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.
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.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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