Essay on PGP as it is used today

[Jerry]

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.

-- 
Jerry

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