2. This problem illustrates a simple application of the CCA attack. Bob intercepts a ciphertext C intended for Alice and encrypted with Alices public key e. Bob wants to obtain the original message M = C^d mod n. Bob chooses a random value r less than n and computes:

Z = r^e mod n

X = ZC mod n

t = r^-1 mod n

Nest Bob gets Alice to authenticate (sign) X with her private key d thereby decrypting X. Alice return Y = X^d mod n

Show how Bob can use the information now available to him to determine M.