[cryptography] Duplicate primes in lots of RSA moduli
marsh at extendedsubset.com
Thu Feb 16 12:52:01 EST 2012
On 02/16/2012 11:05 AM, Jeffrey I. Schiller wrote:
> What I found most interesting in Nadia's blog entry is this snippet of
> (pseudo) code from OpenSSL:
> 1 prng.seed(seed)
> 2 p = prng.generate_random_prime()
> 3 prng.add_randomness(bits)
> 4 q = prng.generate_random_prime()
> 5 N = p*q
> In theory line 3 helps improve security by adding more entropy prior to
> generating the second prime Q. However, and this is
> counter-intuitive (like many things in security), it in fact reduces
> security in low-entropy situations.
Are you thinking this is because it causes the entropy estimate in the
RNG to be higher than it really is? Last time I checked OpenSSL it
didn't block requests for numbers in cases of low entropy estimates
anyway, so line 3 wouldn't reduce security for that reason.
> As she explains, a lot of the poor
> RSA keys found *may* be the results of key generations performed by
> embedded devices and things like home routers NOT LONG AFTER THEIR
> FIRST POWER ON. This would be a very low entropy time.
How often have we seen Linux distros generate SSH keys 2 seconds after
the first boot?
> If line 3 was omitted, many devices would have the same key. This
> isn't great, but it is a far better situation then we have now with a
> lot of devices having the same first prime!
> However, the real bottom line is that if a cryptographic
> operation/protocol calls for strong random input, you better provide
> it or your security is significantly at risk.
Trying to reason about which completely broken thing is less-broken is
madness, unless you're on the attack side.
> Ted Ts'o and I spoke about this the other day (Ted is one of the
> authors of /dev/random, and he is likely reading this list!). One of
> the things that concerns us is the number of virtual machines using
> /dev/random for a random number source.
Don't most Linux distros save some entropy to a file on clean shutdown
and reload it at the next boot? I know OpenBSD did.
> When it was first written,
> linux (and other Unix like operating systems) ran on bare metal and we
> had a reasonably good understanding of the hardware random sources we
> were using.
> However virtual machines change things. Timing intervals that on bare
> metal are likely "random" are probably less so in a VM context. I
> don't know if anyone has done a good study of how "random" /dev/random
> is in common VM environments.
I played with timing on my hosted VPS of the RDTSC (CPU cycle counter)
instruction in a tight loop. A few simple bit operations showed visually
an upper bound of at most 1/5 BoE per RDTSC instruction (when used in
> This concerns me because of the number of TOR nodes that are now
> hosted on Amazon's EC2 (VM) service, particularly since some of the
> adversaries of the TOR network (if that is the right way to describe
> them) are state actors.
Also, it is sometimes possible for an attacker in could environments to
arrange for his own VM to run concurrently on the same physical CPU as
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