[Cryptography] DH non-prime kills "socat" command security

[david]

On 2/4/16 8:30 PM, Henry Baker wrote:
> The purported prime in the socat news story doesn't pass any of the 
> simple primality tests of the type that you describe, so it is obvious 
> to include such primality tests in the QA for these socat algorithms. 
> After factoring out the two small factors 271 and 13,597, the 
> resulting 1002-bit number *still doesn't pass* simple primality tests, 
> but I wasn't able to further factor it in 15 minutes on my really old, 
> really slow laptop. So someone was criminally stupid, or else 
> purposely installed this non-prime backdoor.
I'm digging into the topic and summarizing everything on this github 
repo: https://github.com/mimoo/socat_backdoor

it would be interesting to try several factoring algorithm like 
pollard's p-1, ECM, p+1 ... Also, try and provide some estimations. If 
the factorization of the last composite has a lower bound of X => 
Pohlig-Hellman won't work.

Another question: if it was indeed a mistake, how could that number 
would have been generated? And what are the probabilities that the 
factorization would include big primes/small primes if generated this way?

David