Let S₁ and S₂ be the standard Vigenere and Permutation ciphers, respectively, with P = (Z₂₆)⁴ (so the block length of each is m = 4). Consider the product cipher S₁ x S₂. Letting the Vigenere keyword k₁ = bead, and the index permutation in cycle notation k₂ = (1 4 2). (a) Find the encryption e_(k1,k2)(hack) in S₁ x S₂. (b) Find the encryption e_(k2,k1)(hack) in S₂ x S₁. (c) Find a Vigenere keyword k^'₁ and a permutation k^'₂ such that e_(k1,k2)(x) = e_{(k^' 2,k^' 1 )}(x) for all . That is, find a key (k^'₂,k^'₁) for S2 x S1 that is equivalent to the key (k₁, k₂) for S1 x S2. (d) Do the ciphers S₁ and S₂ commute with each other?