From: "William Allen Simpson" <bsimpson@morningstar.com>
Date: Sun, 5 Nov 1995 05:02:18 +0800
To: cypherpunks@toad.com
Subject: Photuris Primality verification needed
Message-ID: <1972.bsimpson@morningstar.com>
MIME-Version: 1.0
Content-Type: text/plain


Folks, I was somewhat disappointed in the response to our previous
requests for verification of the strength of the prime moduli.

Recently, someone asked for a smaller prime of only 512-bits for speed.
This is more than enough for the strength of keys needed for DES, 3DES,
MD5 and SHA.  Perhaps this would be easier to have more complete and
robust verification as well.

Here are two "important" primes for Photuris use.  If you have some
spare cycles, it would be beneficial for in-depth verification of these
strong primes.

Implementation Optional.  A 512-bit strong prime (p), expressed in hex:

   da58 3c16 d985 2289 d0e4 af75 6f4c ca92
   dd4b e533 b804 fb0f ed94 ef9c 8a44 03ed
   5746 50d3 6999 db29 d776 276b a2d3 d412
   e218 f4dd 1e08 4cf6 d800 3e7c 4774 e833

The recommended generator (g) for this prime is 2.


Implementation Required.  A 1024-bit strong prime (p), expressed in hex:

   97f6 4261 cab5 05dd 2828 e13f 1d68 b6d3
   dbd0 f313 047f 40e8 56da 58cb 13b8 a1bf
   2b78 3a4c 6d59 d5f9 2afc 6cff 3d69 3f78
   b23d 4f31 60a9 502e 3efa f7ab 5e1a d5a6

   5e55 4313 828d a83b 9ff2 d941 dee9 5689
   fada ea09 36ad df19 71fe 635b 20af 4703
   6460 3c2d e059 f54b 650a d8fa 0cf7 0121
   c747 99d7 5871 32be 9b99 9bb9 b787 e8ab

The recommended generator (g) for this prime is 2.


> From: Phil Karn <karn@qualcomm.com>
> 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.
>

Bill.Simpson@um.cc.umich.edu
          Key fingerprint =  2E 07 23 03 C5 62 70 D3  59 B1 4F 5E 1D C2 C1 A2