Application of Matrices on Cryptography
- 1. INNOVATIVE EXAMINATION Applications of Matrices In Cryptography PRENENTED BY, RAM GUPTA SIDDHARTH GUPTA VIJAY GUPTA PIYUSH JAIN
- 2. CONTENTS Cryptography Application of Matrix in Cryptography Encoding Transmission Decoding Decoded Message
- 3. CRYPTOGRAPHY Cryptography, is concerned 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.
- 4. APPLICATIONS OF MATRIX IN 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.
- 5. Message to be sent: 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:
- 6. ENCODING Since we are 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.
- 7. We get, • The columns of the matrix give the encoded message • Encoding is complete.
- 8. TRANSMISSION The message is transmitted in a linear form.
- 9. DECODING To decode the 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
- 10. DECODED MESSAGE The column of this matrix, written in linear form, give the original message Message received: PREPARE TO NEGOTIATE