> >The types of primes found by GIMPS are so incredibly huge
> that they would
> >have no practical purpose for encryption.
>
> Nope, there is a crypto system using the Mersennes. Look for
> a link to it
> at www.mersenne.org. (It is also mentioned in one of the Mxx
> press releases
> from George... or at least in an article ;-) )
Hmm...no kidding. Now, correct me if I'm wrong (I probably am) but aren't
those types of encryption schemes based on multiplying large primes together
to generate the "key", and the fact that it would take a VERY long time to
factor the product means it's relatively secure?
So...how would it be helpful to use certain types of primes during the key
generation? That takes away a huge chunk of the security, especially since
with Mersenne primes being one of the number multiplied, you only need try
38 (not 37...doh!) numbers to try and factor with in order to find the pair.
And of those 38, alot are small enough to be worthless for encryption
anyway.
I know that certain of the algorithms we have available, such as ECM, do
make it faster to hunt for factors, meaning that factoring an unknown pair
can be done faster, but I didn't think that Mersenne primes in particular
are useful for cryptography at all.
Aaron
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