Factorisation of huuuuge numbers
(google RSA cracking to get an idea)
in short: you have a massively large number (1024 bits or 2048 bits or 4096....)
that's the product of two unknown prime numbers (about half it's size.. 512, 1024, 2048 bits...)
The task is to find those two primes ...
each is about'ish 2*10^153 at least (two followed by 153 zeros) in size
compared to the estimated number of atoms in the observable universe (1* 10^80; a one followed by 80 zeros)
you could imagine just HOW large those numbers are.
and that simple trial and error would not get you very far.
And even testing with current methods on networks of thousands of modern computers takes several dozen years.
(A reason why an RSA cerificate is renewed every few years with doubling it's size every now and then, to have those networks have to start over again and grow to keep up as well)
Without going into too much detail (more to keep me sane than to keep you uninformed
)
I thought that calculating the remainders over a "large enough" span of Moduli could reveal an interference pattern, that when analysed would show the exact difference between the two primes.
(knowing the difference is all you need to calculate both primes)
it's... well.... insane, simply put;
at least for numbers that size.
'sid
Glad to see you back. At least it wasn't a math meltdown this time, so we can't say you are insane.
