Proven Primes

[Bill Frantz]

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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Bill Frantz           | Due process for all    | Periwinkle -- Consulting
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