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From: krmaxwell at gmail.com (Kyle Maxwell) Subject: Possibly a stupid question RPC over HTTP On Fri, 22 Oct 2004 14:50:23 +0100, Airey, John <john.airey@...b.org.uk> wrote: > > -----Original Message----- > > From: Kyle Maxwell [mailto:krmaxwell@...il.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. Re-read 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 grade-school 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@...il.com]
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