Eddy Nigg (StartCom Ltd.) wrote:
>   Jean-Marc Desperrier:
>> Eddy Nigg (StartCom Ltd.) wrote:
>>
>>> [...]
>>> However more interesting is this reference:
>>>
>> No, that is not more interesting. It's been known for a year or two that
>> keys around 600 bits were broken, and it was therefore already quite
>> obvious that 768 wasn't safe today.
>
> Well, that's what I knew and what I have been stating not so long ago on
> this list, but I couldn't refer to any reference, even now, it's not
> quite clear. I'd like to see some more details - do you have any?

Well I don't know why neither you nor Paul found it, maybe because you 
searched for exactly 650 bits, it should take only seconds to find 
references to the factorisation of RSA-640 and of RSA-200 (a 200 digits 
number that is in fact 663 bits long).
http://www.rsa.com/rsalabs/node.asp?id=2879
http://www.loria.fr/%7Ezimmerma/records/factor.html

Also I'd need to search for more reference, but I've been reading that 
the factorisation of the 2^1039-1 Mersenne number
http://eprint.iacr.org/2007/205
is computationally equivalent to factoring an ordinary 700 bit number.

In fact, it's right there in the publication :
http://eprint.iacr.org/2007/205.pdf
"7 Discussion [...] We estimate that the effort we spent would
suffice to factor a 700-bit RSA modulus."

>>[...]
>
> Yes, I have this also stated already, but Paul Hoffman had a counter
> argument concerning some needed 128 GB memory available per machine.

It's only the final step that requires a lot of memory.
In practice, the laboratories that broke the above keys managed to get 
it, one should not rely too much on that.

>> How much money is Verisign's 1024 bits"Class 3 Public Primary
>> Certification Authority"  worth for pirates ? Don't you think a lot ?
>
> Not really and we have exactly this been discussion here (see previous
> threads). One of the suggestions was to have 1024 bit keys removed by
> 2012, maybe 2013. In any case I think we should act on it and include
> this requirement into the Mozilla CA policy.

After reading this :
http://www.computerworlduk.com/management/security/cybercrime/news/index.cfm?newsid=9504
and this
http://forum.kaspersky.com/index.php?showtopic=71734
I'm now beginning to realize Kapersky might be much less concretely 
believing they can actually factore that key that I initially thought, 
but still 2012/2013 might be too late for the transition.
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