Non-linearity is one important property that makes DES secure. This problem verifies the nonlinear property by computing the output of S for several pairs of inputs. Show that: S(x1) S(x2) S(x1 x2) for: (a) x1 = 000000, x2 = 000001 (b) x1 (c) x1 = 111111, x2 100000 = 101010, x2 = 010101 We want to verify that IP(x) and IP-1(x) are truly inverse operations. We consider a vector of 64 bits. Show that IP (IP(x)) =x for the first five bits of X.