To Do:

1. Solutions to the last daily post (the one due today) are now posted: Solutions to Daily Due Aug 26. Check your work against them. All daily post solutions are also collected on the Archive page (when I’m on top of things!).
2. CIPHERTEXT CHAIN! This time with affine cipher.
   1. Come up with a short (one word) answer to the question “What’s the coolest math?” This is your plaintext.
   2. Choose a key $(\alpha,\beta) \in (\mathbb{Z}/26\mathbb{Z})^2$. Make sure your choice is suitable as a key, as we discussed in class.
   3. Encrypt the plaintext with affine cipher (by hand, using the cryptography tools sheet if you like). This gives you your ciphertext.
   4. Post your ciphertext on the discord channel #ciphertexts, along with the key.
   5. Choose the most recent user’s post (besides yours) from #ciphertexts, and decrypt it (by hand).
   6. Post the answer in the form “So-and-so thinks the coolest math is…”. Use discord’s “spoiler” feature to hide your answer, in case other students want to practice, or end up using the same ciphertext (this never works quite perfectly).
3. Suppose you eavesdrop on your little sister’s communications, and she is using affine cipher. Her ciphertext is CRWWZ. You know she starts every message she writes with “HA” (she’s weird that way). Decrypt the message. Explain how you did it.
4. Find the inverse (if it exists) of: $2 \pmod{17}$, $8 \pmod{11}$ and $3 \pmod{15}$. If it doesn’t exist, explain why.
5. Come up with the fastest way to compute $3^{519}$ modulo $11$ by hand. That is, count the multiplications you need to do in your full solutions (you can’t use secret knowledge about mod 11 for example, you have to compute anything you plan to use), and try to minimize that number by being clever about your method. It should be doable by hand (i.e., don’t do 500+ multiplications!!) Post the number of multiplications you have to do (but not your secret sauce) in the #daily-collaboration channel, as a sort of friendly competition.
6. Remember to upload to canvas!