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| 1 From owner-cypherpunks@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 | |
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| 9 Wed, 27 Sep 1995 04:48:46 -0400 | |
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| 14 for <cypherpunks@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@qualcomm.com> | |
| 19 Message-Id: <199509260050.RAA14732@servo.qualcomm.com> | |
| 20 To: cypherpunks@toad.com, ipsec-dev@eit.com | |
| 21 Subject: Primality verification needed | |
| 22 Sender: owner-cypherpunks@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 | |
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