$1.)$ Encrypt the message $"$Do not eat gas station sushi" using a Vigen$$re square with keyword "yuck". Show how the keyword is used in the encryption.

$2.)$ Decrypt the message "yziehorgaempwfroeotsoodnwshceh" using a Vigen$$re square with keyword "alone". Show how the keyword is used in the decryption.

$3.)[$Worth $30$ points$]$ The following is some text from my notes:

Looking for repeating substrings can be tedious, and if the cipher is monoalphabetic, then the Kasiski test doesn't help us any. How can we tell from the start whether or not one or more alphabets are being used?

The idea here is that the frequency table of an MSC should look like the one for standard English, just with the letters matching different frequencies. The way we actually go about measuring this is a little different from this, but it gets at the same thing. We use the Index of Coincidence.

The following is that same text encrypted in three different ways. You are told that one is the result of an affine encryption, and that the other two used Vigen$$re ciphers, whose keywords were length

and

$.$ Analyze the three ciphertexts, and explain how you know which is which, using the IC$.$ Make sure you describe what you did along the way.

a$.)$

rsoborgwuvrvviakorgjafskxmnxygaehitvjmolyenuojtykgignirzyqoeuelgnebvzmckninknikrymsboxejzhovyrtykpplyenpnswtgrwvzilclvodzlejzerkcleknirfxrokurefxqoikelgnebvzwaikfeztkujkhtykmdvgleikmsknetknifikuuvtgykgflvujaeswcjnsucjpofqpibkxhvurewuvskgrdrxheempijnnujzaiknxhvritkkvsdgxcyorguojfvxinklvehaintoiskniwreaerixurrpyxuebfaxmvgwuiorgknmszyelzzxlvjmfwkveezjrfsxhzyfukoxgvzwakzlejgqeknmnxciujkxhvordvdsftumntoheeii

b$.)$

svvrpunmvyylwlhapunzbizaypunzjhuilalkpvbzhukpmaoljpwolypztvuvhswohilapjaoluaolrhzpzrpalzakvlzuaolswbzhufovdjhudlalssmyvtaolzahyadolaolyvyuvavulvytvylhswohilazhylilpunbzlkaolpklholylpzaohaaolmylxblujfahislvmhutzjzovbsksvvrsprlaolvulmvyzahukhyklunspzoqbzadpaoaolslaalyzthajopunkpmmlyluamylxblujplzaoldhfdlhjabhssfnvhivbatlhzbypunaopzpzhspaaslkpmmlyluamyvtaopzibapanlazhaaolzhtlaopundlbzlaolpuklevmjvpujpklujl

c$.)$

ncazcgkwqfdtjxekkbshouwktwzvmveedsftxbsluozscyxygquebxvzuaacitpgjontnbgkjszibxoruwezcmijvratmgxygzbjmtrpjcirugavvsxazksdvvqhntvkyvqibxvftbaiigiftaagytpgjontnleigpqxhzyjgrfwybhvcvqgybwkjofibxjigegthvckcpxtiyeeogohbhycfzadeembghttigiwqfeiughrtrqcaemjjxghnpmkjhttfxxkgfebumgykbsscyjvtszizkihwszrcxwkjsipspirehgpfecxqondomqvcgggcgkkjwexmtpzvhxtxbjwgfqcnyvfohtxmuykkhstnlekvvqhufikjwzvqxyjghttcghvzcrribrtkrqcwx

$4.)$ The following is the ciphertext of the notes text above, again encrypted using a Vigen$$re cipher. Show how to use the Kasiski test to determine the length of the keyword used in its encryption. Hint: Analyze the repeating string $"$ypz$".$

qwjozsoasiwmkiryqikjzjnxinvbwtfvwikjldslxiihzkbcitnxciinahsetigtyfjzxzhbcieypzorxqnozymnxutmnrkmmgtlxiicytexeebmoicqnmsdypzwkfzoayjbciitzisktvzsirwmirqxcesjbneijjzmelcniuypzmujiciijqnxyfbolvkzzuljvxckfjgifkiiqjhacslqlgsfptdovypzsejnjvjyiihrwlzrxqqnlazaoazypolvqmoxvwahekhpdrxiqajvwmixwwmlyvskdijypzardezetycvpcdojestcoqvfapvzsoolzxqnecnbopviqajvwmixwwwhxynawyknbbikxioxyjavqvypdrxbmpwvypzmeimsswhwdrtnlzrtj