# Retrieve value of private key after encryption with the public key

Is there a way to find an RSA private key after it is encrypted with the corresponding public key? Does there exist an algorithm to recover the private key in this special case?

• This is called circular security. I believe that the answer is not completely understood in the research community. – mikeazo Apr 18 '15 at 15:57

You could possibly raise (modulo $n$) the private exponent to the power of the public exponent. So then you would need to retrieve $d$ from $d ^ e \mod n$. I don't see how you could retrieve $d$ from that, even if you take into account how $d$ and $n$ are calculated.
Note that you could not do this if you would require the CRT parameters instead of the private exponent $d$.