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According to a Lecture from Lecture notes of a Professor of Purdue University "Diffusion means that a change in any plaintext bit must propagate out to as many ciphertext bits as possible." I can't clearly understand how S-box introduces this diffusion in DES. Can anyone explain with an example? Is it because a change in a single input bit of S box will result in a different number being chosen as output from the lookup table of DES S box?

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Typically Sboxes introduce confusion, on their own. It's the mixing layer, i.e., the $P$ permutation at the output of the sboxes (taken all together) that introduces diffusion.

F function including Sboxes

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P permutation, note the diffusion of the output mixing bits to different Sbox inputs in the next round.

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