RoR Attacks on modified Feistel Network

Question

It is known that a Feistel Network containing 3 rounds is relatively secure against Chosen Plaintext attacks. Now as a game I was given the task to find a possible attack against a Feistel Network with 3 rounds, but the first encryption with a key has no effect. (So the input in the second function is just $L \oplus R$). It should be possible to find out, with significant probability and only to Chosen Plaintexts, if the network produces the results of the chosen inputs or just a random sequence. I just can't wrap my head around it, can anyone help me there?

Thank you in advance!

Answer 1

If you have three rounds and the encryption in the first round has no effect, then the left side of the third round is

$$ L_3 = R_0~\oplus~F(L_0 \oplus R_0, K_2) $$

and when you exchange the left and right side of the initial block

$$ L_3' = L_0~\oplus~F(R_0 \oplus L_0, K_2) = L_0~\oplus~F(L_0 \oplus R_0, K_2) $$

So

$$ L_3~\oplus~L_3' = R_0~\oplus~L_0 $$

This property lets you distinguish the output of the Feistel network from random.