In section 3.5.2, Stinson observes that the security of DES is base...

Question

In section 3.5.2, Stinson observes that the security of DES is based in part on the non-linearity of the S-Boxes. To say that an S-Box Si is linear is to say that for any bitstrings x1 and x2 of length 6, Si(x1⨁x2)= Si(x1) ⨁ Si(x2)
Thus to say that the S-Boxes are non-linear is to say that, for each S-Box, there are pairs of bitstrings for which this equation does not hold. Verify the non-linearity of S1 by finding a pair of bitstrings which do not satisfy the above equality.

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We take for instance S5-box of DES (we can take any of the 8 S-Boxes). For reference purpose, its content is attached at the bottom of this document.

For a 6-bit input, the output has 4 bits and it consists of selecting the row using the outer two bits and the column using the inner four bits.
For example, S5(011011)= value of S5 located on row 01 and column 1101, which means row 1 and column 8+4+1=13=> S5(011011)=09=1001.

Now, in order to prove the non-linearity of the S5-box we take two random values (6-bit): 110100 and 010111....

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