The document describes the process of encoding and decoding a message using a numeric cipher. It explains how each letter is assigned a number, how the message "GREEN_UNIVERSITY" is encoded into numeric matrices using an encoding matrix, and how the encoded message is then decoded back into the original text using the inverse of the encoding matrix.

2. • Encoding message
• Decoding Message

3. • Assign a no. each letter in the alphabet.
• Assign 0 for blank space

4. Letter Assigned No. Letter Assigned No.
---- 0 N 14
A 1 O 15
B 2 P 16
C 3 Q 17
D 4 R 18
E 5 S 19
F 6 T 20
G 7 U 21
H 8 V 22
I 9 W 23
J 10 X 24
K 11 Y 25
L 12 Z 26
M 13

5. • Message: Umme Ruman
• Encoding Matrix: A=
2 3
−1 −2
• Uncoded row matrix : [21 13] [13 5] [0 18] [21 13] [1 14]
• Now multiply each of uncoded row matrices be encoding matrix A.

6. Uncoded Row Matrix
[21 13]
[13 5]
[0 18]
[21 13]
[1 14]
Coded Row Matrix
[29 37]
[21 29]
[-18 -36]
[29 37]
[-12 -25]
Encoding Matrix
2 3
−1 −2

7. • Hence The Encoding Message is:
29 37 21 29 -18 -36 29 37 -12 -25

8. • Coded row matrix:
32 25 15 10 28 14 56 35 40 31 28 23 47 28 65 45
• Encoding Matrix: A=
2 1
1 1
• First, Decode the matrix:
𝐴−1 =
1
𝑎𝑑 −𝑏𝑐
𝑑 −𝑏
−𝑐 𝑎
=
1
2 −1
1 −1
−1 2
=
1 −1
−1 2

9. Coded Row Matrix
[32 25]
[15 10]
[28 14]
[56 35]
[40 31]
[28 23]
[47 28]
[65 45]
Uncoded Row Matrix
[7 18]
[5 5]
[14 0]
[21 14]
[9 22]
[5 18]
[19 9]
[20 25]
Decode Matrix (𝐴−1
)
1 −1
−1 2

10. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 7 = G
Message: G

11. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 18 = R
Message: GR

12. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 5 = E
Message: GRE

13. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 5 = E
Message: GREE

14. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 14 = N
Message: GREEN

15. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 0 = Blank Space (_)
Message: GREEN_

16. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 21 = U
Message: GREEN_U

17. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 14 = N
Message: GREEN_UN

18. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 9 = I
Message: GREEN_UNI

19. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 22 = V
Message: GREEN_UNIV

20. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 5 = E
Message: GREEN_UNIVE

21. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 18 = R
Message: GREEN_UNIVER

22. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 19 = S
Message: GREEN_UNIVERS

23. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 9 = I
Message: GREEN_UNIVERSI

24. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 20 = T
Message: GREEN_UNIVERSIT

25. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
• 25 = Y
Message: GREEN_UNIVERSITY

26. • For the uncoded row matrices read the message as follows:
[7 18] [5 5] [14 0] [21 14] [9 22] [5 18] [19 9] [20 25]
Message: