NET with SMTP id QQzizb16156;
          Wed, 27 Sep 1995 04:48:46 -0400
Received: by toad.com id AA07905; Tue, 26 Sep 95 06:31:45 PDT
Received: from by toad.com id AB07851; Tue, 26 Sep 95 06:31:40 PDT
Received: from servo.qualcomm.com (servo.qualcomm.com [129.46.128.14]) 
          by cygnus.com (8.6.12/8.6.9) with ESMTP id RAA18442 
          for <cypherpunks@toad.com>; Mon, 25 Sep 1995 17:52:47 -0700
Received: (karn@localhost) by servo.qualcomm.com (8.6.12/QC-BSD-2.5.1) 
          id RAA14732; Mon, 25 Sep 1995 17:50:51 -0700
Date: Mon, 25 Sep 1995 17:50:51 -0700
From: Phil Karn <karn@qualcomm.com>
Message-Id: <199509260050.RAA14732@servo.qualcomm.com>
To: cypherpunks@toad.com, ipsec-dev@eit.com
Subject: Primality verification needed
Sender: owner-cypherpunks@toad.com
Precedence: bulk
Status: RO
X-Status: 

Hi. I've generated a 2047-bit "strong" prime number that I would like to
use with Diffie-Hellman key exchange. I assert that not only is this number
'p' prime, but so is (p-1)/2.

I've used the mpz_probab_prime() function in the Gnu Math Package (GMP) version
1.3.2 to test this number. This function uses the Miller-Rabin primality test.
However, to increase my confidence that this number really is a strong prime,
I'd like to ask others to confirm it with other tests. Here's the number in hex:

72a925f760b2f954ed287f1b0953f3e6aef92e456172f9fe86fdd8822241b9c9788fbc289982743e
fbcd2ccf062b242d7a567ba8bbb40d79bca7b8e0b6c05f835a5b938d985816bc648985adcff5402a
a76756b36c845a840a1d059ce02707e19cf47af0b5a882f32315c19d1b86a56c5389c5e9bee16b65
fde7b1a8d74a7675de9b707d4c5a4633c0290c95ff30a605aeb7ae864ff48370f13cf01d49adb9f2
3d19a439f753ee7703cf342d87f431105c843c78ca4df639931f3458fae8a94d1687e99a76ed99d0
ba87189f42fd31ad8262c54a8cf5914ae6c28c540d714a5f6087a171fb74f4814c6f968d72386ef3
56a05180c3bec7ddd5ef6fe76b1f717b

The generator, g, for this prime is 2.

Thanks!

Phil Karn