[12681] in cryptography@c2.net mail archive
Re: Proven Primes
daemon@ATHENA.MIT.EDU (Bill Frantz)
Fri Mar 7 12:51:55 2003
X-Original-To: cryptography@wasabisystems.com
X-Original-To: cryptography@wasabisystems.com
In-Reply-To: <3E682C5F.6030702@algroup.co.uk>
Date: Thu, 6 Mar 2003 23:57:35 -0800
To: Ben Laurie <ben@algroup.co.uk>
From: Bill Frantz <frantz@pwpconsult.com>
Cc: Cryptography <cryptography@wasabisystems.com>
At 9:21 PM -0800 3/6/03, Ben Laurie wrote:
>Bill Frantz wrote:
>> At 3:47 AM -0800 3/6/03, Ben Laurie wrote:
>>
>>>I'm looking for a list or lists of sensibly sized proven primes - all
>>>the lists I can find are more interested in records, which are _way_ too
>>>big for cryptographic purposes.
>>>
>>>By "sensibly sized" I mean in the range 512-8192 bits. I'm particularly
>>>after Sophie Germain primes right now, but I guess all primes are of
>>>interest.
>>
>>
>> Having set a computer to the problem of coming up with a Sophie Germain
>> prime for the E startup protocol (Diffie-Hellman), I offer you:
>>
>> static final BigInteger g = new BigInteger("2");
>> static final BigInteger modulus =
>> new
>>BigInteger("11973791477546250983817043765044391637751157152328012"
>> +
>>"72278994477192940843207042535379780702841268263028"
>> +
>>"59486033998465467188646855777933154987304015680716"
>> +
>>"74391647223805124273032053960564348124852668624831"
>> +
>>"01273341734490560148744399254916528366159159380290"
>> +
>>"29782321539388697349613396698017627677439533107752"
>> + "978203");
>
>And the proof?
Sorry, an exercise for the student. :-)
I thought that finding them was the hard part, and verifying one once found
was relatively easy. I used the probable prime test in the Java BigInteger
package. It sounds like, from some of the list traffic, that there are
better tests.
I guess I'm dumb, but how to you verify a proof of Sophie Germain primeness
with less effort than to run the tests yourself?
Cheers - Bill
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