Solve RSA decoding problems when e is small enough.
Compute factor $q$ and $p$
In order to decode RSA, we need to compute $p$ and $q$ as factor of $n$. Generally, it requires a lot of computating but we have a good resource: stored factor list.
Pip package factordb-python is useful:
import factordb.factordb import FactorDB
f = FactorDB(n)
f.connect()
factors = f.get_factor_list()
Compute $d$
$d$ is defined using $\phi$:
$$ ed \equiv 1 \mod{\phi} \longleftrightarrow d = (1/e) \mod{\phi} $$
while $\phi = (p-1)(q-1)$.
In order to compute this modular multiplicative inverse, pip package pycrypto is useful:
import Crypto.Util.number import inverse
d = inverse(e, phi)
Compute $m$
The plain message $m$ is defined as:
$$ m = c^d \mod{n} $$
where we can:
pow(c,d,n)
The third, optional, parameter is the modulus.