MA 479 / CSSE 490: Cryptography
Homework 4 problems inspired by Mathematics

Rose-Hulman Institute of Technology
A joint effort of the
Department of Mathematics
and the Department of Computer Science & Software Engineering
Spring term, 2002-2003

All these problems are paper-and-pencil problems. You will probably not find a computer program helpful on these problems. Show all steps of your work. I will give some partial credit, esepcially on multi-part problems.
  1. [2 points.] Carefully write up your answer to Problem 3.3 in the textbook. This is the same S-DES example that you did most of in class.
  2. [2 points.] Carefully write up your answers to questions 1-4 of the worksheet from class entitled "Differential Cryptanalysis, Part A". (You did this in class.)
  3. [2 points.] Answer questions 6 and 8-10 of the worksheet from class entitled "Differential Cryptanalysis, Part A".
  4. [4 points.] Answer questions 11-12 of the worksheet from class entitled "Differential Cryptanalysis, Part A".
  5. [4 points.] Carefully write up your answer to the Exercise from the worksheet from class entitled "A Simplified AES Algorithm". (You did most of this in class.)
  6. [8 points.] Perform a differential cryptanalysis of one-round S-AES. Use the following plaintext-ciphertext pairs:
    Plaintext Ciphertext
    0100 1110 0110 1111 0010 0010 0100 1101
    0111 0100 0110 1111 0000 1010 0001 0001
    0100 1101 0111 0010 1101 0101 1101 0000
    0110 1111 0111 0010 1100 0001 0100 1111
    Recover the first nibble of the key. (Let me know if you get stuck; I have further hints.)
  7. [12 points.] Get a description of linear cryptanalysis from me and perform a linear cryptanalysis of one-round S-AES.
  8. [12 points.] Get a description of the "Square Attack" from me and perform a square attack cryptanalysis of four-round S-AES.


    The following problems are from Chapter 4 of your textbook.

  9. [1 point.] Problem 4.17. Do not use Maple. Completely justify your answer.
  10. [1 point.] Problem 4.18(a). Use the Euclidean Algorithm or the Extended Euclidean Algorithm. Show all steps.
  11. [2 points.] Problem 4.19. Use the Euclidean Algorithm or the Extended Euclidean Algorithm. Show all steps.