Similar to Problem 3.1 in the textbook( C. Paar and J. Pelzl, Understanding Cryptography, Springer, 2009. ISBN 978-3-642-04100-6.):

An important property which makes DES secure is that the S-boxes are nonlinear. Verify this property by computing the output of Si for several pairs of inputs. Show that Si(x1)+Si(x2) is different from Si(x1+x2), where + denotes bitwise XOR, for the following three cases. Write your answer in binary.

1. x1 =000000, x2 =000001: What is S1(x1)+S1(x2)? and what is S1(x1+x2)?

2. x1 =111111, x2 =100000: What is S2(x1)+S2(x2)? and what is S2(x1+x2)?

3. x1 =101010, x2 =010101: What is S3(x1)+S3(x2)? and what is S3(x1+x2)?