Math/CMSC 456 Homework
- Homework #1: (Due Friday, February 3)
NOTE: For MATLAB problems, you do not need to hand in the whole printout. A description of what you did (what command you used and a
description of the result: for example, " I used allshifts and the only meaningful shift was . . . " is sufficient).
- p. 55: 1, 4, 6, 7, 23
- p. 59: 1, 2, 3
- I. (a) Encrypt HATE and LOVE using the affine function 13x+22. Why is decryption impossible?
(b) Find two different three-letter words that encrypt to WWW.
(c) Challenge: Find a word (legal in Scrabble) that encrypts to JJJ. (There are 4 such words.)
- II. The ciphertext xvasdw was encrypted using an affine function ax+1 mod 26. Determine a and decrypt the message.
- III. The following was encrypted by an affine cipher:
jidfbidzzteztxjsichfoihuszzsfsaichbipahsibdhuhzsichjujgfabbczggjsvzubehhgjsv
Decrypt it. (Hints: The command "frequency" could be useful. The plaintext has 9 E's, 3 D's, and 3 W's.)
This quote (NYTimes, 12/7/2014) is by Mark Wahlberg from when he was observing college classes in order to play a professor in "The Gambler."
The Matlab files needed to do shifts, etc., are obtainable through the course webpage.
Probably the easiest way is to use the zipped files that are in the section borrowed from Jonathan Rosenberg
(see the course webpage).
The other way is through the webpage for the book.
- Homework #2: (Due Wednesday, February 15)
- pp. 56-57: 11, 19, 20, 22, 25
- pp. 60-61: 7, 11
- p. 104: 1, 5 (do part (a) by the Euclidean algorithm, not by factoring)
- Perfect secrecy of the one-time pad: Read Section 1 and do Exercises 1, 2, and 3 on page 6
Here is a write-up of the Extended Euclidean Algorithm that could
be inserted among the material on page 69 of the book.
- Homework #3: (Due Friday, February 24)
- p. 105: 12, 16
- p. 192: 1, 2, 3, 4, 10, 17
- Homework #4 (Due Monday, March 6)
- p. 193: 7, 12, 13, 15, 16 (Hint: See the Theorem on page 68), 21, 25, 27
- p. 198: 8
- I. In an RSA cryptosystem, suppose you know that n=5352499, e=17, and d=943577.
(a) Use the method of this link to factor n.
(b) Use the method on page 186, with r=de-1, to factor n.
Midterm #1: Monday, March 13
Sections for first midterm: 1.1, 2.1, 2.2, 2.3, 2.9, First section of One-time Pad pdf (see HW 2), 2.11, 3.1,
Extended Euclidean Algorithm pdf (see HW 2), 3.3, 3.5, 3.6,
6.1, 6.2.2, parts of 6.3, parts of 6.4
2015's first midterm and Solutions
2014's first midterm and Solutions (ignore 5(a)(iii))
2011's first midterm and Solutions (ignore Question 2c)
2010's first midterm and Solutions (ignore Questions 1a and 2a)
2005's first midterm and solutions
2003's first midterm and solutions (ignore Questions 2c and 5)
2009's first midterm and solutions (ignore Questions 3a and 6b)
- Homework #5 (due Friday, March 31)
- p. 146: 1, 2, 4, 5, 6
- p. 196: 26
- p. 214: 1, 2, 6, 7
- Homework #6 (due Monday, April 10)
- p. 239: 1, 2, 3, 4
- p. 242: 1
- p. 252: 1, 4a, 5, 6, 8
- Homework #7 (due Wednesday, April 19)
- p. 321: 2, 3, 5, 6
- p. 303: 2, 3, 7, 8
- p. 197: 1 (if you are doing the HW the night before the due date, figure out why I assigned this problem)
- Homework #8 (due Monday, May 1)
- p. 370: 4
- I. Suppose P and Q are points on an elliptic curve and Q=kP for some secret integer k. Peggy claims to know k.
Devise a Zero Knowledge protocol that Peggy can use to convince Victor that she knows k.
The first step is 1. Peggy chooses a random integer r_1, lets r_2=k-r_1, and computes R_1=r_1P and R_2=r_2P.
- II. (a) List the points on the elliptic curve y^2 = x^3 + 1 (mod 11).
(b) Find the sum (2,3)+ (5,4) on E.
(c) Find the sum (2,3) + (2,3) on E.
A dictionary for changing between classical and elliptic curve cryptosystems
Midterm #2: Friday, May 5
- Sections for Midterm #2: 3.7, 4.1, 4.2, 4.7, 7.1, 7.2 (except 7.2.1 and 7.2.4), 7.4, 8.1, 8.4, 9.1, 9.2, 9.3, 9.4, 12.2, 14.1,
14.2, 16.1, 16.2
- Here are some previous second midterms.
Fall 2015's second midterm (ignore 4(d) for the midterm) and Solutions
Spring 2015's second midterm (ignore 4(b) for the midterm) and Solutions
a sample second midterm and Solutions
2006's second midterm (ignore 5(b) for the midterm) and Solutions
another sample second midterm (ignore 5 for the midterm) and Solutions
2003's second midterm (ignore 2(c) for the midterm) and Solutions
2005's second midterm and Solutions
2010's second midterm and Solutions
FINAL EXAM: Monday, May 15, 1:30pm-3:30pm, Physics 1201 (the usual classroom)
Sections for the final: See the lists for Midterm #1 and Midterm #2. Plus Section 16.5. (see the "dictionary" link above (just before Midterm #2))
2015's final and solutions
2011's final and solutions (Ignore 2b; the solution to 2b is incorrect; the answer is 121)
2009's final and solutions (Ignore 1)
2007's final and solutions (Ignore 3(a)(2))
2004's final and solutions (Ignore 2b)
2014's final and solutions (Ignore 1b)