$($Polybius Cipher, $15$pt$)$

a$)[3$pt$]$ Create the Polybius square for the keyword "cryptography". Note: we make the

standard assumption that $i=j$ so we have a $25$ letter alphabet.

b$)[3$pt$]$ Use the Polybius square from a$)$ to encrypt your first name $($stop after the first six letters

if your first name is longer; it it's shorter, add some letters from your last name; replace $j$ with $i$

if necessary$).$

c$)[3$pt$]$ Use the Polybius square from a$)$ to decrypt the ciphertext $"4521415115342143"$

d$)[6$pt$]$ You've intercepted the ciphertext

$35,34,33,12,14,42,34,45,43,13,54$

Based on the form of the ciphertext you suspect a Polybius cipher, but when you decrypt $($with

the standard square$)$ you get nonsense. The sender must have used a Polybius cipher based on

some keyword. You know that the sender is lazy and suspect that the keyword is short $($length $4).$

By bribing the secretary of the sender you find out that the keyword used to construct the

Polybius square did not contain letters in the second half of the alphabet $($N$-$Z$).$

Decrypt the message, reconstruct the Polybius square, and find the keyword used to create it$.$

Hint: the fact that the keyword doesn't contain the letters N$-$Z tells you something about the

square. Use that. Some trial$/$error$,$ guessing may be involved. Include a brief description of how

you managed to break the cipher.