# Pre-Class Assignments, Math 202 Cryptography Calculus I, Fall 2020

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.

### For Sunday August 23

#### Modular arithmetic and affine ciphers

• Chapter 1, pp 1 - 23, although you can demphasize Section 1.4.2 Integer Rings
##### To Watch
Links in "Echo360 and other course videos" topic in onCourse. ~13 minutes total
• Week 1: Overview
• Week 1: Modular Arithmetic

#### Pre-Class Questions

• 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.

### Due Sunday August 30 @ midnight

• Chapter 2: through Section 2.2.2 The One-Time Pad, pp 29 - 38
##### To Watch
Links in "Echo360 and other course videos" topic in onCourse. ~14 minutes total
• 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
• 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.

#### Pre-Class Questions

1. Encrypt the plaintext x = 1101 using a stream cipher with key stream s = 0111.
2. Why are one-time pads unconditionally secure?
3. 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?
4. Use the Mathematica notebook to decrypt the message "CNAVXVSZXFGECBLXGEDXOBISNAXABUNPAIPAVPYSBEUFIIPVBOLPAISBD" using an affine cipher with a key of k= = (23, 13). What is the plaintext?

### Due Sunday September 6 @ midnight

#### AES and finite fields

• 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.
##### To Watch
Links in "Echo360 and other course videos" topic in onCourse
• 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

#### Pre-Class Questions

1. Does an affine cipher perfom confusion? Why or why not?
2. What is the purpose of diffusion in encryption algorithm?
3. Let f(x)=x 2 + 1 and g(x)=x+1 be polynomials in ℤ2[x]. What is f(x) ∙ g(x) ?

### Due Sunday September 13 @ midnight

#### AES Data path and key path

##### To Watch
Links in "Echo360 and other course videos" topic in onCourse

#### Pre-Class Questions

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

### Due Sunday September 20 @ midnight

#### Public key cryptography and RSA

• Chapter 6: Sections 6.1-6.3, pp 149 - 157
• Chapter 7: Sections 7.1-7.3, pp 173 - 179
##### To Watch
Links in "Echo360 and other course videos" topic in onCourse

#### Pre-Class Questions

1. Is nonrepudiation possible with a symmetric cipher? Explain.
2. Give a real-world example where nonrepudiation is desirable.
3. What is the hard math problem underlying the security of RSA?
4. For this question, we'll use the notation from the text for the RSA keys.
Bob publishes the public key kpub=(n,e)=(25021,3).
1. If Alice uses Bob's public key to encrypt the message x=1315, what is the ciphertext y?
2. Bob's private key is kpr=d=16467. Decrypt the ciphertext y from part (a) and verify that you obtain the correct plaintext.