Import key code is not compatible with GMP library

[Legrandin]

I have just noticed that a secret RSA key that was generated by an external tool (e.g. opensll) as DER/PEM
and that isimported via RSA.importKey() won't decrypt/sign correctly if the GMP library is installed.

The problem is that - in the standard representation - RSA key components include q^{-1} mod p, whereas
the code in _fastmath.c requires p^{-1} mod q instead.

You can verify that by importing a key from openssl, and - with GMP installed - by encrypting+decrypting a string: the result is not the original string.

I have not noticed it in my tests so far because I didn't have GMP installed (my fault).
Moreover, _slowmath.py does not use CRT compoenents as _fastmath.c does.

There are no real security concerns here: the only problem is that a) signatures generated in this way cannot be verified b) data cannot be correctly decrypted. Verification and encryption done with import key is not affected.

I have already a very short patch ready: I will send it out in the coming days.
It also extends _slowmath.py to use CRT, which therefore does exactly what _fastmath.c does.

Affects: pycrypto 2.2 and 2.3

[Legrandin (gooksankoo)]

One patch is here:

https://github.com/Legrandin/pycrypto/commit/a2fdd4bada1ef39f2bcf554e30c33d1e4b027132

[Darsey Litzenberger (dlitz)]

Fixed in https://github.com/dlitz/pycrypto/commit/c1ad8f08c96e273f49fd0a37940da04fb42b7c89

Fix released in PyCrypto 2.4.