Exercise 1. Shift Cipher (40 points) Consider the shift cipher as we discussed it in class. Key space k = {0, 1,...,25). Suppose that we are given the following message space distribution, M: Pr[M = 'bye'] = 0.1 Pr[M = 'yes'] = 0.5 Pr[M = 'now'] = 0.4 Answer the following questions and make sure that you show your work. (a) (10 Paints) Compute the probability: Pr[M = 'now' C = 'baa') (b) (20 Points) Compute the probability: Pr[M = 'yes' C = "zft'] (c) (10 Points) As we discussed in class and can see in the previous two parts of this question) the shift cipher is not perfect secure for the case of 2-character and 3-character messages. What do you think about the case where the message space is M = {a,...,2} (i.e. all messages are only 1-character messages)? Does it satisfy perfect secrecy or not? If you believe it does argue about it informally, if you believe it does not provide a counter example. Exercise 1. Shift Cipher (40 points) Consider the shift cipher as we discussed it in class. Key space k = {0, 1,...,25). Suppose that we are given the following message space distribution, M: Pr[M = 'bye'] = 0.1 Pr[M = 'yes'] = 0.5 Pr[M = 'now'] = 0.4 Answer the following questions and make sure that you show your work. (a) (10 Paints) Compute the probability: Pr[M = 'now' C = 'baa') (b) (20 Points) Compute the probability: Pr[M = 'yes' C = "zft'] (c) (10 Points) As we discussed in class and can see in the previous two parts of this question) the shift cipher is not perfect secure for the case of 2-character and 3-character messages. What do you think about the case where the message space is M = {a,...,2} (i.e. all messages are only 1-character messages)? Does it satisfy perfect secrecy or not? If you believe it does argue about it informally, if you believe it does not provide a counter example