Alice is learning about the shift cipher. She chooses a random

three$-$letter word $($so all three$-$letter words in the dictionary have

the same probability$)$ and encrypts it using a shift cipher with a

randomly chosen key $($that is$,$ each possible shift has probability

$1/26).$ Eve intercepts the ciphertext mxp$.$

$1.$ Compute

P$($M $=$ cat $$ C $=$ mxp$)$

$.($Hint: Can mxp

shift to cat?$)$

$2.$ Use your result from part $($a$)$ to show that the shift

cipher does not have perfect secrecy $($this is also true

because there are fewer keys than ciphertexts; see the

proposition at the end of the first section$).$

PLEASE SOLVE BY HAND AND BY PYTHON.