$1.$ The Caesar Cipher is our first historical cryptosystem and has numerous flaws.

$($a$)$ Decrypt the Caesar Cipher ciphertext: IT STY ZXJ RJ YT JSHWDUY DTZW UFXXBTWI

$($b$)$ The Caesar Cipher has an inadequate keyspace. What other problems does it have that make it insecure?

$($c$)$ The Caesar Cipher is often described as having a fixed shift of three positions. Explain why in this case, the Caesar Cipher is not really a cryptosystem at all.

$($d$)$ Is ROT$13$ a cryptosystem?

$2.$ Describe Playfair Cipher $($limit your answer to $50$ words$).$

$3.$ Describe Vigen$$re Cipher $($limit your answer to $50$ words$).$

$4.$ R and Q appear as one$-$letter words in a cryptogram. R has frequency $7,$ and Q has frequency $3.$ Which ciphertext letter is likely to be the substitute for a$,$ and which is likely to be the substitute for i$?$ Explain your reasoning.

$5.$ The two$-$letter word KC appears in a cryptogram. K has frequency $5,$ and C has frequency $2.$ One of K and C is a consonant, and the other is a vowel. Which is likely to be which? Explain your reasoning.

$6.$ BKKL appears in a cryptogram. What are some possible plaintext words for this four$-$letter encrypted word?