openssl/crypto/dh/example

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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