# Constructing Differential Characteristics for Feistel Cipher

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.

• 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... – poncho Aug 14 '19 at 18:39