Re: Mathematics > NSA + GCHQ

["Vladimir Z. Nuri" <vznuri@netcom.com>]

>We haven't discussed this point in  a while, but the belief most
>cryptologists have is roughly this:
>
>The world-wide community of mathematics and cryptology researchers, linked
>through open publication of new research results, is GREATER than the
>cloistered NSA and GCHQ communities of researchers.
>
>Thus, as bright as Brian Snow or Don Coppersmith or John Conway may be, the
>"edge" the NSA may have once had is largely gone. Which is not to say that
>they are not still a formidable technical organization, with substantial
>computer resources.

I've thought about this, and still wonder if the NSA may have an 
edge. imagine have huge, unlimited resources to spend on whatever
you want. all other mathematicians/researchers in the world are subject to 
having to scrape fund money together via grants. 

guess who grants the
grants? government. and in some cases, I think that it is possible the
grant process is subject to manipulation by government agencies. the
really hot stuff may not be getting funded, because the NSA secretly
pulls the plug and the researcher just thinks, "gosh darn it, didn't
get the grant". a great conspiracy theory, eh? 

as for commercial R&D, it is always ultimately directed toward making
money. this limits the freedom of the researcher as well.

now consider that the NSA is the world's single largest employer of
mathematicians. believe I have seen this claim in some articles on
them. now realize that none of their research is allowed to
be publicized. that is, they can read the open literature, and they
also have their own resources to go past it. individual researchers
outside of the NSA do not have the advantage of seeing what the
NSA is doing. hence a bit one-sided here as well.

consider now that the NSA is not just the largest mathematical
employer, but that they aggressively go after the *best* without
anyone realizing it. consider the spiel: "do a patriotic service
for your country. be among the few, the proud, the spooks". this
they give to the greatest mathematicians you can imagine. it's not
too unlikely. I suspect there are a lot of researchers working for
the NSA with academic "cover stories". hence people you think are
extremely talented and are not working in it are actually working
for it.

some theories, nothing more.

on the other hand, many people have spoken of the compartmentalization
of the government, esp. the NSA, and how this makes it myopic and
ineffectual. I'm not so sure about this. the atomic bomb creation
was pretty compartmentalized at first, yet it was very effective.

>But modern crypto systems are, as we all know, based on fundamental
>mathematical results, e.g., the difficulty in finding the factors of a
>large number, the difficulty in extracting logarithms, etc. And while
>advances in factoring have occurred, often at government labs (think of
>Sandia), the fast factoring of a 1000-decimal-digit number appears
>unachievable.

something to consider is that there has been no major incentive for
anyone to really find such an algorithm until recently, say within
the last 10 years or so. I believe it is mistaken to pretend that
mathematicians have been trying to find an efficient factoring algorithm
since the dawn of math. perhaps out of amusement, but not seriousness.
there is no practical reason why large numbers needed to be factored
in math other than curiousity, until recently. what I am saying is
that I doubt the worlds greatest mathematicians of the past spent much
time trying to find a fast factoring algorithm.