Essay on PGP as it is used today

[Stefan Claas]

Jerry wrote:

> On Mon, 22 Jul 2019 07:07:32 -0400, Robert J. Hansen stated:
> >> I went to an EFF (Electronic Frontier Foundation) meeting  and a big
> >> and tall guy came to me and told me that he had a way of Breaking PGP
> >> and told me he had been working on a database program that made this
> >> possible and spouted off terms I had never heard before.  
> >
> >Yeah, these conspiracy theorists always show up.
> >
> >> I went back inside, and I couldn't find him. I had questions.  
> >
> >You're in the right place.
> >
> >Mathematicians have come up with different ways to estimate how many
> >primes there were under a certain value -- what we call the prime
> >counting function, or "π(x)" in mathematicalese.  There are lots of
> >ways to do it, but they all give answers very close to each other:
> >these are estimates, not precise numbers.
> >
> >The first estimate for π(x) was "x divided by the natural logarithm of
> >x".
> >
> >Let x be 100.  The natural log of 100 is about 4.6.  100 divided by 4.6
> >is about 22.  Thus, we expect there to be about 22 primes under 100.
> >There are in fact 25 -- so while this method isn't perfect it's
> >definitely enough to get us in the neighborhood.
> >
> >If we do that same equation for a 2048-bit key, it turns out there are
> >10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
> >000 000 000 000 000 000 000 different prime numbers that could go into
> >it.
> >
> >Google's total data storage is about 10 exabytes.  In 10 exabytes you
> >could store about 40 000 000 000 000 000 prime numbers.
> >
> >There's just no way anyone on earth has a list of prime numbers that
> >they're trying one after another.  Not only isn't there enough hard
> >drive space, but the hard drives required would literally be bigger
> >than the entire Milky Way galaxy!
> 
> I am not sure about that. If a good data compression algorithm was
> employed, they might be able to save the space of a solar system or two.
> 

<https://www.quora.com/Hypothetically-if-a-group-of-hackers-had-a-sorted-list-of-all-the-primes-all-the-way-up-to-the-largest-prime-could-they-break-any-RSA-encryption-Assuming-that-the-primes-any-RSA-encryption-uses-are-both-in-the-list>

Regards
Stefan