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 _______________________________________________ Gnupg-users mailing list Gnupg-users@gnupg.org http://lists.gnupg.org/mailman/listinfo/gnupg-users