1. The document describes a method for encoding and decoding text using matrices and ASCII codes.
2. It uses a 3x3 matrix as an encoding key to encrypt the word "Mahmoud" by converting it to ASCII values, transposing the matrix, multiplying by the key, and converting the result to binary.
3. To decode, it takes the inverse of the key matrix, multiplies it with the encrypted values, and performs the reverse steps to recover the original word.
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Message coding using matrices
1. Arab Academy for Science, Technology and Maritime Transport (AASTMT)
College of Engineering and Technology
Department of Communications and Electronics
Advanced Engineering Mathematics
Assignment 1
Coding message using matrices
Name: Mahmoud Sadat Badran Ibrahim
ID: 13 220 199
2. Coding: Its a technique of hiding the content of a text, voice conversation or any
Kind of data pass through any communication system, and coding used
Mainly to secure Information.
ASCII codes represent text in computers, communications equipment, and other
devices that use text. Most modern character-encoding schemes are based on
ASCII.
CHAR DEC HEX CHAR DEC HEX
@ 64 40 ` 96 60
A 65 41 a 97 61
B 66 42 b 98 62
C 67 43 c 99 63
D 68 44 d 100 64
E 69 45 e 101 65
F 70 46 f 102 66
G 71 47 g 103 67
H 72 48 h 104 68
I 73 49 i 105 69
J 74 4A j 106 6A
K 75 4B k 107 6B
L 76 4C l 108 6C
M 77 4D m 109 6D
N 78 4E n 110 6E
O 79 4F o 111 6F
P 80 50 p 112 70
Q 81 51 q 113 71
R 82 52 r 114 72
S 83 53 s 115 73
T 84 54 t 116 74
U 85 55 u 117 75
V 86 56 v 118 76
W 87 57 w 119 77
X 88 58 x 120 78
Y 89 59 y 121 79
Z 90 5A z 122 7A
[ 91 5B { 123 7B
92 5C | 124 7C
] 93 5D } 125 7D
^ 94 5E ~ 126 7E
_ 95 5F 0 48 30
3. Note: in decoding the zeros will be neglected
In this example I will use the matrices and ASCII code to Encode and Decode simple text
consist of one word.
System components:
1-The word Mahmoud.
2- Key for coding.
3- Operations of coding
The key used for the coding will be a Matrix with size of 3*3
1194
863
512
*Operation of coding:
A- Encoding:
1- Insert the word in a matrix. Mahmoud
du
omh
aM
0
0
2-Convert characters to its ASCII equivalent from table in previous page.
du
omh
aM
0
0
10011748
111109104
489777
3- Make transposition for the converted matrix.
10011748
111109104
489777
10011148
11710997
4810477
4- Multiply the transpose matrix by the key.
10011148
11710997
4810477
*
1194
863
512
=
22281614829
26441804989
17451133658
5- Now I have encrypted word in form of numbers that has no meaning. I can convert
each number in that matrix to its binary equivalent to send it through any digital system.
4. B- Decoding:
1- Get the inverse of the key to use it in the decode process.
1194
863
512
5.475.1
5.015.0
11173
2-Multiply the encrypted matrix by the inverse key matrix.
22281614829
26441804989
17451133658
*
5.475.1
5.015.0
11173
=
10011148
11710997
4810477
3- Make transposition for the result matrix.
10011148
11710997
4810477
10011748
111109104
489777
4- Convert Numbers to its ASCII equivalent Characters.
10011748
111109104
489777
du
omh
aM
0
0
5-Exectract the Characters from the matrix and neglect the zeros.
du
omh
aM
0
0
Mahmoud