MCS 223 Individual Assignments

Do these problems on your own. (See the statement of the College's academic honesty policy.)
Trim "fringes." Solutions will be graded on the basis of clarity of presentation as well as correctness.

Problem
number
Problem Due date
1 Complete the solution. T 1/6
2 Problems 1-3, Cryptograms and Spygrams, p.3
Hint: -4 <deciphering shift <7
(-7 <enciphering shift <4).
T 1/6
3 Quote 100 consecutive letters of random text
and tally the individual letter frequencies.
T 1/6
4 Make a table showing the multiplicative inverses (reciprocals) modulo 26 of the numbers 1, 2, 3, 4, ... , 25, 26. (Some do not exist.) Keep a copy for your reference. M 1/12
5 Find all the solutions of
(a) 20 x = 4 (mod 30)
(b) 20 x = 10 (mod 30).
M 1/12
6 Handout: "Modular Arithmetic and Affine Ciphers" M 1/12
7 Barr 1.1: #1-6, 9-11, 14 M 1/12
8 Barr 1.1: #7-8, 12-13, 15-24 (as many as you can get) T 1/13
X Extra credit: Determine number of monoalphabets that change every letter.  
9 Little Orphan Annie crypt (handout) R 1/15
10 The Gold-Bug crypt (handout) M 1/19
11 Matrix inverse mod 26:   (ps)  (pdf)  ( html) R 1/22
12 In-class: Lewand sect. 3.3 #1, 2 R 1/22
X Extra credit: Solve one or more of the Exam 3 cryptograms:
  • Cipher 077
  • Cipher 134
  • Cipher 138
  • Cipher 168
F 1/30
13 Solve the columnar transpostion cipher IPLAI HLTCH EFAOH ORWKR ACTIT AMLNO NPTRO DCEMO RTTBE LEXAR SABDI AEMSN PWOAS LUNOE EHR. It contains the words "the probable." (The solution was begun in class 1/27.) W 1/28
14 Let g = gcd(345, 543).
  • Find g by the Euclidean algorithm.
  • By the extended Euclidean algorithm, find integers s and t such that 345 s + 543 t = g.
  • Solve 345 x = 12 (mod 543).
W 1/28
X Extra credit: Solve Lewand 4.3#3. (Turn in your computer output.) F 1/30

Make-up assignments

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