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Subject: Re: Crypto overhaul
To: Jules Gilbert <repeatable_compression@yahoo.com>,
 Poul-Henning Kamp <phk@phk.freebsd.dk>,
 Nathan Whitehorn <nwhitehorn@freebsd.org>,
 "freebsd-security@freebsd.org security" <freebsd-security@freebsd.org>,
 Ben Laurie <ben@links.org>, pg@eth1.com,
 Jeremiasfeliz <jeremiasfeliz@hotmail.com>
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 <CAG5KPzws=jmF2wLeEAz8Lzn7Ugude=0w5neoQjeDjYnGtJpS9Q@mail.gmail.com>
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From: Eric McCorkle <eric@metricspace.net>
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Date: Sat, 28 Oct 2017 20:20:54 -0400
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On 10/27/2017 19:17, Jules Gilbert wrote:
> These days no one talks about how wonderful CPM was, we used it because
> at one time, it was the only OS available.
> 
> So what is our excuse for using SSL?, because I'm fairly certain the NSA
> and just about everyone else in the neighborhood has hacked it.
> 
> Question for the group...  Does anyone believe that factoring is
> actually hard.  It was once, I know.  But today?
> 
> I'm not a crypto person, but even I wrote a simple factoring program. 
> In C, using MAPM.  I produce a few of the left-most bits for a,b, where:
> 
> c = a*b;
> 
> where a is:  3 .. sqrt(c)
> 
> and (of course,) b must be: greater than sqrt(c)
> 
> from this I bisect the space of 3 .. sqrt(c) and begin the recursive
> descent.  The program does about 5,000 prime pairs an hour and this
> using MAPM!!
> 
> I gave away the source code, let me know if you didn't get a copy. 
> You'll need g++ and MAPM

This isn't the place for discussions of number theory, but I don't see
what you could possibly use for a binary search here.

More generally, discovering a polynomial-time prime factorization
algorithm would likely win you a fields medal, given that it's one of
the oldest open problems in mathematics.  So it's extremely unlikely
that a solution exists.