Application of Matrices on Cryptography

Application of Matrices on Cryptography

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  INNOVATIVE EXAMINATION Applications ofMatrices In Cryptography PRENENTED BY, RAM GUPTA SIDDHARTH GUPTA VIJAY GUPTA PIYUSH JAIN
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  CONTENTS  Cryptography  Applicationof Matrix in Cryptography  Encoding  Transmission  Decoding  Decoded Message
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  CRYPTOGRAPHY  Cryptography, isconcerned with keeping communications private.  Cryptography mainly consists of Encryption and Decryption.  Encryption is the transformation of data into some unreadable form.  Its purpose is to ensure privacy by keeping the information hidden from anyone for whom it is not intended, even those who can see the encrypted data.  Decryption is the reverse of Encryption.  It is the transformation of encrypted data back into some intelligible form.  Encryption and Decryption require the use of some secret information, usually referred to as a key.  Depending on the encryption mechanism used, the same key might be for both encryption and decryption, while for other mechanism , the keys used for encryption and decryption might be different.
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  APPLICATIONS OF MATRIXIN CRYPTOGRAPHY  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, used by the sender is called the encoding matrix and its inverse is called the decoding matrix, which is used by the receiver.
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  Message to besent: PREPARE TO NEGOTIATE And the encoding matrix be We assign a number for each letter of the alphabet. Such that A is 1, B is 2, and so on. Also, we assign the number 27 to space between two words. Thus the message becomes:
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  ENCODING  Since weare using a 3 by 3 matrix, we break the enumerated message above into a sequence of 3 by 1 vectors.  Note that it was necessary to add a space at the end of the message to complete the last vector.  We encode the message by multiplying each of the above vectors by the encoding matrix.  We represent above vectors as columns of a matrix and perform its matrix multiplication with the encoding matrix.
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   We get, •The columns of the matrix give the encoded message • Encoding is complete.
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  TRANSMISSION The message istransmitted in a linear form.
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  DECODING  To decodethe message:  The receiver writes this string as a sequence of 3 by 1 column matrices and repeats the technique using the inverse of the encoding matrix.  The inverse of this encoding matrix is the decoding matrix.  The inverse of this encoding matrix is the decoding matrix.  Matrix obtained is
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  DECODED MESSAGE The columnof this matrix, written in linear form, give the original message Message received: PREPARE TO NEGOTIATE
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