[GNU Crypto] More informations about non-primality test

[Giuseppe Mazzotta]

Since somebody asked me more, I'll post another message on this list.

The theorical background is not yet demonstrated (I suppose there
is a sort of conjecture below) but we can verify the usefulness of my
test with a simple bigger (?) test.

My test can actually tell (with any odd number):
- the number is not prime (mathematical security);
- else cannot tell if the number is prime or not (undeceivability, ALL
prime numbers are undeceivable for my test, but not the inverse of this
proposition)

Let's suppose to have a very big supercomputer that checks randomly
generated numbers for their primality via a standard algorithm (Fermat,
Rabin-Miller, Solovay-Strassen, Lucas-Lehmer, Ellipitc Cuver Method or a
combination of these), and let's suppose to put in parallel my test on
the same numbers: if my test always tells an "undeceivable" result, my
test is useless, if my test else in at least one case shows to negate
the "traditional" result, well...in future, to have more secure keys, we
should always perform my test and luckily it is very short in CPU time.

I have not yet done this big test, but I am preparing a source code (in
C language) release that will be soon available and perhaps somebody 
else can do it; I will also inform other people interested in prime 
numbers research in these days. In the mean time, you can test any
number via my server-side application at

http://www.nexogen.it/gm/primality/

Please note that other links in that page are broken, everything will be
alright in a few days (when I'll finish the translation, I'll post
another message in this list)

I have just implemented the Rabin Miller; I have the source code (in 
different languages) of every other test mentioned above, but I haven't 
yet translated them to PHP...

Please contact me if interested, you can also post on my new forums:

Mathematical subjects:
http://www.nexogen.it/forums/viewforum.php?f=1

Programming related:
http://www.nexogen.it/forums/viewforum.php?f=2

-----------------------------
Think different. (A.Einstein)