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.
APEX Calculus
Text Website
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