Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51]
Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.) [63 39 90 90 17 21 20 60 57 31 111 103 77 51]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take <space> = 0, A = 1, B= 2, and so on.
Thus, for example, "ABORT MISSION" becomes
[1 2 15 18 20 0 13 9 19 19 9 15 14].
To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 x 2 matrix
of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A.
14 1
][
32 2
[
- [2
=
Encrypted Matrix =
which we can also write as
9 87 20
15 20 13 19 9 14
18 0 9 19 15 0
49 95 69 14
7 81 60 57 95 57 42
14
32
Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)
[63 39 90 90 17 21 20 60 57 31 111 103 77 51]
We can first arrange the coded sequence of numbers in the form
[9 7 87 81 20 60 49 57 95 95 69 57 14 42].
To decipher the encoded message, multiply the encrypted matrix by A-1. The following question uses the above matrix A for encoding and decoding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb60d532a-9aac-45a2-a466-49da1bb79676%2F44123685-a87a-4a86-8e6a-6b25e038398a%2Fvlhojml_processed.png&w=3840&q=75)
Transcribed Image Text:Matrices are commonly used to encrypt data. Here is a simple form such an encryption can take. First, we represent each letter in the alphabet by a number, so let us take <space> = 0, A = 1, B= 2, and so on.
Thus, for example, "ABORT MISSION" becomes
[1 2 15 18 20 0 13 9 19 19 9 15 14].
To encrypt this coded phrase, we use an invertible matrix of any size with integer entries. For instance, let us take A to be the 2 x 2 matrix
of a matrix with two rows (using zero in the last place if we have an odd number of characters) and then multiply on the left by A.
14 1
][
32 2
[
- [2
=
Encrypted Matrix =
which we can also write as
9 87 20
15 20 13 19 9 14
18 0 9 19 15 0
49 95 69 14
7 81 60 57 95 57 42
14
32
Decode the following message, which was encrypted using the matrix A. (Include any appropriate spaces in your answer.)
[63 39 90 90 17 21 20 60 57 31 111 103 77 51]
We can first arrange the coded sequence of numbers in the form
[9 7 87 81 20 60 49 57 95 95 69 57 14 42].
To decipher the encoded message, multiply the encrypted matrix by A-1. The following question uses the above matrix A for encoding and decoding.
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