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)?

Similar to Problem 3.1 in the textbook: 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(1)+Si(2) is different from Si(1+2), where + denote bitwise XOR, for the following three cases. Write your answer in binary. 1. 1=000000,2=000001 : What is S1(1)+S1(2)? and what is $1(1+2)? 2. 1=111111,2=100000 : What is S2(1)+S2(2)? and what is S2(1+2) ? 3. 1=101010,2=010101 : What is S3(1)+S3(2)? and what is S3(1+2)