For the following problems, use 0 as the starting index for the alphabet; i.e., ' a ' =0, , 'b' =1, and etc. In Java, you can use "type castings" such as (int) and (char) to convert between a character and its ASCII code. Note: How does a letter's ASCII code relate to its index in the alphabet? Refer to an ASCII table online. In Java, a negative integer mod 26 will compute to a negative remainder. To map that remainder to a positive one over Z26, we simply need to add 26 to it. For the Vigenre cipher over the alphabet (i.e over Z26 ), given plaintext "the king of denmark tells his son hamlet to avenge his murder" (with no spaces) and key "thebard", compute the ciphertext by hand. Show all you works. (You are allowed to verify the ciphertext obtained with your implementation from Problem 3.) For m=50, find its prime factorization using the F.T.A and compute (50) (i.e., its Euler function). Then find all the a values in Z50 that is relatively prime to 50 ; i.e., GCD(a,50)=1. Lastly, for each of those a values, find its Multiplicative Inverse over Z50. Show all your works. In Java, implement the Vignere cipher over the alphabet (i.e over Z26 ); that is the encryption public static String Enc(String plain, String key) and decryption methods public static String Dec(String cipher, String key)