Miscellaneous definitions
Reversible public key scheme
For a public key encryption scheme with message space
If

$M=C$ and 
$D_d\left(E_e\left(m\right)\right) = E_e\left(D_d\left(m\right)\right) = m$ for all$m \in M$
Then we have a reversible PK scheme. (the notes seem to imply that the second property follows from the first; I am unsure)
We can use reversible PK schemes for digital signatures by reversing the encryption and decryption processes. In the case of RSA this means we encrypt a message we send with our private key and the recipient decrypts it with our public key.
$=_p$ and $\leq_p$

$A \leq_p B$ means there is a polynomial time (efficient) reduction from problem$A$ to problem$B$ 
$A =_p B$ means$A \leq_p B$ and$B \leq_p A$