3. You intercept an enemy transmission that you believe was encrypted using the Vigenere cipher:

ULEFIZBCXFICBWRDVRUMSUABPJGIIZBVREINE

(a) You believe that the key length used to encrypt the message was either 1, 2, 3, or 4. Using displacement coincidences, find the number of coincidences corresponding to each of the possible key lengths. Based on this, what do you suspect is the key length?

(b) Based on the guessed key length, you proceed to separate out the ciphertext into groups according to their shift values. After conducting a frequency analysis on each group, you determine that the 2nd group (i.e., the group starting from the 2nd letter) used a key value of 4 and the 3rd group (i.e., the group starting from the 3rd letter) used a key value of 13.

Using this information, find the full key and use it to decrypt the message.

(c) Why was the frequency analysis conducted in part (b) only conclusive for some of the groups of letters and not all? What would you need to be more certain about the conclusions you can draw from a frequency analysis?