Upload to Canvas a PDF scan of your work for problems 1–4. For this assignment, you will probably prefer to type. Any mode of typing is fine, just export to PDF and upload a PDF.

Assignment: due Monday, 11:59 pm

  1. The following ciphertext was encrypted with a Vigenère cipher. Determine the key length by counting matches between shifts of the ciphertext. Include a list of number of matches corresponding to each shift, up to 30.
jmxejtahwseoidysjwxmwpdtzalgplsialyggqelzweaamymzwelrycdvmcidikcdheuazcvesafaulfrzmjvzpwdivqozjoweglsmjoapxtrebwnqxsnmaohzvpifvlsejqluwwjenegfsezxgulasjmvvzpwaijezqsnsfqowizowcfofaimvqfrpqdvzpcsmjgkpgqzwvzpwaijezhsqtvpwginpsxwmiccfywlvauaulloavojwyaakgohlvaestotxdvgtelphqxgdtjapsufpzaztgwyrkzecdpzavljgdilmjkgowspaezhippapcxsobltsyuqqdnavippwpayipmwplsgavlwjjxqzfqmesjkdqkpvevkrwnxewfvgmibcdngqgnqwuswenukfaqjekmnltiomegjrijkagk

  1. Use your function findVigKey to produce the key used to produce the above ciphertext, and then use the function vigenere to decrypt the ciphertext. Include the decrypted ciphertext.

  2. Suppose you had only been given the following fragment of the above ciphertext:

jmxejtahwseoidysjwxmwpdtzalgplsialyggqelzweaamymzwelrycdvmcidikc

Does your method from Question 1 reliably determine the key length? Given the correct key length, does your method from Question 2 correctly determine the key? Interpret your results. Through experimentation, estimate how many characters of ciphertext are needed for the methods of Questions 1 and 2 to work.

  1. Suppose that a plaintext string is encrypted using a Vigenère cipher with key length 4, and then the resulting ciphertext is encrypted using a second Vigenère cipher with key length 6. Explain why the composition of these two ciphers is a Vigenère cipher. What is the key length of the composite cipher? Justify your answer, either with a mathematical argument, or with a computer demonstration on a suitably chosen example.