One-round feistel network (DES) attack I can't find out how to break 1 round of feistel network (obtaining the key).



I understand why this equation takes place:

$R_1 \oplus L_0 = f(R_0, k_1)$

EDIT: The function f looks like this:


But how can i find the key ($k_1$) from it?

I saw it's possible in a few references:

http://www.cs.technion.ac.il/~cs236506/04/slides/crypto-slides-05-bc-tutor.4x2.pdf
http://people.scs.carleton.ca/~maheshwa/courses/4109/Seminar11/atttack%20on%20DES.pdf
https://www.icg.isy.liu.se/courses/tsit03/forelasningar/cryptolecture04.pdf
KPA on Feistel cipher?

Thanks!
Since

$$X' = F(X, k) = P(S(E(X) \oplus k ))$$

the value of key $K$ is an element of the set

$$ \{V \oplus E(R_0): V \in S^{-1}(P^{-1}(Z)) \}$$

where 

$$Z = R_1 \oplus L_0$$

and

$$
S^{-1}(P^{-1}(Z)) 
$$
is the set of possible inverse images of the parallel map of the Sboxes $S$ which is not one to one.

Total number of possible keys is $2^{16}$ because Sboxes are not bijective, there are $4$ possible inputs leading to same output.