Re: Compromised entry guards rejecting safe circuits (was Re: OSI 1-3 attack on Tor? in it.wikipedia)

[Ben Wilhelm <zorba-tor@xxxxxxxxxxxxx>]

Anon Mus wrote:
> Ben,
>
> Yes you are right factorising this is hard, but thats not what I've
> been 
> suggesting. What if every time you generated a pair of keys you stored 
> the result somewhere!
> Say you owned a huge network of say mil/gov computers which communicate
>
> securely using sefl generated rotating keys. As any client finishes
> with 
> a key pair they send them off to a central storage location.  If they 
> are not there already they are added to the store.
> To find the private key(s) you only need to search through the list of 
> public keys. If you only find 1% of the server communities private keys
> then you've got many extra nodes to add to your dummy network.
>
> Hopefully you understand this and I'll get some sleep tonite ( :D ).
>
> -K-
You're continuing to drastically underestimate the numbers involved. 
Let's say that a computer is a cube, one half foot on each side. Now 
let's take the Earth, and *cover the Earth with solid computers* to a 
depth of one mile. This gives us approximately 232 billion billion 
computers. If you assume that each computer can generate a thousand 
private/public pairs per second (I believe this is an exaggeration for 
commodity hardware, though you could likely build a custom system to do 
so) then that means we get 2.32 * 10^23 keys every second.
I'm going to go handwavy here and assume that one key is approximately 
equal to one prime. This isn't true, but we'll end up within an order of 
magnitude of the right answer, and honestly more precision than that 
isn't needed.
With 7.5127 * 10^74 primes, attempting to cover 1% of the keyspace at 
2.32 * 10^23 keys per second would take approximately one million 
million million million million million million *years*. Excuse me for 
not being particularly worried about this. And remember, this assumes 
the entire surface of the planet is covered, a mile thick, with 
computers. Last I checked this was not the case.
(Again, this also ignores the issue of where you store all this data.)

Seriously, sit down and think about the numbers some. The numbers are 
*gigantic* - so gigantic that "brute force" becomes implausible, even if 
you assume the adversary owns all the government and corporations of our 
world and has access to alien supercomputers.
-Ben