This page uses MathJax to display mathematical notation, so please let me know if any part isn't clear.

Be sure to check back, because this page will be updated often during the semester.

All chapter references are to the text Understanding Cryptography by Paar and Pelzl.

- Chapter 1, pp 1 - 23, although you can demphasize Section 1.4.2 Integer Rings

- Week 1: Overview
- Week 1: Modular Arithmetic

- No questions to turn in for the first week.

If you didn't see this before Monday's class, be sure to complete before Wednesday.

- Chapter 2: through Section 2.2.2 The One-Time Pad, pp 29 - 38

- Week 2: Encoding messages as numeric values
- Week 2: A few notes on stream ciphers
- Week 2: Note on the size of the key space

- Follow the instructions on the main course webpage to download Mathematica to your own computer.
- Download the notebook aug31.nb and open it in Mathematica. Follow the instructions to work through the notebook. You'll use this to answer the last two Pre-Class Questions.
- In case Mathematica is being tempermental for you, here's a pdf of the notebook so that you can at least take a look at the content.

- Encrypt the plaintext x = 1101 using a stream cipher with key stream s = 0111.
- Why are one-time pads unconditionally secure?
- Use the Mathematica notebook to encrypt the message "Verbing weirds language" using a Caesar cipher with a shift of k = 17. (You should remove any spaces). What is the ciphertext?
- Use the Mathematica notebook to decrypt the message "CNAVXVSZXFGECBLXGEDXOBISNAXABUNPAIPAVPYSBEUFIIPVBOLPAISBD" using an affine cipher with a key of k= = (23, 13). What is the plaintext?

- Chapter 3: Section 3.1, pp 55 - 58, and Section 3.8 & 3.9, pp 81 - 82
- Chapter 4: Sections 4.1 - 4.3, pp 87 - 99

Don't get boggged down in the notation in Section 4.3. We'll hit the high points we need in the videos and in class.

- For general background, History/Intro to AES (~2:00 - ~18:00) by Christof Paar
- AES explained as a Flash animation (~5 minutes)
- Week 3: Clarification on Problem 3.12 from Problem Set #2
- Week 3: GCDs and multiplicative inverses mod m
- Week 3: Introduction to AES and finite fields

- Does an affine cipher perfom confusion? Why or why not?
- What is the purpose of diffusion in encryption algorithm?
- Let f(x)=x
^{ 2 }+ 1 and g(x)=x+1 be polynomials in ℤ_{2}[x]. What is f(x) ∙ g(x) ?

- Chapter 4: finish the chapter, pp 99 - 117
- A stick figure guide to AES (for reference)

- Multiplying matrices (for reference, if needed)
- AES explained as a Flash animation (re-watch)
- Week 4: Details of AES

- Perform the following matrix multiplication and addition: \[ \left( \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{matrix} \right) \cdot \left( \begin{matrix} 0 \\ 1 \\ 1 \end{matrix} \right) + \left( \begin{matrix} 1 \\ 0 \\ 0 \end{matrix} \right) \mod \ 2 \]
- In which layer(s) of AES does confusion occur? Why?
- In which layer(s) of AES does confusion NOT occur? Why?

- Chapter 6: Sections 6.1-6.3, pp 149 - 157
- Chapter 7: Sections 7.1-7.3, pp 173 - 179

- Asymmetric encryption - Simply explained gives a nice introductory motivation (~5 minutes)
- How RSA works by F5 DevCentral (~ 14
minutes)

Note that what they call the "totient of n" is what we've called the Euler phi function \( \phi(n) \).

- Is nonrepudiation possible with a symmetric cipher? Explain.
- Give a real-world example where nonrepudiation is desirable.
- What is the hard math problem underlying the security of RSA?
- For this question, we'll use the notation from the text for the RSA keys.

Bob publishes the public key k_{pub}=(n,e)=(25021,3).- If Alice uses Bob's public key to encrypt the message x=1315, what is the ciphertext y?
- Bob's private key is k
_{pr}=d=16467. Decrypt the ciphertext y from part (a) and verify that you obtain the correct plaintext.

- Chapter 7: Section 7.4, pp 179 - 182

- Extended Euclidean Algorithm Example (I like this better than the text's explanation)

- Mathematicians Will Never Stop Proving the Prime Number Theorem from Quanta Magazine
- Chapter 10: Sections 10.1-10.2, pp 259 - 270

- Introduction to Digital Signatures
by Jeff Suzuki (~5 minutes)

The process of RSA signatures is very clear, but one slightly weird thing in the video is that it has Bob specifying the message that Alice signs, rather than Alice signing a message that they want to send to Bob.

- Based on the Prime Number Theorem, approximately how many primes are less than 2
^{1024}? - What is the purpose of a digital signature?
- Suppose Alice and Bob want to exchange an AES key to use for a secure conversation.
- If Alice generates the AES key, whose RSA credentials will they use to encrypt the key to send to Bob?
- If Alice wants to sign the message containing the encrypted key, whose RSA credentials will they use to sign the message?

- Chapter 8: Section 8.1, pp 205 - 208
- Chapter 11: Section 11.1, pp 293 - 296, and the list of Properties of Hash Functions at the end of Section 11.2, pg 303

- Public key cryptography - Diffie-Hellman Key Exchange by Art of the Problem (~8 minutes)
- Hashing Algorithms and Security by Computerphile (~7 minutes)

- What's an advantage of Diffie-Hellman key exchange over using RSA to exchange a key for AES?
- Suppose Alice and Bob agree on values \(p=37\) and \( \alpha=5 \) for Diffie-Hellman.
- If Alice picks a private key of a=9, what will be their public key A?
- If Bob picks a private key of b=14, what will be their public key B?
- What will be the shared key?

- What is one purpose of a hash function?

- Re-read the Tutorial Problems from last week to remind yourself of the terminology introduced there.
- Chapter 8: Skim Section 8.2. There's a lot here, so don't get too bogged down. We'll talk about the major results we need during class.

- Solve the discrete log problem \( 3^x \equiv 26 \mod 31 \)
- What is ord(26) in \( \mathbb{Z}_{31}^* \)?
- Explain the connection between questions 1 & 2.

- Section 10.3: The Elgamal Digitial Signature Scheme. Focus on 10.3.1 and 10.3.2, pp 270 - 273

- Week 10: Elgamal digital signatures

- What is the hard math problem underlying Elgamal digital signatures? Where does this problem appear?
- What is the purpose of the ephemeral key k
_{E}used in an Elgamal digital signature? - If Bob receives a message signed with Elgamal, (x,(r,s)) from Alice, what values does Bob need to verify the signature?

- Chapter 10: Section 10.4, pp. 277 - 284

- Week 11: The Digital Signature Algorithm

- What is the hard math problem underlying the Digital Signature Algorithm? Where does this problem appear?
- What are the possible lengths of the message x that can be securely signed by DSA? How does this compare to Elgamal signatures?
- The text suggests using SHA-1 for the hash in DSA. Do a little research. Is this hash function still recommended?

- Chapter 13: Section 13.3, pp 342 - 349
- For more details on Transport Layer Security specifically:
- What is Transport Layer Security (TLS)? (Cloudflare)
- What Happens in a TLS Handshake? | SSL Handshake (Cloudflare)

- Cipher Block Chaining Mode (Udacity)
- Counter Mode (Udacity)

I think this is a super clever, simple idea that uses a block cipher like in AES to create the key used in a stream cipher

- This Is What Happens When Bitcoin Miners Take Over Your Town (Politico)

This is kind of long, so feel free to skim. It's worthwhile, though, to see some real-life consequences. - Cryptocurrency miners go to federal court to block 'crippling' electric rate hike (KUOW)
- Things Blockchain Is Supposed to Revolutionize (Slate)

- But how does bitcoin actually work? (3Blue1Brown)
- How secure is 256 bit security? (3Blue1Brown)
- Smart contracts (Simply Explained)
- The History of Ethereum (Blockgeeks)

- What is the cryptographic problem that makes Bitcoin mining difficult?
- Explain one significant difference between Bitcoin and Ethereum.
- Look for a non-cryptocurrency proposal for using blockchain technology. What's the purpose of blockchain for this application?