9.18 The problem illustrates a simple application of the chosen ciphertext attack. Bob intercepts a ciphertext C intended for Alice and encrypted with Alice"s public key e. Bob want to obtain the original message M = Cd mod n. Bob chooses a random value r less than n and computes
Z = re mod n
X = ZC mod n
t = r1 mod n
Next, Bob gets Alice to authenticate (sign) X with her private key (as in Figure 9.3), thereby decrypting X. Alice returns Y = Xd mod n. Show how Bob can use the information now available to him to determine M.
 
 
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