Re: 42nd Known Mersenne Prime Found == 2^25,964,951-1 == The number has 7,816,230 digits

From: Décio Luiz Gazzoni Filho (decio_at_decpp.removethis.net)
Date: 02/28/05 

Date: Mon, 28 Feb 2005 11:27:44 -0300

Thomas Pornin wrote:

> According to David Wagner <daw-usenet@taverner.cs.berkeley.edu>:
>> Does finding another Mersenne prime have any implications for
>> cryptography?
>
> That's very indirect: the continuous search for even greater Mersenne
> primes implies that some people are still working on making faster
> computations on big integers, finding faster ways to test for primality,
> and generally speaking improving mankind's knowledge of arithmetics.
> This, in turn, may have some long term consequences on implementations
> and attacks of cryptosystems which use big integers.

1. The kind of big-integer multiplication used for Mersennes is far removed
from what you'd use in crypto (FFTs instead of Karatsuba).
2. The Lucas-Lehmer primality test for Mersennes has been established for
years, and it's unlikely that someone finds a more efficient test.
3. There's not much arithmetic involved, just modular squaring (and the
modulo comes for free with the squaring when using IBDWT).

> Of course, on the short term, searching for Mersenne primes is just
> another creative way to further deplete the Earth oil and coal stocks,
> and increase greenhouse effect.

I don't contribute to the greenhouse effect -- my country runs mostly on
hydroelectric power.

Now, if only you people over there quit being afraid of the `nucular'
boogeyman...

Décio