Consider the following plaintext values that we will use in the questions below:

P₁=10,P₂=18,P₃=27

Instead of asking you to run the entire algorithm on these values, you will use Wolfram Alpha to do the main set of computations.

p = 237 q = 29 Note that you will be able to choose your own value of E. Answers may vary, but we should see similar results. 1. Suppose we chose a value of E that is n_ot relatively prime to b = (231)(291) = 616. Encrypt and decrypt all the values. What issue do you notice? Any idea why this happens? 2. Suppose we let q = 23, thereby having nondistinct primes. Encrypt and decrypt all the values. What issue do you notice? Any idea why this happens? 3. Suppose we calculate D by mistakenly nding it by using ED E 1 ( mod n), instead of mod b. What issue do you notice? Any idea why this happens? 4. Suppose we choose prime factors such that n is smaller than our largest value to encrypt (which, for us, is 27). What issue do you notice? Any idea why this happens? 5. To help drive the point home, suppose we have a simplistic encryption algorithm where C : f (P) : 4 2P, but suppose we make a mistake and write P = f'1 (C) = g i 4. First, identify the issue. Then, perform the encryption decryption process on our three plaintext values above. What is the critical issue that prevents this algorithm from working properly? Though the RSA encryption algorithm is a bit challenging to understand without getting into some additional theorems, the issue you observed in 5) is exactly the same issue we encountered in 1)-4)