Let f(x) be a function from binary strings (of a fixed length N) to binary strings. For the purposes… Show more Let f(x) be a function from binary strings (of a fixed length N) to binary strings. For the purposes of this problem, let’s say that f(x) has the equal difference property if the following is satisfied: Whenever x_1, x_2 , x_3, x_4 are binary strings of length N that satisfy x_1 ⊕ x_2 = x_3 ⊕ x_4 , then f (x_1)⊕ f (x_2 ) = f (x_3 )⊕ f (x_4 ). (a) Show that if α,β ∈ GF(2^8 ) and f (x) =αx + β for all x ∈ GF(2^8 ), then f(x) has the equal difference property. • Show less