Recall that encryption under the Vigen`ere cipher just corresponds to m shift ciphers, one for each of the letters in the key word.

(i) (2 marks) Suppose you apply a Vigen`ere cipher using the key word WORD, followed by a second Vigen`ere cipher using the key word CIPHER. Is the result again a Vigen`ere cipher? If yes, provide the resulting key word and explain how you obtained it.

(ii) (4 marks) In general, suppose a Vigen`ere double encryption is performed using first a key word of length m1, followed by a key word of length m2. Is the result again a Vigen`ere cipher? If yes, how do you obtain the corresponding key word, and what is its length?