1. Shift cipher (Caesar cipher). Using the convention in the text (i.e. a->0, z->25) decrypt the ciphertext GEOSMDAOWE using a shift cipher key of 12. Now encrypt the plaintext ibm using a cipher key of 25. a. What is your decryption of the ciphertext GEOSMDAOWE? b. What is your encryption of the plaintext ibm? c. How many possible keys exist if we assume a 26 letter alphabet and omit the key of 0 (i.e. the ciphertext must differ from the plaintext)? d. Mathematically what is the procedure for determining the key if you know a single plaintext/ciphertext letter pair (e.g. f and W)? 2. [5] The ciphertext JOBMCTGFU was produced by an affine cipher mod 26. You have reason to believe plaintext starts with sl. a. Whats the key? b. Decrypt the entire message. c. What kind of attack is this? 3. [5] Suppose we encrypt a message with an affine cipher using key K1, then encrypt the ciphertext with an affine cipher using key K2. Is this double encryption more secure than just doing a single encryption? Support your answer mathematically. 4. [5] Substitution cipher. Using the following substitution key encrypt and decrypt the following plaintext and ciphertexts. ZAERTYUIOPQSDFGHJKLMWXCVBN abcdefghijklmnopqrstuvwxyz a. Ciphertext to be decrypted IORRTFDTLLZUT b. Plaintext to be encrypted a little lamb c. How many possible keys exist for a 26 letter alphabet? 5. [5] Let E1 and E2 be two independent flips of a fair coin. Find the entropy H(E1) and joint entropy H(E1,E2). Why is H(E1,E2)=H(E1)+H(E2)?