40 + 5
ASSIGNMENT 2
SMA3043 (ELEMENTARY NUMBER THEORY)
SEMESTER 2 2021/2022
[45 MARKS]
DEADLINE: 19 JUNE 2022 (SUNDAY)(WEEK 12)
LECTURE GROUP A/B/C/D/E
LECTURER: ______________________
GROUP NO.: ______________________
DATE OF SUBMISSION: _____________
NAME
MATRIC NO.
SIGNATURE
ASSIGNMENT 2
SMA3043 (ELEMENTARY NUMBER THEORY)
SEMESTER 2 2021/2022
[45 MARKS]
DEADLINE: 19 JUNE 2022 (SUNDAY) (WEEK 12)
Instructions:
1. Form a group based on your Assignment 1 group.
2. By using your own creativity, answer ALL questions on a SINGLE poster in PDF format
and A4 size.
3. Use the cover page provided.
4. Your group poster MUST include complete questions, work steps, and answers (either
handwritten or typed).
5. Submit your group pdf file through MyGuru.
6. Marks will be given based on correct answers (40 marks) as well as your teamwork
and creativity to design an attractive poster and submit the pdf file within a given time
(5 marks).
7. Only 1 member will do the assignment submission.
8. By completing Assignment 2, you are expected to achieve:
CLO 3: Demonstrate the ability to reason on solutions involving cryptography.
CLO 4: Work in teams to complete the assigned task.
9. You may refer to the videos below to help you to understand this task.
a. https://youtu.be/4SWuYzJTEVQ
b. https://youtu.be/PMPWgRRCyVA
Answer ALL questions.
The ciphertext message below was encrypted using affine transformation 𝐶 ≡ 𝑃 +
𝑘(𝑚𝑜𝑑 26), 0 ≤ 𝐶 ≤ 25.
YFXMP
CESPZC
JTDBF
PPYZQX
LESPX
LETND
a) By completing the following table, find the most frequently occurring letter in the
ciphertext.
Letter
Number of
Occurrence
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
[4 marks]
Question (b) is based on the information in tables below and answer in Question (a).
Letter
Numerical
equivalent
Frequency
(in %)
A
B
C
D
E
F
G
H
I
J
K
L
M
0
1
2
3
4
5
6
7
8
9
10
11
12
7
1
3
4
13
3
2
3
8
<1
<1
4
3
Z
Letter
Numerical
equivalent
Frequency
(in %)
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
13
14
15
16
17
18
19
20
21
22
23
24
25
8
7
3
<1
8
6
9
3
1
1
<1
2
<1
The tables show that the most frequently occurring letters in English text are E, T, N, R, I, O
and A, with E occurring substantially more than the other letters.
b) Determine what is the letter that represents C and P in affine transformation 𝐶 ≡ 𝑃 +
𝑘(𝑚𝑜𝑑 26), 0 ≤ 𝐶 ≤ 25. Then, show that the value of 𝑘 ≡ 11(𝑚𝑜𝑑 26).
[10 marks]
c) What is the plaintext message?
[26 marks]
END OF QUESTION