Luby-Rackoff on Feistel ciphers On page 46 of these lecture notes, it seems to say that if we have a Feistel cipher, and plaintexts $(L_0, R_0)$ and $(L_0^*, R_0^*)$ with corresponding encryptions, then we can determine the key? But isn't this not the case by Luby-Rackoff? I'm not entirely sure what the slides are even saying. They say that we can compute $R_3 \oplus R_3^*$, but so what? How does this help determine the key?
Xor can help find bits not yet known, whether most significant or least significant; and help the adversary find more information about both ciphertext and plaintext, especially if a table of potential plain texts or even keys is stored in conjunction with bitwise Xor. 

Some reading:

http://www.researchgate.net/publication/2633994_Luby-Rackoff_Ciphers_over_Finite_Algebraic_Structures_or_Why_XOR_is_not_so_Exclusive

Although this has minor typos, the notes on Feistel networks and Xor is excellent:

https://github.com/FredericJacobs/Cryptography-Stanford-Notes/blob/master/crypto-notes.md

Luby-Rackoff, as you may already know, is a key component of the Feistel network and it is not secure in 1,2, or 3 layers. Luby-Rackoff must have a 4 independent layered Feistel network structure from independent seeds to be considered a strong pseudo-random permutation. No less than 3 independent rounds must be used to even be considered a pseudo-random permutation though it is much weaker. Some consider a 3 round Feistel to be a secure pseudo-random function, but 4 rounds proves to be more secure. 

No more than 8 corresponding outputs from the 32 pairs of inputs of the Xor should exist.

I suggest learning more about Xor and differential cryptanalysis.

Please focus most on pages 4-7 and 11-16, but the whole article is interesting if you have time:  http://cs.ucsb.edu/~koc/ccs130h/notes/dc1.pdf

It covers the tables and Xor technique in much better detail.