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I have to construct for every i-round of Feistel cipher, for $i \in \{3,4,5,6,7,8\}$, a differential characteristic with there properties:

$Pr[\Delta x = a \overset{f_i}{\rightarrow} \Delta y = b] = 1/2$

$Pr[\Delta x = a \overset{f_i}{\rightarrow} \Delta y = c] = 1/2$

$Pr[\Delta x = b \overset{f_i}{\rightarrow} \Delta y = b] = 1/8$

$Pr[\Delta x = c \overset{f_i}{\rightarrow} \Delta y = c] = 1/4$

Can somebody help me to create characteristics for every i-round? I missing an S-Box, therefore I have no any plan how could I solve this task.

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    $\begingroup$ Without the sbox, I don't see how you can construct such a differential. Certainly there are sboxes where no such high probability differential exists. If this is a question from class, I suspect that you misunderstood the assignment somewhat... $\endgroup$ – poncho Aug 14 '19 at 18:39

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