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

To Read
To Watch
Links in "Echo360 and other course videos" topic in onCourse. ~13 minutes total

Pre-Class Questions


Due Sunday August 30 @ midnight

One-time pads

To Read
To Watch
Links in "Echo360 and other course videos" topic in onCourse. ~14 minutes total
To Download

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

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

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 Read
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

To Read
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.

Due Sunday September 27 @ midnight

The Euclidean Algorithm and Fast Exponentiation

To Read
To Watch
Links in "Echo360 and other course videos" topic in onCourse No questions to submit today since you shoud be prepping for Exam 1.

Due Sunday October 4 @ midnight

The Prime Number Theorem and RSA Digital Signatures

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

Pre-Class Questions

  1. Based on the Prime Number Theorem, approximately how many primes are less than 21024?
  2. What is the purpose of a digital signature?
  3. Suppose Alice and Bob want to exchange an AES key to use for a secure conversation.
    1. If Alice generates the AES key, whose RSA credentials will they use to encrypt the key to send to Bob?
    2. If Alice wants to sign the message containing the encrypted key, whose RSA credentials will they use to sign the message?

Due Sunday October 11 @ midnight

Diffie-Hellman Key Exchange and Hash Functions

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

Pre-Class Questions

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

Due Sunday October 18 @ midnight

The Discrete Log Problem

To Read

Pre-Class Questions

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

Due Sunday October 25 @ midnight

Elgamal Digital Signatures

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

Pre-Class Questions

  1. What is the hard math problem underlying Elgamal digital signatures? Where does this problem appear?
  2. What is the purpose of the ephemeral key kE used in an Elgamal digital signature?
  3. If Bob receives a message signed with Elgamal, (x,(r,s)) from Alice, what values does Bob need to verify the signature?

Due Sunday November 1 @ midnight

The Digital Signature Algorithm

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

Pre-Class Questions

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

Due Sunday November 8 @ midnight

Counter Modes, M-I-T-M Attacks, and TLS

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

Pre-Class Questions

None for today since I was so deliquent in getting this posted.

Due Sunday November 15 @ midnight

Blockchain and Bitcoin

To Read
You'll get more out of these readings if you've watched the videos first.
To Watch
Links in "Echo360 and other course videos" topic in onCourse

Pre-Class Questions

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