Cryptography. Cryptography is concerned with keeping communications private. Today governments use...
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Transcript of Cryptography. Cryptography is concerned with keeping communications private. Today governments use...
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Cryptography
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Cryptography is concerned with keeping communications private.
Today governments use sophisticated methods of coding and decoding messages. One type of code, which is extremely difficult to break, makes use of a large matrix to encode a message.
The receiver of the message decodes it using the inverse of the matrix. This first matrix is called the encoding matrix and its inverse is called the decoding matrix.
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A = 1 E = 5 I = 9 M = 13 Q = 17 U = 21
B = 2 F = 6 J = 10 N = 14 R = 18 V = 22
C = 3 G = 7 K = 11 O = 15 S = 19 W = 23
D = 4 H = 8 L = 12 P = 16 T = 20 X = 24
Space = 27
Y = 25
Z = 26
Assign a number to each letter in the alphabet with out a blank space
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To encode “CLEAR NOW”, break the message into groups of 2 letters & spaces each.
CL EA R_ NO W_ Convert the block of 2-letter into a 2 x 1
matrix each3
12
5
1
18
27
14
15
23
27
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To encode a message, choose a 2x2 matrix A that has an inverse and multiply A on the left to each of the matrices.
If A = , the product of A and the matrices give
The message received will appear as 6 15 10 6 36 45 28 29 46 50
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If you don’t know the matrix used, decoding would be very difficult. When a larger matrix is used, decoding is even more difficult. But for an authorized receiver who knows the matrix A, decoding is simple.
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1
101 01 2
1 2 12 01
2
A
10 6 32
1 15 121
2
The receiver only needs to multiply the matrices by A-1 on the left to obtain the sequence of numbers.
The message will be retrieved with reference to the table of letters.
For example,
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This is an encoded message you received:16 18 5 16 1 18 5 27 20 15 14 5 1 15 20 9 1
20 5 27
The agreed encoding matrix is .
What is the encoded message?
2 0
1 1