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Re: Possibly a stupid question RPC over HTTP
From: Kyle Maxwell <krmaxwell () gmail com>
Date: Sun, 24 Oct 2004 22:30:13 0500
On Fri, 22 Oct 2004 14:50:23 +0100, Airey, John <john.airey () rnib org uk> wrote:
Original Message
From: Kyle Maxwell [mailto:krmaxwell () gmail com ]
I think you may mean something slightly differently; given any large
prime p, I can factor it completely extremely quickly:
p = 1 * p
There are no other factors; this *is* the prime factorization. :) Bill
Oh no, the whole security of computing has just fallen over, since you've shown that primes don't exist. What next,
proving that black is white and getting run over on a zebra crossing?
A prime is defined as being divisible by itself and 1 only, so for the purpose of the definition, 1 is not a factor.
<flame>
I was trying to give you the benefit of the doubt in my explanation,
but your response makes it clear that you're not thinking straight. By
your (almost correct) definition of prime, the factorization is
trivial! And yes, 1 is a factor. If you can break the prime into ANY
other factors, then it's NOT a prime.
You're talking about solving a problem that DOESN'T EXIST BY
DEFINITION. Reread my response  this time without being stupid 
and you'll see that I was trying to explain to you that the problem is
the general factoring of large numbers (into primes for what should be
obvious reasons). This is NOT the same as factoring large primes as
that's a solved problem. If this is still difficult to understand, any
handy gradeschool maths book should provide additional explanation.
Testing for primality, which is a related but different problem, is
solved, but proving that a number is composite is unfortunately not
the same as knowing its factors.
</flame>
As to the question of whether this is a solved problem: we may have to
agree to disagree; if it were the NSA, given their past interactions
with the crypto community, I think it likely that they'd have over
time moved to another type of cryptography. BTW, brute forcing a key
does not break the system  and as others have shown in this thread,
it's impossible to precompute all the keys unless you've broken every
single PRNG out there, and that's even less likely.

Kyle Maxwell
[krmaxwell () gmail com]
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