Application of matrices in cryptography

.

1. APPLICATIONS OF MATRICES IN CRYPTOGRAPHY

2. Cryptography Keeping private Communication ENCRYPTION and DECRYPTION

3. Sender Plain text Cyper text ENCRYPTION Receiver Cyper text DECRYPTION Plain text

4. USE OF MATRIX Plain text Cyper text Jack MATRIX Cyper text Jill INVERSE OF MATRIX Plain text

5. 1. Convert the message in to numbers. Ex: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A B C D E F G H I J K L M N O P Q R S T U V 23 24 25 26 W X Y Z 2. Build the numbers in to Matrix. 3. Multiplying the matrix with our choice matrix. 4. We get a new matrix. 5. Convert the matrix in to string= cyber text  encoded message. RULES FOR ENCODING

6. RULES FOR DECODING Convert the encoded message into matrix. Multiplying the above matrix with the inverse of our choice matrix. We get another(plain text) matrix. Convert Matrix into message(original message)

7. Plain text Encoding Cyper text Using matrix A Decoding Using the matrix A -1 Plain text

8. EXAMPLE: Message to be Sent ATTACK NOW  Plain text Encoding A = 1 2 1 3 AT=[1 20] 1 2 = [21 62] 1 3 TA=[20 1] 1 2 = [21 43] 1 3

9. CK =[3 11] 1 2 = [14 39] 1 3 _N =[27 14] 1 2 = [41 96] 1 3 OW=[15 23] 1 2 = [38 99] 1 3 Encoded ATTACK NOW = 21 21 14 41 38 62 43 39 cyper text DECODING A = 3 -2 -1 1

10. AT=[21 62] 3 -2 =[1 20] -1 1 TA=[21 43] 3 -2 =[20 1] Decoded message: -1 1 1 20 3 27 15 CK=[14 29] 3 -2 =[3 11] 20 1 11 14 23 -1 1 _N=[41 96] 3 -2 =[27 14] -1 1 OW=[38 99] 3 -2 =[15 23] -1 1

11. [1 20] [20 1] [3 11] [27 14] [15 23] A T T A C K _ N O W ATTACK NOW  plain text