On Feb 20, 2012, at 8:38 AM, Jakob Bohm wrote:
> On 2/17/2012 10:16 PM, Wim Lewis wrote:
>> Even aside from TPM or other HSMs, hardware random number generators have 
>> been a common feature of PC motherboard chipsets for a decade or so. I 
>> assume, perhaps optimistically, that the /dev/?random devices that modern 
>> OSs provide make use of these RNGs as well as other system entropy sources 
>> (interrupt timing and so on).
> Unfortunately not!   [....]

How disappointing. :( Good to know, though.

> Some [low-entropy keys] could also be from the Debian/Ubuntu bug I mentioned 
> in an earlier post.

The paper mentions that they found some keys that were on the Debian/Ubuntu 
blacklist, but it sounds like these do not account for the weak keys they 
found: "21419 X.509 certificates and PGP keys are affected [factorable due to 
shared factors]. Note that affected moduli are much more frequently shared than 
non-affected ones. None of the affected moduli are blacklisted." (With more 
data, that number went up to 26965.)

Their other numbers: 30099 n-values were found on the Debian/Ubuntu blacklist, 
but only 2 immediately factorable; 71024 n-values are shared by more than one 
certificate, but many of those instances are intentional/benign.

Nadia Heninger has a post on Freedom-to-Tinker ( 
https://freedom-to-tinker.com/blog/nadiah/new-research-theres-no-need-panic-over-factorable-keys-just-mind-your-ps-and-qs
 ). She's not one of the authors of the Lenstra paper but is part of a 
different group that was doing similar research and finding similar results. 
From that post:

> this problem mainly affects various kinds of embedded devices such as routers 
> and VPN devices, not full-blown web servers. [....] 
> 
> So which systems are vulnerable? Almost all of the vulnerable keys were 
> generated by and are used to secure embedded hardware devices such as routers 
> and firewalls, not to secure popular web sites such as your bank or email 
> provider. Only one of the factorable SSL keys was signed by a trusted 
> certificate authority and it has already expired. [....]
> 
> Embedded devices are well known to have entropy problems. However, until now 
> it wasn't apparent how widespread these problems were in real, 
> Internet-connected devices.



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