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5a) Use matrix B= 3 2 to encode the message "COME ON". 5b) Decode the following message that was encoded using B 8. 37 39 32 50) Is it possible to use the matrix c-(; ) C = to encrypt and decrypt messages? Explain why.

5a) Use matrix B= 3 2 to encode the message "COME ON". 5b) Decode the following message that was encoded using B 8. 37 39 32 50) Is it possible to use the matrix c-(; ) C = to encrypt and decrypt messages? Explain why.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.8: Introduction To Cryptography (optional)
Problem 14E
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Suppose there is a correspondence between letters and numbers where each letter is represented by the number shown below. Spaces are ignored. A. E G J K L 4 5 P Q 8. 10 11 12 13 N R ST V Y 14 15 16 17 18 19 20 21 22 23 24 25 26 To write your message in numbers, you divide the message in pairs of letters and associate them to the following numbers. For example if you want to encode the word "ELEPHANT" you start with the pre-encoded message (E) - (:). (E)-(). (4) - (;). (") (). 14 20 which results in (1) (:) (:) (4)- To encode a message using a matrix A, you need to multiply A on the left by each two letter message. If A- (; ). you encode the first two letters EL with -1 You repeat the same procedure for the entire pre-encoded message and create the encoded message. To decode the message, you multiply A-1 to the left with each pair. For example to decode (?). you find the inverse of A which is ( ) A so which corresponds to the letters EL and then you apply the same procedure to all the encoded message. 5a) Use matrix B to encode the message "COME ON". 5b) Decode the following message that was encoded using B 5c) Is it possible to use the matrix to encrypt and decrypt messages? Explain why.
Transcribed Image Text:Suppose there is a correspondence between letters and numbers where each letter is represented by the number shown below. Spaces are ignored. A. E G J K L 4 5 P Q 8. 10 11 12 13 N R ST V Y 14 15 16 17 18 19 20 21 22 23 24 25 26 To write your message in numbers, you divide the message in pairs of letters and associate them to the following numbers. For example if you want to encode the word "ELEPHANT" you start with the pre-encoded message (E) - (:). (E)-(). (4) - (;). (") (). 14 20 which results in (1) (:) (:) (4)- To encode a message using a matrix A, you need to multiply A on the left by each two letter message. If A- (; ). you encode the first two letters EL with -1 You repeat the same procedure for the entire pre-encoded message and create the encoded message. To decode the message, you multiply A-1 to the left with each pair. For example to decode (?). you find the inverse of A which is ( ) A so which corresponds to the letters EL and then you apply the same procedure to all the encoded message. 5a) Use matrix B to encode the message "COME ON". 5b) Decode the following message that was encoded using B 5c) Is it possible to use the matrix to encrypt and decrypt messages? Explain why.
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