[dogsky]

Interesting. But from got the prime1 and prime2, from there how do you obtain the private certificate?

[alexkus]

You now know the two primes (p,q) which multiply together to make n (the public key modulus). We also know e (the public key exponent).

d (the private key) is:-

    d = e^-1 mod ((p-1)(q-1))

To work this modular inverse out you use the extended Euclidean algorithm.

This is why you need to know the factorisation of n=(p*q). You can't compute d (the private key) with just the composite n.

[cryptbe]

You don't need to use p or q. See http://vnhacker.blogspot.com/2014/04/idea-to-solve-cloudflar...

[benmmurphy]

i think this took me as long as coding the recovery tool :(

https://github.com/jjarmoc/csaw2012_cert_app/blob/master/lib...

https://github.com/ius/rsatool

[jjarmoc]

Yah, that's the trickiest part. I was pretty ecstatic when I found a real world use case for toy code that I spent way too much time on :)

[cryptbe]

I wrote a tool some time ago. It's 10 lines of Python using pyasn1.