Solutions to Math 135 Prelim #2 1. (a) AB = 2 1 3 2 1 2 5 1 5 25 = = MOD 26. 33 90 90
(b) If C =
5 25 MOD 26, then det(C) = 225 = 9 MOD 26. We nd det(C)1 = 3 MOD 26 90 since 9(3) 1 0 (mod 26), and so C 1 = 3 0 25 0 75 03 = = MOD 26. 9 5 27 15 25 15
2. (a)
Math 124 Winter 2009
Assignment #5
This assignment is due at the beginning of class on Thursday, March 26, 2009. Late
assignments will not be accepted. You must submit solutions to all problems marked with an
asterix (*).
YOUR ASSIGNMENT MUST BE STAPLED A
Math 124 Winter 2009
Assignment #4
This assignment is due at the beginning of class on Thursday, March 5, 2009. Late
assignments will not be accepted. You must submit solutions to all problems marked with an
asterix (*).
YOUR ASSIGNMENT MUST BE STAPLED AN
Make sure that this examination has 12 numbered pages
Cornell University
Final Examination
August 8, 2006
Mathematics 135
The Art of Secret Writing
Time: 2 hours
Name:
Instructor: Michael Kozdron
Section: 01
Read all of the following information before st
Make sure that this examination has 10 numbered pages
University of Regina
Department of Mathematics & Statistics
Final Examination
200910
(April 21, 2009)
Mathematics 124
The Art and Science of Secret Writing
Name:
Student Number:
Instructor: Michael Koz
Solutions to Math 135 Final Exam (Summer 2006)
1. (a) Alices public modulus is m = p q = 23 37 = 851.
(b) Converting the message BAT to base twenty-six gives BAT = 1 262 + 0 26 + 19 = 695.
Therefore, since the RSA encryption function is E (x) = xe MOD m,
Math 124 Winter 2009
Assignment #6
This assignment is due at the beginning of class on Tuesday, April 7, 2009. Late assignments will not be accepted. You must submit solutions to all problems.
YOUR ASSIGNMENT MUST BE STAPLED AND PROBLEM NUMBERS CLEARLY LA
I
x hG
xv h!
k dol7!k q u p k q n z q x u z v kux zq l q x k ccDhaoawm'wv7phDacfw_awmyhn q z v n x z l t l k j x u k nx kx x k u v n z t k s k zx u z v k v kux n u t n q u m ~ch7'hQ!wzQwvhoahh|UiiUwmh6zyah6~qa3iyzch~hDDhawv7hYzpi q v q n q x z l t q
Math 135 Prelim #2 July 24, 2006
This exam has 6 problems and 7 numbered pages. Name: Instructor: Michael Kozdron
You have 75 minutes to complete this exam. Show all work neatly and in order, and clearly indicate your nal answers. Answers must be justied
Mathematics 124 Midterm March 19, 2009
This exam has 12 problems on 6 numbered pages and is worth a total of 75
points.
You have 75 minutes to complete this exam. Please read all instructions carefully, and check
your answers. Show all work neatly and in
11X g w g F PEC X S g V g 3H g S g eacQS Wj3H g QS g aYa)Ry"acfw_cF g bQagaeQuQpe|WfebU V X H wX VTP V T V S v SX vX C S H X EX v C C ` d E SX X H S w P F T ~ H Ex w d T E V @ cfw_ gw g |uRyH PE C F ~H E w S PE CS E d HX C eycfw_QS g ` RuQIbDy4w QuQIYRS
Mathematics 124The Art and Science of Secret Writing
Winter 2009 (200910)
Final Exam Solutions
Instructor: Michael Kozdron
1. If we write the ciphertext in three columns with eleven rows, then we have
DTG
IHO
LEO
IMD
GOF
ETO
NHR
CET
ERU
ION
SFE
We can now