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Homework 4 - Computer Network Security | ECE 646, Assignments of Cryptography and System Security

George Mason University (GMU)Cryptography and System Security

Material Type: Assignment; Class: Cryptography/Comp Netwk Sec; Subject: Electrical & Computer Enginrg; University: George Mason University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 02/10/2009

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Homework 4
due Tuesday, October 3rd, 2006, 7:20 PM
at the beginning of class
Reading Assignment:
•W. Stallings, Cryptography and Network-Security, Preface, Chapter 4.1 – 4.3, 8.1
•A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, chapters 2.4.1,
2.4.2, 2.4.3
Tasks:
1. (Project Track Only) The final project specifications are due on paper at the beginning on class on
October 3rd. In addition submit them in PDF format via e-mail to [email protected] using ECE646-
Project-Spec as the subject and please name your file projectid-specifications.pdf (e.g. HI-1-
specifications.pdf). Your project ID is the short string of letters and numbers in front of your project
name on the Project Group List page.
Please include the project ID on all project related paperwork and e-mails.
2. (All) Start with the first lab. Bring 4 copies of your PGP-ID card from the lab and your official GMU-
ID card with you. Here is the PGP-ID card for the [email protected]:
pf2

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Download Homework 4 - Computer Network Security | ECE 646 and more Assignments Cryptography and System Security in PDF only on Docsity!

Homework 4

due Tuesday, October 3

rd

, 2006, 7:20 PM

at the beginning of class

Reading Assignment:

  • W. Stallings, Cryptography and NetworkSe curity, Preface, Chapter 4.1 – 4.3, 8.
  • A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, chapters 2.4.1, 2.4.2, 2.4.

Tasks:

  1. (Project Track Only) The final project specifications are due on paper at the beginning on class on October 3 rd. In addition submit them in PDF format via emai l to [email protected] using ECE ProjectS pec as the subject and please name your file projectids pecifications.pdf (e.g. HI specifications.pdf). Your project ID is the short string of letters and numbers in front of your project name on the Project Group List page. Please include the project ID on all project related paperwork and emai ls.
  2. (All) Start with the first lab. Bring 4 copies of your PGPID card from the lab and your official GMU ID card with you. Here is the PGPID card for the [email protected]:

Problems (all tracks):

Please use very legible handwriting or type the answers. In either case you can draw diagrams and write formulae by hand but they have to be legible and the diagrams have to be labeled clearly. Answers that neither the TA nor the instructor can read receive 0 points. You are allowed to work in groups on these problems but you have to write your own solution in your own words. Copying the solution from someone else (in class or otherwise e.g. Internet) is a serious honor code violation and will be treated as such.

  1. (10 points) Examining the ring ℤm. a. Find the additive inverse of all elements in ℤ 5. b. Which elements in ℤ 5 and ℤ 26 do have multiplicative inverses? c. Determine the multiplicative inverse of all those elements in ℤ 26.
  2. (2 points) What is the key space of the affine cipher?
  3. (10 points) Break the following ciphertext, knowing that it has been obtained by encrypting a short English message using the affine cipher: JBMB SZHME JJBGF WGFJB MYKZV HJKOF HMZEJ SFHGE JBMGF CKAMJ SDMGF EJMGF Please note that all spaces and punctuation characters have been removed from the message before encryption, and the letters of the ciphertext have been arranged for convenience and increased readability in the groups of five characters. Please use analytical method (i.e., for each possible hypothesis regarding the possible frequency of letters in a short English message, form and solve a set of two equations with two unknowns). Use tables you have developed as a solution to the previous Problem to confirm or reject each hypothesis, and recover the correct key. Please note that an exhaustive key search attack, i.e., trying all possible keys, or solutions to the equations, one by one, using a computer, will not be accepted as a valid solution.
  4. (8 points) Use the basic form of Euclid's algorithm to compute the gcd of the following numbers. Write down every step. a. 4893 and 2921 b. 3531 and 2343
  5. (10 points) Use the extended Euclidean algorithm to compute the inverse of the elements a in ℤm. Write down every step. a. a = 5, m = 26 (hint: used in question 3) b. a = 23, m = 293