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Published byBryan Carney Modified over 3 years ago

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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 = 1E = 5I = 9M = 13Q = 17U = 21 B = 2F = 6J = 10N = 14R = 18V = 22 C = 3G = 7K = 11O = 15S = 19W = 23 D = 4H = 8L = 12P = 16T = 20X = 24 Space = 27Y = 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 each

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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 dont 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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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?

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