$(35$ points$)$

A Caesar cipher is a simple approach to encoding messages by shifting each letter in

a message along the alphabet by a constant amount $k.$ For example, if $k$ equals $3,$ then

in an encoded message, each letter is shifted three characters forward: $\text{'}$a$\text{'}$ is replaced

with $\text{'}d\text{'},\text{'}b\text{'}$ with $\text{'}e\text{'},\text{'}$c$\text{'}$ with $\text{'}f,$ and so on$.$ The end of the alphabet wraps back around to

the beginning. As you can see, the Caesar cipher is fairly easy to break and in fact, the

code can be broken by trying various key values until one works. An improvement can

be made to this encoding technique if we use a repeating key. Instead of shifting each

character by a constant amount, we can shift each character by a different amount using

a list of key values. If the message is longer than the list of key values, we just start

using the key over again from the beginning. For example, if the key values are

$317425$