The following encryption scheme encrypts each block of length $n$ of the plaintext separately:
$c_i = k_1 \oplus F(k_2 \oplus p_i)$
Where $F$ is a strong pseudo-random permutation (i.e. it is easy to calculate $F(.)$ and $F^{-1}(.)$), and $|k_1|=|k_2|=n$.
$a.$ Is this encryption safe against a CPA attack with a single block? multiple blocks?
$b.$ Show an efficient attack to discover the two keys.
So I thought of choosing $p=0$, and then we easily get $k_1 \oplus F(k_2)$, and we can do the same with $p=1$. But then we have two equations with our two variables being $k_1$ and $F(k_2)$, so we can get $k_1$, but how does that help with $k_2$ if we cannot calculate $F^{-1}$?
Am I in the right direction? Any help would be appreciated.