full-disclosure - Possibly a stupid question RPC over HTTP

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From: andfarm at teknovis.com (Andrew Farmer)
Subject: Possibly a stupid question RPC over HTTP

On 22 Oct 2004, at 06:50, Airey, John wrote:
>> On Thu, 21 Oct 2004 13:21:10 +0100, Airey, John
>> <john.airey@...b.org.uk> wrote:
>>> This gives you two options. One, use brute force to break
>>> the SSL encryption. Two (and it's entirely possible that the
>>> security services have this already) come up with a
>>> mathematical way to factor large primes rapidly.
>>
>> 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
>> Gates made the same mistake in his book _The Road Ahead_. Factoring
>> large primes is trivial; the prime factorization of large numbers is
>> hard, and I guess that's what you meant.
>
> The whole security of encryption rests on the belief that prime 
> factorization isn't possible in a reasonable time, and it may well 
> have been solved.

Need we tell you again?

READ THE DEFINITION OF A PRIME NUMBER. Here's a site with a good 
definition:

	http://mathworld.wolfram.com/PrimeNumber.html

A prime number, BY DEFINITION, cannot be factored. Factoring products 
of large primes - for example,

	8732977253934620914004266951938806186093326019599

- is believed to be a Hard problem, and that's what RSA is based on.

(The factorization is at the bottom of this message.)


> Why would any government admit that it had cracked RSA security and 
> its derivates?

It wouldn't. Partially because:

  - Governments use RSA too.

  - Businesses use RSA as well.

Declaring RSA broken would kill e-commerce overnight.


> I realise that we are getting into the realms of conspiracy theories 
> now, however history shows that the UK did not wish it to be made 
> public during the war that it had cracked the Enigma code. Why should 
> it be any different now?

Because we aren't at war with Rivest, Shamir, and Adleman?


> A prime is defined as being divisible by itself and 1 only, so for the 
> purpose of the definition, 1 is not a factor.

Okay, so you do remember your elementary school math. So explain how 
"prime factorization" is possible, then.

<snip half a sig>


> Even if Embryonic Stem Cell Research yielded medical treatments, how 
> could enough eggs be obtained to make them viable? We can't even get 
> enough organs for transplant donation.

Easily. Eggs are much easier to obtain than organs.



Since you scrolled down to see it: Mathematica factors

	8732977253934620914004266951938806186093326019599

to

	2925219829459042790944067 * 2985408879697632628675397

in about 2 minutes.
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