I am newbie in cryptography and pycrypto. 
I have modulus n and private exponent d. From what I understand after reading some docs private key consists of n and d. 
I need to sign a message and I can't figure out how to do that using pycrypto. RSA.construct() method accepts a tuple. But I have to additionally provide public exponent e to this method (which I don't have).
So here is my question. Do I have to compute e somehow in order to sign a message?
It seems I should be able to sign a message just by using n and d (that constitute private key). Am I correct? Can I do this with pycrypto?
Thanks in advance.
No, you can't compute e from d.
RSA is symmetric in d and e: you can equally-well interchange the roles of the public and the private keys. Of course, we choose one specially to be private and reveal the other -- but theoretically they do the same thing. Naturally, since you can't deduce the private key from the public, you can't deduce the public key from the private either.
Of course, if you have the private key that means that you generated the keypair, which means that you have the public key somewhere.
I have modulus and private exponent. How to construct RSA private key and sign a message?