1 From owner-cypherpunks (a] toad.com Mon Sep 25 10:50:51 1995 2 Received: from minbne.mincom.oz.au by orb.mincom.oz.au with SMTP id AA10562 3 (5.65c/IDA-1.4.4 for eay); Wed, 27 Sep 1995 19:41:55 +1000 4 Received: by minbne.mincom.oz.au id AA19958 5 (5.65c/IDA-1.4.4 for eay (a] orb.mincom.oz.au); Wed, 27 Sep 1995 19:34:59 +1000 6 Received: from relay3.UU.NET by bunyip.cc.uq.oz.au with SMTP (PP); 7 Wed, 27 Sep 1995 19:13:05 +1000 8 Received: from toad.com by relay3.UU.NET with SMTP id QQzizb16156; 9 Wed, 27 Sep 1995 04:48:46 -0400 10 Received: by toad.com id AA07905; Tue, 26 Sep 95 06:31:45 PDT 11 Received: from by toad.com id AB07851; Tue, 26 Sep 95 06:31:40 PDT 12 Received: from servo.qualcomm.com (servo.qualcomm.com [129.46.128.14]) 13 by cygnus.com (8.6.12/8.6.9) with ESMTP id RAA18442 14 for <cypherpunks (a] toad.com>; Mon, 25 Sep 1995 17:52:47 -0700 15 Received: (karn@localhost) by servo.qualcomm.com (8.6.12/QC-BSD-2.5.1) 16 id RAA14732; Mon, 25 Sep 1995 17:50:51 -0700 17 Date: Mon, 25 Sep 1995 17:50:51 -0700 18 From: Phil Karn <karn (a] qualcomm.com> 19 Message-Id: <199509260050.RAA14732 (a] servo.qualcomm.com> 20 To: cypherpunks (a] toad.com, ipsec-dev (a] eit.com 21 Subject: Primality verification needed 22 Sender: owner-cypherpunks (a] toad.com 23 Precedence: bulk 24 Status: RO 25 X-Status: 26 27 Hi. I've generated a 2047-bit "strong" prime number that I would like to 28 use with Diffie-Hellman key exchange. I assert that not only is this number 29 'p' prime, but so is (p-1)/2. 30 31 I've used the mpz_probab_prime() function in the Gnu Math Package (GMP) version 32 1.3.2 to test this number. This function uses the Miller-Rabin primality test. 33 However, to increase my confidence that this number really is a strong prime, 34 I'd like to ask others to confirm it with other tests. Here's the number in hex: 35 36 72a925f760b2f954ed287f1b0953f3e6aef92e456172f9fe86fdd8822241b9c9788fbc289982743e 37 fbcd2ccf062b242d7a567ba8bbb40d79bca7b8e0b6c05f835a5b938d985816bc648985adcff5402a 38 a76756b36c845a840a1d059ce02707e19cf47af0b5a882f32315c19d1b86a56c5389c5e9bee16b65 39 fde7b1a8d74a7675de9b707d4c5a4633c0290c95ff30a605aeb7ae864ff48370f13cf01d49adb9f2 40 3d19a439f753ee7703cf342d87f431105c843c78ca4df639931f3458fae8a94d1687e99a76ed99d0 41 ba87189f42fd31ad8262c54a8cf5914ae6c28c540d714a5f6087a171fb74f4814c6f968d72386ef3 42 56a05180c3bec7ddd5ef6fe76b1f717b 43 44 The generator, g, for this prime is 2. 45 46 Thanks! 47 48 Phil Karn 49 50 51
