Let Z10 = L = Problem 1 {0, 1, ...,9}. Consider the symmetric encryption scheme in which a message M M[1]M [2]M (3]M[4] e Zio is a four-digit string, a key as Perm(Z10) is a random permutation on Z10, and the ciphertext C = C[1]C[2]C[3]C[4] = E7(M) e Zi, is computed as follows: Alg E7(M) For i = 1, ..., 4 do P[i] + (M[i] + i) mod 10 C[i] + 7(P[i]) Return C (a) [2 points) Specify a decryption algorithm D such that SE = (K, E, D) is a symmetric encryp- tion scheme (Lecture 2 Slide 2) meeting the correct decryption requirement (Lecture 2 Slide 3). (b) [4 points) Is this scheme a substitution cipher as per the definition of Lecture 2 Slides 13, 14? Why or why not? (c) [4 points) Is this encryption scheme perfectly secure as per the definition of Lecture 2 Slide 47? Why or why not? Let Z10 = L = Problem 1 {0, 1, ...,9}. Consider the symmetric encryption scheme in which a message M M[1]M [2]M (3]M[4] e Zio is a four-digit string, a key as Perm(Z10) is a random permutation on Z10, and the ciphertext C = C[1]C[2]C[3]C[4] = E7(M) e Zi, is computed as follows: Alg E7(M) For i = 1, ..., 4 do P[i] + (M[i] + i) mod 10 C[i] + 7(P[i]) Return C (a) [2 points) Specify a decryption algorithm D such that SE = (K, E, D) is a symmetric encryp- tion scheme (Lecture 2 Slide 2) meeting the correct decryption requirement (Lecture 2 Slide 3). (b) [4 points) Is this scheme a substitution cipher as per the definition of Lecture 2 Slides 13, 14? Why or why not? (c) [4 points) Is this encryption scheme perfectly secure as per the definition of Lecture 2 Slide 47? Why or why not