Check out this tool for drawing pictures of the function $f(x)=ax \pmod{n}$. Try it for $n=5$ and $n=6$ with different $a$’s. Figure out what it is doing.

Come up with a short (one word) answer to the question “What’s the coolest math?” This is your plaintext.

Choose a key $(\alpha,\beta) \in (\mathbb{Z}/26\mathbb{Z})^2$ . Make sure you choice is suitable as a key, as we discussed in class.

Encrypt the plaintext with affine cipher (by hand, using the cryptography tools sheet if you like). This gives you your ciphertext.

Post your ciphertext on the discord channel #ciphertexts, along with the key.

Choose the most recent user’s post (besides yours) from #ciphertexts, and decrypt it (by hand).

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).

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.

Come up with the fastest way to compute $3^{519}$ modulo $11$ by hand. That is, count the multiplications you need to do, and try to minimize that number. 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.

Hand items #4,5 in on canvas as your record for today’s daily post.