Re: Breaking RSA & Securing RSA
From: Joseph Ashwood (ashwood_at_msn.com)
Date: 07/22/05
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Date: Fri, 22 Jul 2005 00:14:15 GMT
"Regis" <nobody@thisaddress.com> wrote in message
news:mj90e1p38qvhtt2et5cvl5vu6atqdu5hnj@4ax.com...
> On Thu, 21 Jul 2005 22:12:28 GMT, "Joseph Ashwood" <ashwood@msn.com>
> wrote:
>
>>Actually I tend to agree with Colin on this one. Because one of the NSAs
>>(and GCHQ, and other such groups throughout the world) primary mandates is
>>to collect information that is nominally protected to improve the
>>information collection of the associated country having a system dedicated
>>to breaking 1024-bit RSA seems like a reasonable expenditure. It is
>>unlikely
>>that such a device will be brought to bear on an average individual, but
>>considering the wide spread usage of 1024-bit RSA keys I would expect that
>>there is actually a reasonable amount of traffic from various governments
>>protected by such keys (although most have probably gone on to 2048-bit by
>>now). This would indicate that the expenditure on a system capable of
>>factoring 1024-bit numbers could be considered reasonable. If I'm wrong,
>>it's still better to assume that your attackers are more capable than they
>>really are.
>> Joe
>
> I understand what you're saying, but you guys always fail to remember
> one very important detail -- the NSA does not have a monopoly on the
> world's leading mathematicians. There are plenty of mathematicians
> all over the world who don't work for the NSA, and if those
> mathematicians haven't stumbled upon any new breakthroughs in
> factoring massively large numbers, why would you believe that the few
> working at the NSA already have?
>
> If such a breakthrough were to occur at some point, it would
> undoubtedly come from the 99.99% of the world's mathematicians that
> don't work for the NSA, as opposed to the 0.01% that do.
It's not their mathematicians that I feel are the threat, like you said
there are many more IQ points in the wild than in their captivity. What
worries me is instead their available money. Most attackers are limited not
by their capabilities, but by their available resources. An institution
tasked with the information security of a major country has massive
resources. I don't remember the exact values involved, but IIRC the money
required to build the 1024-bit cracker was approximately $1billion (10^9),
considering that the Iraq war/invasion/whatever the other thread is calling
it now has totaled over 200 times that value the resources are clearly
available. Add to this the publicly available information about their
fantastic fab facility and it's pretty much a recipe for them to be capable
of building something on this scale. Have they? I don't know. Has China? I
don't know. Has England? Probably not, they don't have the resources of a US
or China, but they are close to the US, they might even share one for all we
know.
The level of funds available to the massive governments of the world is just
plain scary. Thinking about it realistically though, I'd have to say that
most of the world is susceptible to the "I'll pay you $1million for
everything you know about ...." which is probably more efficient anyway.
Joe
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